®mm\\ Wtitotttttg ^ifetMg THE GIFT OF _ ^Xljfc--^. ..ft.....«^.O..P. a_.a|c.p3 Cornell University Library TC 355.H69 Notes on mltering lock gajfs. 3 1924 004 678 763 «,, DATE DUE PETTI rm CAVLORD PRINTED IN U S.A. Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924004678763 No. 26. PROFESSIONAL PAPERS OP THE CORPS OF ENGINEERS OF THE UNITED STATES ARMY. PUBLISHED BY AUTHORITY OF THE SECRETARY OF WAR. Headquarters Corps of Engineers. 18 92. PROFESSIONAL PAPERS OF THE CORPS OF ENGINEERS, U. S. ARMY. No. 26. NOTES ON MITEKING LOCK GATES, BY FIRST LIEUTENANT HARRY F. HODGES, COUPS OF ENGINEERS, U. S. A. WASHINGTON: GOVERNMENT PRINTING OFFICE. 1 8 9 ti . Office of the Chief of Engineers, United States Army, Washington, B. C, July 14, 1892. Sir : First Lieut. Harry F. Hodges, Corps of Engineers, U. S. Army, has submitted the accompanying pamphlet, with plates, on the subject of lock gates. It contains information of great value to officers of the Corps of Engineers and to the profession at large, and I recommend that authority be granted to have it printed, with its plates, at the Government Printing Office, as a professional paper of the Corps of Engineers, and that 1,500 copies be obtained for the use of the Engineer Depart- ment upon the usual requisition. In view of the permanency of its value and to save expense in case future editions are called for, I further recommend that the work be stereotyped. Very respectfully, Thos. Lincoln Casey, Brigadier- General, Chief of Engineers. Hon. S. B. Elkins, Secretary of War. [First indorsement.] War Department, July 15, 1892. Approved as recommended by the Chief of Engineers. By order of the Secretary of War : John Tweedale, Chief Clerk. LETTER OF TRANSMITTAL. United States Military Academy, West Point, N. Y., July 12, 1892. General : I have the honor to forward by this mail a pamphlet and plates which I have prepared on the subject of lock gates. In view of the large amount of lock construction now in the hands of the Corps of Engineers, I have thought that the matter contained therein might be of assistance to some officers engaged on such work. I am, sir, very respectfully, your obedient servant, Harry F. Hodges, First Lieutenant, Corps of Engineers. Brig. Gen. Thomas L. Casey, Chief of Engineers, TJ. S. Army. TABLE OF CONTENTS. CHAPTER I. Page. Water pressure on lock gates „ 7 CHAPTER II. Leaves with straight backs 23 CHAPTER III. Leaves with curved backs 43 CHAPTER IV. Construction and spacing of horizontal frames 53 CHAPTER V. Vertical framing £8 CHAPTER VI. Sheathing 67 CHAPTER VII. Vertical strains 72 CHAPTER VIII. Manceuvring, and choice of type 90 CHAPTER IX. Examples 100 APPENDIX I. Calculation for framing 109 APPENDIX II. Volume of the tension flange 116 APPENDIX III. Proportioning web plates 119 APPENDIX IV. Metal frames for straight-backed leaves 121 APPENDIX V. Selection of wooden frames 125 MITE RING LOCK GATES. CHAPTER 1. WATER PRESSURE ON LOCK GATES. Locks, as applied in canals and harbors, are used to permit the safe par. 1. passage of vessels from one water level to another. The separation of the levels is secured by means of movable barriers, called gates. It is not the object of the present treaties to discuss the construction of the complete lock, but of the gates alone, which, while forming but a small item in the cost of the whole structure, are nevertheless its most vital parts. The duty of the gate is to receive the pressure of the water in the upper pool and to transmit it to the side walls and bottom of the lock. A gate of the ordinary mitering pattern consists of two leaves turning about vertical axes in the side walls, and abutting against each other on the middle plane of the lock. In many instances a single leaf has been used, spanning the entire opening ; in such cases the motion may be by sliding the gate lengthwise on rollers, by turning it about a vertical axis in one of the side walls, or by turning it about a horizontal axis in the lock floor. Gates of the mitering pattern may be classified according to their form into girder gates, in which the principal stress in the horizontal frames is transverse ; and arched or cylindrical gates, in which the transverse stress in the horizontal frames is small. According to their motion they are classified as rolling or turning gates. Certain of the parts of the turning gate leaf have received special names. Par. 2. The vertical edge, generally a continuous post, about which rotation takes place, is called the quoin post or heel post. The other vertical edge is called the miter post or toe post. The leaf is supported by the pivot at the foot of the quoin post, assisted sometimes by a roller near the miter post. The top of the miter post is formed into a gudgeon, which turns in a collar held back to 7 Nomenclature. MITERING LOCK GATES. Par. 3. Stresses. Par. 4. Parts. the masonry by the anchorage. The bottom of the quoin post is formed into a footstep to receive the pivot. The horizontal and vertical members are called frames. The leaf shuts against a projection from the bottom of the lock, which is called the miter sill. The stresses occurring in single-leaved gates are usually less difficult of analysis than those in the mitering type, since the single leaf shuts directly across the lock, and is therefore in the condition of a girder resting upon two points of support and loaded uniformly with a pressure acting normally to the sheathed surface. The stresses in leaves of the ordinary mitering type are somewhat more complex and will be treated first. The leaf is exposed to forces arising from five causes, viz : The water pressure on the sheathing ; the reaction at the quoin post, miter post, and miter sill; the weight of the leaf; the upward pressure of the water on the bottom of the leaf ; accidental blows or wave shocks. The first and second will in most cases govern the design of the leaf. The remainder may be resisted by suitable bracing.* The leaf consists of framing and sheathing. The duty of the framing is to take up the structural stresses and to transmit them to the points of support ; the duty of the sheathing is to distribute the load to the frames. In metal gates the sheathing may add materially to the structural strength of the leaf, being riveted to the frames and forming in part the flanges of the latter ; in wooden gates it is of service only in distributing the load. The framing consists ordinarily of horizontal and vertical members, with diagonal braces when necessary, and is calculated to resist all the forces which act to strain the leaf. It generally comprises a number of horizontal frames, each carrying a certain calculable part of the load, and united together by the quoin and miter posts and by a number of intermediate vertical frames. In a few modern gates it consists of one very strong hori- zontal frame at the top and a number of verticals, which divide the load between the top frame and the miter sill. This form presents some advan- tages and will be discussed in Par. 153. ; For many years it was held that the load on any horizontal frame , < tai8. s of was a direct function of the depth of that frame below the surface of the upper pool, and that in consequence the upper frame was subject to a very small stress, while those between the bottom of the lock and the lower pool were all under the maximum pressure. The error in this hypothesis may be made plain, as follows : " In addition to the above a stress may be thrown on certain frames of the leaf by the operating mechanism. This stress may be reduced to an inconsiderable amount by care in manoeuvring, and is not further regarded in the discussion. Par. 5. L o a nrizontals WATEE PBESSURE ON LOCK GATES. Let d represent the weight of a unit of volume of the water, H and h the depths of the upper and lower pools respectively. If the leaf under pressure be composed of equidistant horizontal frames of equal strength, and a perfectly pliable sheathing without vertical framing, the load on each frame will depend upon the depth alone, and will be pro- portional to the ordinate of the broken line a h c, Fig. 1. The frames being of equal strength will deflect proportionally under the load, and will lie, after bend- ing with their middle points along some broken line as e f g, if we suppose the support of the miter sill removed. If now we suppose the leaf to have also a system of vertical frames the rigidity of which is indefinitely great as compared to the horizontal rigid- ity, and if we suppose the leaf to be supported at the sill, the middle points of the frames will lie after deflec- tion along some line, as i I. In practice, since the leaf must have some rigidity in both directions, the position occupied by the middle points of the frames will be along some curved line, as I n, intersecting e f g in some point, as m, and approaching i I or e f g more nearly as the vertieal or horizontal rigidity is the greater. Above the point m the load on the hori- zontals is increased beyond that due to the depth, since the deflection is greater; below that point the load is lessened. The effect of the verticals has therefore been to change the loading from that represented by the ordinate of a b c. Two methods have been in use for proportioning the framing. By the first, the loading has been assumed to be distributed to the frames in accord- ance with the depth of the latter below the water's surface, taking no account of the influence of the vertical rigidity. By the second, the load as changed by the verticals has been assumed to be taken up by the horizontals as though the fitting of the leaf against the miter post and sill were perfect and the contact at the two places simultaneous. The former method, much used in England, gives a leaf which is too weak near the top and is apt to wear out there first. The latter method, advocated by some French 2623— No. 26 2 Par. 6. Highlit v 10 MITEKESTG LOCK GATES. engineers, gives a leaf which is lighter and strong enough so long as the fundamental hypothesis is realized in construction, but which becomes too weak near the top or bottom so soon as the fitting ceases to be perfect. A moment's thought will show the danger of relying upon the permanency of this necessary perfection under varying conditions of temperature and service. If the leaf has just the right length to fit the sill on one day, it may be too long or too short on the next; while, unless the contacts at the posts and sill be simultaneous, the effect of the vertical rigidity upon the distribution of the load becomes unquestionably modified. Thus, if the leaves miter before touching at the sill, the framing is without support at the bottom, and the load will go to the horizontals nearly in accoi'dance with the law of variation with the depth; while if the leaves touch at the still first, the lower horizontals will be unloaded, since that part of the miter post is unsupported by the opposite leaf, and the upper frames will be correspondingly overstrained. It becomes necessary, therefore, to inquire what the greatest load is which can fall on any member under reasonable conditions of service. Par. 7. Since the change due to the verticals, indicated in par. 5 depends upon the vertical and the horizontal stiffness, it is desirable to obtain comparable expressions for the rigidities in the two directions. The vertical frame is always straight. A measure for its rigidity will be the product of its coefficient of elasticity by the moment of inertia of its cross section about its own neutral axis. The horizontal frame may be either straight or curved in plan. When straight, it will have a rigidity measured as before by the product of its coefficient of elasticity by the moment of inertia of its cross section about its own neutral axis. When curved, the stiffness is greater than would be given by the above rule, and would probablv be measured by the product of the coefficient of elasticity by the moment of inertia of a section about the line joining the centers of support at the quoin and miter posts. There is, however, much uncertainty attending any effort to compare the rigidities of an arched support and a transverse girder. Hence, in the case of the leaf curved in plan, the horizontal rigidity of the curved frames is hardly comparable with the vertical rigidity belonging to the straight frames. For this reason it is better to avoid the difficulty bv proportioning the verticals, as in Chapter V, with a view to developing the same unit stress in the two systems, rather than to obtaining a certain ratio between their rigidities. When necessary to use them, the expressions for the rigidities will be E v I v , against bending about a horizontal axis; and E h l h , against bending about a vertical axis. WATER PRESSURE ON LOCK GATES. 1 1 In metal leaves, the sheathing acts with both horizontal and vertical frames; in wooden leaves, it assists only the system parallel to which it is applied There is difficulty in estimating accurately the moments of inertia of the two systems of framing, since the latter are rarely both continuous. When the frames of one are cut where they cross those of the other, the moment of inertia of the interrupted system will depend upon the method of making the connection rather than upon the original scantling of the members. This must be kept in view in estimating I v and I h . When the leaf is closed it will be in one of three conditions, viz : Par - 8 - /■ \ t -n (* f Conditions of (1) It will fit perfectly against the opposing miter post and imperfectly mitermg. against the sill; (2) It will fit perfectly against both post and sill, or (3) It will fit perfectly against the sill and imperfectly against the post. Either the first or the third of these conditions may be eliminated by Pa1 '- 9 - reasonably careful original workmanship. When the framing of the leaf horiz<^tais. maDy consists of a number of horizontals, each of which is expected to do its share of the work, a perfect fit against the opposing miter post becomes of prime importance, since, if contact be established at the sill before the posts meet, the latter will be forced together at the top while remaining apart at the bottom. The upper frame will be first loaded, and as it and the miter posts yield and bend under the rising water, the other horizontals will be brought successively into play until equilibrium is established or until some member breaks. The upper frames will take a large part of the load which belongs to the lower ones; their load thus abnormally increased may reach one- third of the total water pressure on the leaf (vide par. 15tf). It would be a manifest waste of material to attempt to provide for such a state of affairs, if it can be avoided. We must, therefore, in the original fitting of the leaf with, multiple horizontal frames, make it of such a length that it will touch at the post as soon as it does at the sill, even at the lowest working tempera- ture. After such fitting, the cushions or abutting surfaces of the miter posts should be planed off slightly toward the top, so as to insure contact along the bottom part first ; then, no matter how much the leaves may droop at the nose in course of service, the effect of the water pressure will always be to cause contact along the miter post as soon as or before the leaves touch the sill. Contact at the latter will usually follow only after slight yielding of the horizontals. In the rare case of leaves with no horizontal frames intermediate Par. 10. between the top and bottom, the fitting is of less importance. There being intemedutehor* •it r izontals. no lower horizontals to oppose any yielding of the leaf in the direction of 12 MITEBING LOCK GATES. its length, contact is sure to take place on the sill, where it is desired. The stresses in such a framework are extremely simple and are discussed in par. 153. Par. 11. From what precedes we see that, in the ordinary case, the original fitting »Br\°iSs c . ' '"" ° of the leaf may be trusted to eliminate the dangers arising from premature contact at the sill, and that consequently we have to provide against the stresses due to the first and second conditions of par. 8. In the first the contact occurs at the post before it does at the sill ; for a certain time, therefore, the load of the rising water will be distributed to the horizontals nearly in accordance with the law of variation with the depth, since at first the leaf will be unsupported at the bottom and its vertical strength can not be full}' brought into action. As the horizontals bend, contact will be established more or less perfectly along the sill. The load which comes on the leaf after establishment of this contact will be distributed to the horizontals in accordance with some law affected by the presence of the verticals. In the second condition the leaf fits perfectly against both post and sill. The total pressure will then be distributed according to the law as affected by the presence of the verticals. It becomes, therefore, necessary to proportion all the members to resist the greatest stress according to either law. Par. 12. The load according to the law of variation with the depth may be taken ,i t ptu! ling(iu6t0 without material error for any frame, except those at the top and bottom as equal to the weight of water resting on the strip of sheathing extending half way over the intervals between the frame considered and the one next above and beloAv. Thus, for any frame at a distance y from the bottom, and lying between the levels of the upper and lower pool, as 3, Fig. 1, the load is S [H-i/] X [P ?] P er linear unit. For any frame, as 6, Fig. 1, lying below the level of the lower pool, the load is 6 [H-/(] X \j s ~\ per linear unit. For the upper and lower frame the strip of sheathing is, of course, to be meas- ured in one or both directions, according to whether the sheathing termi- nates at the frame or extends beyond it. Par. 13. To find the law of distribution as affected by the verticals is a less easy matter. We are forced, in order to render the discussion reasonably simple, to make certain hypotheses, viz: That the longitudinal thrust from the other gate leaf (vide par. 37) has no effect in bending the horizontals, that the vertical rigidity is uniformly distributed throughout the length of the leaf, and that the horizontal rigidity of each frame is uniformly distributed over the strip of the leaf supported by it. Loiuling due to verticals. WATER PRESSURE ON LOCK GATES. 13 The first of these introduces no appreciable error. The slight inaccu- racy which exists, may be put on the side of safety by so arranging the surface of contact at the miter posts that the thrust passes on the downstream side of the neutral axis of the frame. The second may depart from the truth, but does not do so noticeably when three or more vertical frames are used, or when the sheathing is stiff and forms a large factor in the vertical rigidity. The third similarly introduces no perceptible error unless the distance Par. 14. *ig.8. V H between frames is large. It a would seem to the writer use- less to strive after greater accu- racy than is obtainable under these hypotheses, since the error introduced, and unavoidable, in the estimate of the rigidity of the leaf, precludes any close calculation of the distributed loading. Let Fig. 2 represent a vertical section of the leaf loaded by the water bearing upon it in the manner represented by the ordi- nates of the broken line a s t. Preserving former notation, the load per square unit of the leaf above the lower level will be 6 [H-i/], and below that level d [H-fe]. Since the vertical sectionis in equilibrium, the algebraic sum of the applied and resisting forces must be zero ; and the algebraic sum of the moments of these forces about any point, as 0, must be zero. The applied force is the pressure of the water ; the resisting forces are the reactions at the sill and at each of the horizontal frames. Calling these reactions P and p y we have v . p SW-dh 2 - ) ^+ p =nr -sr' and } (1) _ SW-dh 3 ~ 6 6 -jc PyV general equations from which P and p 7 can be found when we know the law of variation of p y with y. Par. 15. 14 MITEEING LOCK GATES. Par. 16. The latter law will depend upon the relative strength and arrangement of the horizontal and vertical members. For each particular arrangement a new law will be developed. It is therefore impossible to find general values of p 7 and P which shall be applicable to all leaves. We may, how- ever, obtain results of practical value by assuming a law of distribution of the reactions ; finding p y and P according to that law ; and then constructing the frames to correspond to the assumed distribution. Par. it. It is not uncommon to assume the horizontals as equal and uniformly spaced. The results of this hypothesis will be referred to later, in par. 28, et seq. For the present it is enough to say that conclusions more simple and more in accordance with practice in construction may be obtained by assuming the law such that after deflection the resistance to further bending of any horizontal section is the same. The function p y then becomes known as a constant multiplied by the width of the strip of sheathing supported by the frame considered ; and any vertical section of the leaf will be in the condition of a beam resting one end against a rigid support and urged in one direction by a system of forces proportional to the ordinates of a s t, Fig. 2, while it is urged in the other and kept in equilibrium by forces P and £>H, the latter uniformly distributed along its length. Par. i§. The general equations (1) now become SW-6 h 2 p H + P - 2 2 whence we have p^-SW-Sh 3 2 6 6 SR-Sh s ; and *=ir sir (2) P _<5H 2 + 6¥ -Sh 2 ,„. *~~6~ 3 H "2" W Par. 19. To construct the leaf of frames which shall fulfill with sufficient close- ness the required condition of equal resistance after flexure, we must know the deflection at any horizontal section; and hence the form of the mean fiber of the vertical section. The coefficient of rigidity of a vertical strip F T of a width of unity is — y— ^ in which I is the length of the leaf. The gen- v eral equation of flexure applied in this case gives E T I T d 2 x -d . py 2 « /TJ , N y 2 - J rV =Py+ 2 (H ~ 7,) 2 Par. 20. WATEE PEESSUEE ON LOCK GATES. 15 for the part below the lower pool; and e^ = Py + pi_ s (R _ h) £ + icr*)- for the part above the lower pool, the origin being taken at 0, Fig. 2, and the axes of X and Y, as indicated on the figure. Integrating these equations twice we have, E y I v dx_?tf ptf_8Ht?dhtf, c I dy~ 2 ^ 6 6^6^ **E V I ,_Py> pf dR ^ + dh ^ + Cv + K _ r" X -~6" + "24' ~^4~ + 24 + ^ + IV for the lower segment. E T I T %_Py a . py 3 _d(R-h) 3 6t/_Sfh 8ifW_Shhj Ql I dx~ 2 ^ 6 6 J_r 24 6^4 6 " t ~ T T + ¥ ~~24~^ + i20 "2T + 12 12 +^ +JV for the upper segment; C, K, C and K' representing the constants of inte- gration. Remembering that the two branches of the curve must be tangent to p a r. 21. each other at y — h; that they must have the same value of x at that point; that the lower branch of the curve passes through the origin; and that the value y zr h must give in the equation of the upper segment a deflection — /, equal to the deflection of the upper horizontal under the load p per square unit of supported sheathing, we are enabled to find at once the con- stants, as follows : Ji 7„5 rzu Sh 5 E T I T / C = 120' K = 0. S W , SUli . 120 +" 24 + ■v d ¥ 120H I H 24 Representing the rigidity of the upper frame by E t I t *, the distance to Par. 22. the one next below by y and taking the vertical section at the middle of the leaf, the deflection of the top frame becomes known as 1 p l 4, y -/= 76.8 E, L 2 • *This would be equal to !* h X ^ if the horizontals were all equal and equally spaced. 16 MITEEING LOOK GATES. Par. 23. The equation of the curve of mean fiber of the middle vertical section of the leaf is therefore E v I vic dy 5 ,/"p -6B\ 3 /P S¥\ 5 h 3 y» -120 + *V 24 24 J +y \6 + 12 J / SBh 3 E T I T / \ _dh? ., + y \ 24 ~ 120 + 120H ~ !H J _ 120 U for the upper segment ; and E V L, Sp SB tfA\ Fy -X ■ )■ ,.3 I "~ V\^A~ 24 + 24 J + 6 f SV Sh 3 B 6W A* B r I r f \ + 2/ Vl20H + "24 ~ 120 ~ 24 ~ !H J ( ' for the lower segment. These will give the deflection at any point of the vertical section, since the values of P and p are known from eqs. (2) and (3). If the support of the water in the lower pool be neglected, the equa- tion of the curve of mean fiber of the middle vertical section is E T I T 6 f Sy'B. 6y 3 W 6 yW E T I T /y I - 120 ~ 36 + 36 _ 120 ~ IB. { ' Par. 24. By plotting the curve given by eqs. (4) and (5), or by eq. (fr), accord- ing to data, the deflections at any point may be found. To make the leaf follow the curve exactly, the horizontals must have a strength inversely proportional to the deflection of the leaf at the points which they occupy, since each one must carry a load of p per square unit of supported sheathing with the deflection given by the equations. Par. 25. The curve taken by the mean fiber of a vertical section is typified in fo^Tombi'neS Fig. 3, the example taken being the same as the one discussed in Appendix loadiDg. 1, in which p is equal to the load per square foot due to 12.1 feet head of water. By inspection of the figure we see that the effect of a change in the deflection a-b or a-b' of the upper frame under the load p per square unit of supporting surface is to rotate the curve about the origin at the miter sill. It is known that all the frames must be safe against the load per square foot due to the depth below the surface, as well as against the load p per square foot. Let us now assume a scantling for the frames below the level of the lower pool, which will bear safely the load per square foot of S (H.-h), which is always greater than p ; and let us calculate the deflection under this load. This will be 1 6(R-h)Py ^ — 76.8 E f I f ' in which E f I f is the rigidity of the frame and strip of supported sheath- WATEE PKESSURE ON LOCK GATES. 17 ing, while y is, as before, the width of the latter. Let e c, Fig. 3, rep- resent this deflection. Then will the straight line b s c d represent by Y ■*«-■- ° its ordinates the deflection which 42'.5 40.'0 37.5 35'.0 32.5 30'.0 2T.5 25.0 22.5 Fig. 3. 2o:o 17.5 15.0 12'.5 io:o o'.o would be assumed by a leaf with- out support at the sill, and in which the frames are exactly proportioned to their loads distributed according to the depth. If now we give to the top frame such a scantling that under the load p per square foot it will deflect a distance a b z= e c — (p and construct the curve with this value of f, it will have the position b s o, and the ordi- nates of the portion b s, where the curve lies- below the straight line, will be found to differ but little from a b for leaves with ordinarily strong vertical frames. In this por- tion of the leaf the frames should be so constructed that the deflection of each will be proportional to the ordinate of the curve, i. e., the frames at b and s should have equal strength, and those between should be some- what weaker. As the difference in ordinate is Par. 26. very slight, it will generally be advis- able to make those between b and s all of the same strength, viz, such as to deflect a distance r s rr in which e represents base of Napierian system, 20 MITERING LOCK GATES. ASP M 4 for the part below the lower pool. Since n* is nearly 31, we have — , as practically £, hence the bending moments given by the above formulae are practically the same as those produced by a uniformly distributed load per square unit of supported sheathing of - v coh (9 H) J for unsupported leaf; L J { } coh (d H) J for upper part of supported leaf, and s\ R-h - (H-/0 cos(ey)coh[e(R-y)i 1 I v J coh(6K) J Par. 30. for lower part of supported leaf; expressions which may be found more convenient of application than the formulas involving the bending moments. To justify the hypothesis under which the above formulae were deduced, the frames should be constructed of the same scantling, and uni- formly spaced. If, therefore, we admit the necessity of providing against stresses due to imperfect fitting we must clearly make all the frames as strong as the lower ones, or capable of bearing the load 6 (H — h) per square unit of supported sheathing. This would be a manifest waste ; hence in constructing leaves according to these formulae or M. Lavoinne's calcula- tions, the stresses due to the depth are usually neglected, and the leaf con- sidered as always in perfect fit on the three supported sides. Further, it is not uncommon to vary the strength of the horizontals according to the loading found from the formulas, thus vitiating the original hypothesis of equal and equally spaced resistances. Par. 31. J n many experiments upon small leaves M. Galliot has found deflec- tions in reasonable accord with those given by his formulae. The latter have, therefore, a practical confirmation, though not theoretically accurate For small leaves, where the contact at all sides is simultaneous, they have, an undoubted value, giving a lighter framework than any other method of construction. For large leaves, or for those in which the value of the hori- zontal and vertical rigidity can not be reliably determined, the writer would WATEli PRESSURE ON LOCK GATES. 21 be in favor of the safer and heavier framework given by the rule of Par. 27, and in practice would probably adopt it in all cases. It should be stated that the loading derived from M. Galliot's formula generally fails to give the theoretical equality of forces and moments required by eqs. (1) Par. 15. In some cases the discrepancy is consider- able, vide Appendix 1. It has been not unusual in lock construction to neglect the support of Par. 32. the water in the lower pool. Where there exists danger of this support failing at any time, it should undoubtedly.be neglected. Where, however, this danger does not exist, the practice leads to an unjustifiable waste of material. The subject of loading can not be completely discussed without antici- Par. 33. pating to some extent the conclusions of Chapter V on the subject of verti- fomamm leaves. cal framing. We have seen, Par. 16, that to produce any given or assumed distribution of load to the horizontals a certain relation is necessary between the horizontal and vertical rigidities. In Chapter V we shall find the method of determining the vertical strength necessary to properly load the hori- zontals proportioned according to the laws of Par. 27 ; and shall further find that when the leaf is very high and very narrow an exaggerated verti- cal rigidity will be required to throw upon the horizontals, when supported at the sill, a load which shall cause them to resist equally after deflection. When this is the case we may do one of three things, viz : First. We may proportion the horizontals according to the law of Par. 27, and give to the verticals any practicable rigidity less than that found by the method of Chapter V. In this case, since the verticals are too flexi- ble to throw to the top of the leaf its full share of the load when supported at the sill, the upper horizontals will be less loaded than their strength permits, while the lower ones will carry a load greater than |_ 3 3H 2 J; but since the lower ones are proportioned to bear the heavier loads, due to lack of support at the sill, the framework will be safe, though evidently too strong near the top. Second. We may assume some practicable vertical rigidity for the leaf, and by the application of some suitable formula, as M. Galliot's, Par. 31, we may deduce the loads which this rigidity will throw on an assumed sys-. tern of horizontals, with support at the sill. We may then alter the hori- zontals to correspond to this loading throughout the leaf, thus presupposing perfect contact at the sill at all times ; or we may make them to correspond to 22 MITERING LOCK GATES. this loading near the top and to the loading due to the depth near the bot- tom, thus obtaining a framework of the same strength near the bottom as by the rule of Par. 27, but lighter near the top. The amount by which the upper frames are lightened will depend upon the formula used. M. Galliot's is the only one known to the writer which can be quoted here. Third. When the leaf is so high and so narrow as to require no vertical between the quoin and miter post, we may leave out all vertical frames, make the sheathing so thin that its rigidity may be neglected, and propor- tion the horizontals according to the law of variation with the depth, thus obtaining the most perfect leaf with the least expenditure of material. This method is applicable to those cases where no verticals are needed to help support the weight of the leaf. So soon as verticals are introduced their effect upon the loading should be considered. Par. 34. Except in extreme cases, the simplicity and safety of the rule of Par. 27 recommends it for use when the strength of the verticals employed approaches anywhere near that required to distribute the load to the hori- zontals in the manner assumed. The construction will be safe whenever the vertical rigidity of the leaf, as built, is less than or equal to that required to thus distribute the load. Par. 35. From the foregoing we see that there are two general methods of taking the vertical rigidity into account. In the first a certain distribution of the load to the horizontals is assumed, and the horizontal and vertical framing suitable to this loading is deduced ; while in the second, the hori- zontal and vertical rigidities are assumed and the loads thrown by the verticals on the horizontals are calcidated by some formula, as M. Gal- liot's, the horizontals being perhaps modified to suit this loading. CHAPTER II. LEAVES WITH STRAIGHT BACKS. It has been already shown that the horizontal frames may be treated as beams acted upon by a uniform load applied normally to the sheathed surface, and that the amount of this load may be calculated from the depth, or from the quoted formulae, according to circumstances. The form of the horizontal members now demands attention. In all succeeding discussions the following notation will be preserved, viz : 6 c, Fig. 4. Half span between centers of hollow quoins — C Length of chord of frame rr I ■=. b a. Complement of % miter angle — a — angle a b c. Angle of upstream flange of frame with chord at post =

*] + -i'" • ■ • (10) Par. 58. Referring to eq. (10) it is seen that an increase in A and the corre- sponding decrease in A' will decrease the volume by lightening both the compression and tension flanges. It is, therefore, desirable to cause the centers of pressure at the quoin post and miter post, to take a position as far downstream as possible. By chamfering the edge of the miter post and rounding the quoin post the surfaces of contact can be so far reduced as to force the center of pressure to lie below the median line of the frame. The exact position of these centers is unknown; but since by eq. (10) the worst position is that which is nearest the upstream surface, we shall con- sider it as ranging between the median line of the leaf and the axis of the downstream flange. For these limits of the most dangerous position of the line of pressure eq. (10) becomes by substituting proper values of A and A' Par. 59. V _ ! / P F _j_P F cot « , 9T'\ Vl ~c 1,12 D + ~T~ +Z L ) 1 / pT J) P COt a , rjv \ 1 p I 2 LEAVES WITH STRAIGHT BACKS. for the most dangerous position on the axis of the frame, in which T'is Hi* 1 * - px2 -P lcota \dr- and 1 V^\2D 2D —T~ ) dx ' and 31 1 1 cot a ; and V — If J?Z. 4-2T y" 1 " *Vi2D Jfj Z 2 cot a + 2 T "H s 4 for the case when the most dangerous position of the centers of pressure is on the axis of the lower flange, in which T "J,. (W-b— -s— )** J I ± I '. - D Z cot a. and x a is Let us give to c, £ and s values bearing to each other the ratios of 10, 12 and 8, as in the case of mild steel; if then we substitute sets of values of D and I and find by trial the value of #, which corresponds to a mini- mum weight, we shall know the proper miter angle for a frame of the assumed dimensions when the line of pressure occupies one of its limiting positions. These values have been found and tabulated in Tables I and II. The trial has shown that, for practicable values of the variables, the C economic angle remains sensibly the same, so long as the ratio =- of the half width of the lock to the depth of the frame does not alter. This ratio is, therefore, taken as the argument of the tables. ECONOMIC ANGLES FOR FRAMES WITH VARYING FLANGE SECTION. Table I.— When center of pressure is on axis of frame. c 5 6 7 8 9 19° 10 11 17° 12 13 14 a = 25° 23° 21° 20° 1 8° 1 6° I 5 ° •5° r J ^ABLE II. — When < •enter of pressure i s on axis of lower flange. C D — 5 6 7 8 25° 9 10 22° 11 12 13 H a = 34° 31° 28 23° 21° 20° 19° 18° Par. 60. In using these tables, it should be kept in view that they are deduced for the case of frames so large that the flange sections may be varied from 32 MITEKING LOOK GATES. point to point to suit the changing stress. Such frames will occur only in very large leaves; for the majority of cases the flange sections will be kept the same throughout, and Table III of Par. 72 will apply. Par. 61. In practice the most dangerous position of the line of pressure will generally lie somewhere between the positions for which the tables are constructed. From the data of the problem the designer will always know C; he may find D by the process given in Par. 76, and may find A and A' by fixing the shape of his cushions and applying the principles of Par. 45. Then, by substituting in eq. (10) he may by trial find the proper value of a for his particular case. A value obtained by interpolation between those tabulated will be of assistance as a guide in the search for a minimum volume; and will often reduce the number of trials to three or four. The volumes found in such trials change very gradually when near the minimum, and hence a differ- ence of one or two degrees will not materially affect the weight of the frame. Par. 62. In thus fixing the proper value of the miter angle, the most dangerous upstream position of the line of pressure has been taken as a guide. This position throws the greatest stress on the leaf (yiite eqs. (8) and (9)) and at the same time indicates the least value of I, and hence the shortest girder (cf. Tables I and II). Since it is necessary in any event to provide against the possible stresses due to this position of the line of pressure, it may be done most cheaply by the shortest frame. Par. 63. In designing the flanges, however, trial must be made of both the extreme upstream and the extreme downstream position of the line of pres- sure. This may be done in eq. (8) and (9) by substituting the proper values of A and A' and proportioning the varying cross section of the flanges to resist the greatest stress. Par. 64. An inspection of these equations shows that when the line of pressure lies below the median line of the leaf, portions of the downstream flange near the ends are subject to reversed stress; and that if the frame be deep and the contact near the downstream face, the lower flange may be in com- pression throughout (vide Appendix II). This arises from the fact that when the contact is not on the neutral axis, the stress given by these equations is due to two causes, viz, a bending moment -~ 9~> caused directly by the load, and a compression ^- — > distributed over the sec- tion in accordance with the ratio of A and A'. When the compression due LEAVES WITH STKAIGHT BACKS. 33 to the latter cause exceeds the maximum value of the tension due to the bending moment, the lower flange will be compressed for its whole length. It is not generally possible to vary the cross section of the flanges to Far. 65. suit the stress. The angle irons and sheathing' are usually for convenience constant ttange ° ° J area. made of the same weight throughout each flange, and these constitute the major part of the section. The preceding discussion has therefore a very restricted practical value, finding application only in the case of exceptionally strong frames, in which the maximum stress requires more metal than is supplied by the angles, sheathing, and single cover plate. The ordinary frame has the same section throughout each flange. The two flanges of the riveted frame may differ in area, but each generally pre- serves the same section for its entire length, this section being regulated by the maximum stress. The guiding stress may therefore be found for the compression flange by making x — ~ in eq. (8), and for the tension flange, the maximum tension, though not necessarily the maximum stress, may be found by making Far. 66. I 2 m eq. (9). K r 1 /j,P pi cot a X' \ -D\^8 + 2 ) W Tm = ^(pr_pi™t_«A\ (12) D V~8 ~ 2 The value of K m will be greatest when X' has its greatest value, i. t\, Far. 67. when the center of pressure occupies its extreme upstream position. The tension at the middle of the downstream flange will be a maximum for the same position of this center; the lower flange is, however, subject to com- pression at the ends as well as tension at the middle ; the expression for the compression is -~- cot a ^ , and will have its greatest value for the extreme downstream position of the center of pressure. For large values of a the maximum tension at the middle exceeds the par. 68. maximum compression at the ends of the downstream flange ; a decrease in a causes the former to diminish and the latter to increase until they become equal in intensity; a further decrease in a causes the maximum end com- pression to exceed the maximum middle tension. Since the lower flange is by the hypothesis, uniform in size, its cross section will evidently be a minimum when the maximum compression at the end requires the same area to resist it, as does the maximum tension at the middle. The volume 2623— No. 26 5 34 MITERING LOOK GATES. of the frame will be a minimum at some value of a. slightly different from that which makes the cross section a minimum, since the length, as well as the section, is affected by a change in a; but when near the minimum the guiding stress should be taken to be the compression at the end, instead of the tension at the middle, since the two stresses are very nearly the same in intensity, and a slight further decrease in a shortens both flanges and the web of the frame. The stress in the lower flange when near its minimum is therefore pivot a A lk - " 2 d v lrf ; instead of the value of the tension at the middle from eq. (12). In eq. (13) it should be remembered that T k is compressive, and that A corresponds to the extreme downstream position of the center of pressure. Par. 69. The volumes of the flanges will be found by multiplying eqs. (11) and (13) by 7 , in which c represents as before the unit compressive strength of the material. The cross section of the web will be regulated by the maxi- mum shear, -~- , at the end ; and we may assume it as of the same thickness throughout, as it would be so constructed in all but the very largest frames. p I 2 Its volume will therefore be ~— , in which s represents the unit shearing Par. 70. strength. Its volume of the whole frame is therefore v * = ~[^ + 4^'" + *">]+ff ■ ■ Cu> in which A'" represents the distance from the axis of the downstream flange to the extreme upstream position of the line of longitudinal thrust; while A" represents the distance from the axis of the upstream flange to the extreme downstream position of the same line. Par. 71. Allowing the line of thrust to occupy, as before, any position in the downstream half of the beam, we have A'" — ~ D, and A" — D. The ex- pression for the volume becomes, V _. I (iJ! , 3 _# cot a\ p_P C substituting in this for I its value , differentiating with respect to a; and LEAVES WITH STRAIGHT BACKS. 35 placing the first differential coefficient equal to zero, we find as the condi- tion for a minimum p \ScD X cos 4 a "' 4 <■ 3 sin a 3 C 2 /sin 2 a — cos 2 a\ ; \ sin 2 a cos 2 ct ) C 2 sin 2 « cos 2 a _ 1 s cos a. or reducing, 1/3 C . , c V8T) Sm * + j sm a cos "a — j cos 5 4 a j -j- sin 3 82, 83 we obtain conditions of minimum stress and volume, as follows: 3 d sin 3 « — cos 4 d — (23) from which the angle of minimum stress may be found by trial ; and 9 c a ~j sin 3 d + cos 2 a sin 2 « — cos '«r0 . . . (24) from which the angle of minimum volume may be found by trial. The use of these equations is as indicated in Par. 84. When it is neces- sary to construct the frames of timbers of a fixed depth and it is desirable to reduce the fiber stress as much as possible, eq. (23) may be used. The beam which, with a value of a derived from eq. (24) gives in eq. (22) a value of S' equal to the safe working strength per square inch of the metal, will be the most economic frame. C For practicable values of y the angles are tabulated below : Table IV. — Economic angles for timber frames of uniform section. c d a for least stress. a for least volume. 6 8 10 12 i5 20° 30' 1 8° 50' 1 7 30' 1 6° 40/ 15° 3°' 17° 35' 16 05' 15° ic/ 1 4° 20' 13° 30' LEAVES WITH STRAIGHT BACKS. 41 The value of d will generally be fixed by the size of timbers available. Advantage ordinarily results from having it as large as possible Knowing C and having fixed upon d, take the value of a from Table IV". Substitute the proper values for the quantities in the second member of eq. (22) place the result equal to the allowable fiber stress per square inch, and solve for b. The dimensions of the frame will then be known. For an illustration, see Appendix V. To recapitulate; if the problem be to find the most economic straight- Par. 94. backed metal frame of varying flange area, we must first select D, either as determined by the conveniences of access to the interior of the leaf or by the method of Par. 76. This may readily be done since C will be given by the conditions of the problem, and p may be found by the methods given t) 1 pot OL in the previous chapter. Then, taking an approximate value of ~ > fix the extent of the surface of contact at the posts and find the values of X and X' for the most dangerous upstream position of the centers of pressure, as shown in Par. 45. Then taking as a guide a value of a obtained by interpolation between those given in Tables I and II, find by trial from eq. (10) the value of a corresponding to the minimum weight. The stress and hence the flange area at different points on the length of the frame may be found from eqs. (8) and (9); and the web plate with its stiffeners may be V 1 proportioned from the shear, -h~ — pec. If the frame is to have flanges uniform in size but different from each other, D should be found as in Pars. 73, 74, and X' as in Par. 45, a from Table III, and the flange stress and constant flange area from eqs. (11) and (13). This case will be more usual than that of the frame with the varying flange section. If the frame is to be of rolled metal with flanges the same in area, find j and a by trial from the handbooks, so as to satisfy eqs. (18) and (20), with the proper working value of S' in eq. (18). The value of a will then be given by eq. (20). If the frame is to be of timber of uniform rectangular cross section, assumed as within apparently suitable limits, find the economic angle from the third column of Table IV, and from eq. (22) with the allowed unit stress substituted for S', find the breadth b. Should this be impracticably large or small, try another value of d. Since all the frames of the leaf must work at the same miter angle, and Par. 95. must for convenience have the same depth, the value of p used in deter- mining D and a should be the load on the average frame. Advantage wil 2623— No. 26 6 42 MITEKING LOOK GATES. therefore be derived from so spacing the frames that the total load on each one shall be the same. This leads to a slight widening of the intervals near the top of the leaf, where the load per square unit of the supported sheath- S H S h 3 ing, viz, o — o tt2 is less than the corresponding load, d (H — h) on the lower part, vide Par. 25. The designer should never lose sight of the economy resulting from keeping the most dangerous position of the centers of pressure as far down- stream as is permitted by the strength of material employed for the cushions. For girder frames the surface of contact should not extend into the upstream half of the frame. Should it do so the formulae given in the preceding pages must be modified to suit the most dangerous position which the line of pressure can occupy in the individual case considered. CHAPTER III. LEAVES WITH CURVED BACKS. When the back of the leaf is a broken line in plan, the form is almost Pa'- »«• always that which results from cutting the upstream corners of a straight- brokeu line's.^ backed leaf near the quoin and miter posts, giving it the appearance shown in the upper frame of the great lock at Havre, PI. n. The formulae applicable to the straight-backed frame may be used with sufficient accu- racy in this case for the determination of D and a. The stress in the flanges will be different near the ends on account of the difference in depth, but may be found readily either analytically or graphically. Leaves with curved backs are usually made with the upper member Par. 97. circular in plan. They fall into one of three classes: the continuous arch, 0U rv!S backs! th the bowstring girder, and the Gothic arch. The stresses and laws of economy in the various types may be deter- mined by discussing the general equations of equilibrium, Par. 38, as applied to the separate classes. It is more convenient to deduce the formulas in a slightly different manner, as follows: Let Fig. 9 represent the lines of flange centers of a frame loaded upon its upstream side, which we will suppose circular in curvature; and let the intersection of the lines of the flange centers be at the centers of pressure of the surface of contact. Let b d be a tangent to the par. 98. curve at b and denote the angle d b a by cp. Let w represent the variable angle which any portion of the 1 curve makes with the line a b. Preserving in other respects the notation of the preceding chapter, Par. 36, and neglecting the transverse strength of the web, we have, by decompo- sition of the thrust at b, K = R ™1 and T = R *™(«- R — $ l K = p l and T = P lcos< P _ P [ cot a 2 sin a " 2 sin tp 2 sin (p 2 43 44 MITEBESTG LOCK GATES. Denote the radius of the upstream flange by p and substitute it in the above expressions for its value -r- -. • and we obtain by reducing, K=pp ( 25 ) and T = pp cos, (p — p p cot a sin (p (26) In the middle section we obtain, taking moments about o,KxOC = RX fo— moment about o of load on c b. The load on the elementary length of the arc is p p d go; its moment about o isp p d go (p sin go — o c sin go), which is equal to p p d go (p sin go — p vers (p sin go), or p p 2 d go sin go (1 — vers cp), which reduces to p p 2 sin go cos

cos 9' 2 sin a z or reducing, K = p p. Similarly, taking moments about c we have, after reducing, T = p p cos cp — p p cot a sin (p , which are identical with (25) and (26). By taking moments at any other point of the beam we should arrive at the same result, and we therefore conclude that when the upper chord is circular the normally applied load generates chord strains which are the same at any point of the flanges. Par. 99. The frame will be lightest in section when the arithmetical sum of K and T is a minimum. It remains to find the values of a and cp which will produce this result. C In (25) and (26) substitute for p its value -. , and we have v J v J 2 cos asm ' dcp ~ 2 cos a: sin 2

< a, compression in upper, tension in lower flange,

a, compression in upper, compression in lower flange; and we have further seen that with a continued increase in cp beyond a, the compression in the lower flange increases more rapidly than that in the upper flange diminishes. The minimum cross section occurs, therefore, when

. a V a V a V a V 33° 1,000 28° 1,030 23° 1,124 1 8° 1,3'S 32° 1,002 27° 1,043 22° i,iS3 17° i,375 3i° 1,006 26° I.059 21° i, 186 .6° i,44i 30° 1,012 25° 1,078 20° 1,224 15° 1,581 29° 1,020 2 t 1,099 I 9 ° 1,268 14° 1,607 From this it is apparent that the curvature may be considerably reduced without great increase in the volume. In the leaves proposed for the large lock, 100 feet wide, building by the United States at Sault Ste. Marie, Mich., the value selected for a. is 21°. For the gates of the Cas- cade locks, 80 feet wide, the value of oc is 21° 48'. The preceding discussion has been made under the hypothesis that ter ofp'ressure. 11 tne center of pressure coincided with the center of figure of the surface of contact. The effect of a departure from this may readily be determined. Par. 103 Position of'een Considering first the metal arch, we know that, from its form, the great mass of metal is far out from the neutral axis of the frame. Since from the cur- vature, the curve of equilibrium can not depart far from the neutral axis, the bending moment in any section is small, even when the center of pres- sure departs as far as possible from the center of figure. No material error will be committed in assuming the compression resisted by parallel forces located at the centers of gyration of the two halves of the arch. Thus, let Fig. 10 represent a plan of the portion of two arched frames near the miter posts, and let a-a b-b represent the lines at which the metal of the frames * As shown by example in Appendix I, the volume of the minimum fully arched frame is less than half that of the minimum girder frame. LEAVES WITH CUEVED BACKS. 47 and part of the sheathing may be assumed as concentrated, viz, the loci of the centers of gyration of the half frames and that part of the sheathing which acts with them, vide Par. 121. Let the broken and dotted line c-c represent the neutral axis, assumed as passing through the centers of gravity of all the frame sections; and let p-p be the line of pressure in some one of its positions, separated from a-a and b-b by the distances A and A'. Then will the pressure p p be divided between the upstream and downstream flanges, in the inverse ratio of the segments A and A' into which the line of pressure p-p divides the distance between lines of flange centers; or, calling this distance z/, we shall have the total stress in the upstream flange equal to PP~j (28) and in the downstream flange, Pp\ (29) The total stress, and hence the weight of metal, in the flanges may be Par. i©4. determined from the above expressions, taking care to use for A and A' the values corresponding to the most dangerous position of the line of pressure; thus, in computing the upstream flange, the pressure must be taken in its extreme upstream position as determined from Par. 45; and for the down- stream flange the pressure must be taken in its extreme downstream posi- tion. The curve of pressure may be constructed graphically for the eccentric positions of the centers of pressure by the method shown in Par. 42. No material error will be committed if it be considered as the arc of a circle parallel to the median line of the frame, and passing through the most dan- gerous positions at that one of the posts where the surface of contact is the broader. The web is exposed to a compressive stress, normal to the upstream Par. 105. flange, and equal per unit of length to that portion of the load p, which is transmitted to the downstream flange. Thus, supposing the total compres- V P sion to be p p and the amount borne by the upstream flange to be -^ , found from eq. (28), then will the web transmit to the downstream flange a load of -~- per unit in length, and will be exposed to this normal compressive stress, which we may call the shear. It will generally be too small to govern the selection of the web plate, which will be regulated with a view 48 MITERLNG LOCK GATES. to endurance and convenience of riveting. About the same limits may be observed as in girder frames, viz, 5/16" and 5/8." Par. 106. The wooden arched frame, having usually a rectangular cross section, r r<.'s *" rV 0I1 i n can not be treated as consisting of two flanges located at the centers of wooden arches. gyration. According to the usually accepted theory of pressure, a normal compressive stress acting on a rectangular pressed surface will produce a compression per unit of area varying uniformly from one edge to the oppo- site one of the rectangle, unless its line of action pierces the center of the pressed surface. The law of variation of the pressure per unit of section is such that the extreme fibers, which are those most strained, undergo a unit compression of "(*-«d) P A Par. 107, jn which P is the total pressure on the section, A the area, A the distance of the extreme fibers from the center of pressure, and D the dimension of the rectangle parallel to which the pressure is assumed to vary; or in this case the depth of the frame. Substituting the proper values for the quantities in the above expres- sion, we obtain ¥(<-«d) w for the unit stress on the upstream fibers, and ¥(«-«£) w for the unit stress on the downstream fibers, in which A and A' must be given values corresponding to the most dangerous positions of the center of pressure as in Par. (104). Par. io§. It will generally be convenient in metal arched frames to make the surface of contact about one-third the depth of the frame. In that case, supposing the cushion symmetrical, as it should be, with respect to the median line, the greatest stress on the metal, per unit of area, will be the same in both flanges and will be, by eq. (28) or (29) ^ — , in which a is the area of the half beam. The unit stress is therefore just what it would 4 be if the total pressure were q j>p applied along the median line; hence we see that when the pressure p p can vary its position within the middle third of a frame, consisting of two heavy flanges and a thin web, the leaf should be calculated to carry a uniformly distributed pressure of 4/3 that actually in action. LEAVES WITH CUEVED BACKS. 49 By reference to eq. (31) we see that in the rectangular wooden frame Par. 109. the position of the center of pressure at the edge of the middle third of the section produces a unit stress on the extreme fibers of -j ^ on the one side and zero on the other, and that a departure beyond the middle third produces a tendency to extension at one edge. It is therefore important to keep the surface pressed with the middle third of the miter posts ; and we may say that for the wooden arched frames of rectangular cross section the surfaces of contact should be such that the center of pressure can not pass outside the middle third of the section ; and that, if it be allowed the above range of variation, the leaf must be constructed to carry twice the actual pressure. The metallic bowstring frame is a riveted girder, with the upstream Par. no. flange circular and the downstream flange straight. The total flange stresses string V^ers" are found by eqs. (25) and (26) when the center of pressure lies at the intersection of the axes of the two flanges. A departure of the pressure from this point may readily be provided for if the surface of contact at the posts be so shaped that the pressure can never go above the point in which the prolongation of the axis of the upstream flange pierces the surface of contact. The fulfillment of this con- dition usually results from the construction of the leaf, which is so curved that it has at the posts the depth desired for the surface of contact. Should the upstream limit of the center of pressure lie on the center line of the upstream flange, the greatest stress will be as given by the formulae. Should it lie below, the stresses will be decreased; in this case the simplest method will be to find the bending moment at the middle section when the center of pressure is at its most dangerous upstream limit and to propor- tion the flanges to bear the stress induced by it. Theoretical economy can not be found in this type of frame until the Par. 1 1 1. angles q> and a become equal, when the stress in the lower flange disap- pears, and the frame reduces to an arch. The best value of a to adopt will depend in each individual case upon the width of the surface of contact. When this is fixed, the most advantageous value of a will be that which makes the tension which occurs at the middle of the downstream flange when the center of pressure is at its extreme upstream limit about equal to the compression which occurs at the end of the downstream flange when the center of pressure is at its extreme downstream limit. The lower flange may then be made of the same thickness throughout and ease of construc- tion will result. Although it has been frequently used, this type possesses constructive disadvantages on account of the curved metal work. It may usually be 2623— No. 26 7 Timber 1 string girders 50 MITERING LOOK GATES. replaced with advantage by the straight-backed or broken-backed frame in metal leaves. Par. 1 1 a. The bowstring girder, either simple or trussed, is frequently applied to timber constructions, and has given very good results. The stresses in the chords may be found with practical accuracy for the simple form In eqs (25) and (26), with possible modification for variation in the center of pressure. The trussed bowstring -* f---f- •— ^--^r ' girder may be analyzed as follows: Hgii. ! j ^^^^\^'"y^ Let Fig. 11 represent such a frame. 5n ^-- '' yS Preserving the adopted notation, s' ^'°\\ s^ take moments about the point d, /■'''\~-~^~~'^ and we have, calling 9 the angle J^~-^~^ oad; K X c d = E X ' '' minus the moment of load from a to c. But /tan 9 n 7 I sin (a + 9) cd — p vers y + — 9 — ; and t d zz ~ — ^ — Li Li COS C/ and the moment of the load is equal to f° j / I tan 9 \ . I p pd tt> ( p cos

s'm(a-\-9) , - . a — . -— ±~± — J - — p p cos cp vers a> — p p sm

tne f ram es should be equal in scantling and the weakest in the structure. The latter method of uniform spacing and varying strength may con- duce to greater simplicity of framing, owing to the fact that it divides the vertical members into equal segments. There is, however, no theoretical reason why one system should be better than the other or why a combi- nation of the two should not be employed. The more modern practice in France appears to incline to equal spacing, while still leaving great latitude to the designer. Par. 3 33. As stated in Par. 27, the method above outlined does not give a leaf in which the frames are accurately proportioned to the loads which will actually CONSTRUCTION AND SPACING OF HORIZONTAL FRAMES. 57 fall upon them, either when the support at the sill fails or when it is perfect and simultaneous with that at the miter post. It does, however, give a structure strong enough to bear the maximum stresses induced by either accident of support; and, since both are liable to occur in the life of the same leaf, it seems best to provide for them. Should the reasoning upon which it is based not seem satisfactory, the frame strength or spacing should, of course, be made to conform to the condition of loading adopted by the designer, whether that of uniform variation with the depth, as in Par. 5, or that of M. Lavoinne or M. Galliot, as in Par. 129. Equality of maximum fiber stress in the frames may be brought about under any system of load- ing, either by varying the intervals, the strength, or both. The absolute distance apart of the frames must be regulated with Par ' ,s *- Frame spacing regard to the proper support of the sheathing and to the examination and for metal > eaTes - repair of the leaf. In the single-sheathed gates the former consideration will govern; in double-sheathed leaves both must be kept in view. For leaves with a single skin it is best to so space the main frames that the plating, while remaining of moderate thickness, shall not require inter- costal stiffening, which adds considerably to the first cost. This is generally practicable because, owing to the absence of the air chamber, the maximum local water pressure is that due to the greatest difference in level of the two pools. The leaves proposed for the Cascade Locks, Oregon, have a frame spacing of about 30 inches, a single skin A" thick, and a maximum local pressure of 24 feet. No intercostal stiffening is contemplated. For double-sheathed leaves the maximum local water pressure will be that due to the depth of the bottom of the air chamber below extreme high water in the upper pool, and may much exceed the lift of the lock. The frame spacing should be so regulated as to allow of easy examination of the interior and should, if possible, be at least 30 inches, although in some old gates it has been reduced to less than 2 feet. When the pressure is such that no sheathing of practicable thickness will bear the local load with such an interval between supports, then intercostal ribs should be used as shown in Par. 158. The leaves proposed for the locks at St. Mary's Falls Canals, Michigan, have a frame spacing of 30," a local pressure of 42.5 feet at the bottom of the air chamber, a double sheathing of |" plate, with intercos- tal ribs at 15" intervals in the lower strakes. In wooden leaves the dimensions, and consequently the spacing of the Par. 135. horizontals, are more or less influenced by the size of timbers available. In very heavily loaded leaves the frames are sometimes placed in contact with each other. 2623— No. 26 8 CHAPTER V. VERTICAL FRAMING. Par. 138. The vertical frames of the leaf perform a double duty, viz, they dis- tribute the load to the horizontals and they stiffen the leaf against vertical forces. The latter function will be considered in a subsequent chapter. The former duty will in general form the basis for the design, since it alone throws any bending stress on the members. Par. 139. As indicated in Par. 35, there are two general methods of designing the framework; in the one the vertical system is assumed, being taken as sufficient to support the vertical strains to which the leaf Avill be subjected; the loads thrown by this system upon the horizontals are then calculated by some method, as that of M. Lavoinne or of M. Galliot; the bending moment on the verticals is then found from these loads; and the vertical system as first assumed is then corrected, if found too weak to stand the moment. In the second method, the horizontal system is fixed in accordance with some assumed law of loading, and a vertical system is designed such that it will throw upon the horizontals loads which are suitable to them. Thus, we may assume the loading to vary with the depth, as is very commonly done; and we then know that we must have absolutely no vertical rigidity; or we may assume the loading as in Par. 27, and we may deduce the nec- essary vertical rigidity as will be explained shortly. Par. 140. Both methods lack theoretical accuracy; the first because no formulae have yet been devised which give with more than approximate closeness the effect of an assumed vertical rigidity upon a system of horizontal frames ; the second, because in order to provide against imperfect fitting, the lower part of the leaf must be constructed to carry loads varying directly with the depth, and will in consequence require an absolute absence of vertical stiffness, which is not practically attainable. There is, however, less uncer- tainty attending the use of the second method, since we can readily find the limit beyond which the vertical rigidity must not pass, and by keeping within this limit may design a system which, while safe against its own stresses, can not throw upon the horizontals greater loads than those for which they are calculated. 58 VERTICAL FRAMING. 59 If the horizontals were such that their strength at different points Par. 14 1. in the height of the leaf varied inversely as the deflections of the ver- tical strip, found from eqs. (4) and (5), then the rigidities of the two systems would have to be such that their deflections would be the same at any point; the true value for one rigidity in terms of the other might then be found by equating the values for the horizontal and the vertical deflection at any point of the leaf. Since, however, the horizontals proportioned by the rule of Par. 27 do not correspond exactly with the theoretical construction, except at the point of the height where the load S (H— y) due to the depth is equal to the load p zz —5— — q tt 2 due to the verticals, this point should be taken for the determination of the rigidity. It corresponds to a value 2 H h? of y equal to — o~ + o tt2 — 3/"- -^ or an y gi ven values of H and h, the deflec- tion of the middle vertical section may be found from eq. (5) ; that of the horizontal system from the well-known expression J — 76-8 E f I f ' and the relation between the rigidities of strips one unit wide may be found by equating the two deflections. Taking first the case of a leaf unsupported by water in the lower pool, we have p - 3 ; - 6 ; y - 3 ^ ana /- 3 768 E f I f By substitution in eq. (4) or eq. (6) we obtain E V I V _ 11 855 H 4 zE f r f - v- giving a relation between the rigidity E f I f of a horizontal strip one unit E V I V wide, and the rigidity \ of a vertical strip one unit wide, when the ver- S TT tical system is such as to load the horizontal with the force p z= — „— per square unit of supported sheathing. Taking now the case of a leaf sup- ported for half its height by the water in the lower pool, we have J. H 7 ATT » 17 W AT> 6W h=j; p=z 24 »,, in.,, m 3 , etc., m m represent the distance between horizontal frames. When the leaf is supported at the sill the load on any horizontal will (s s - p 3 )m. be iit n j>„ per unit of length. When the leaf does not touch the sill the load will be m u ,s„. Each vertical strip of the leaf one unit wide is, therefore, in equilibrium under *■ ^-ft'" 1 - the action of a system of forces m n (s n — p u ) applied at the horizon- tals and a reaction p 7 )m. < 8 6- Ps' 7 "' pjm. * '«j~7' a , m (ZSn-Zpn) 2 s — 2 V applied at the sill. If we are designing a vertical system to have an assumed rigidity and Par> xi ^- wish to determine the stresses endured by such a system, we may find the forces p n by Galliot's formula. This method is especially suitable where the leaf is so small that the contact at the sill may be considered perfect at all times. When the horizontals are proportioned according to the rule of Par. 27, the greatest loads p n are known at once to be 6 ( — — _ _ \ per \_ o 3 n." J square unit of supported sheathing. The load per square unit on the ver- tical system is the difference between this and the pressure due to the depth. Having found the forces m n (s n — p n ) the greatest bending moment occasioned by them in the vertical system may readily be determined and the verticals designed to bear this moment with the same fiber stress as was permitted in the horizontals. The system so designed will generally have a rigidity well within the limit found in Par. 145, for leaves designed accord- ing to the method of Par. 27. For an illustration see Appendix I. Since the forces m n (s n — _p„) are parallel, the graphical method maybe Par. 14§. employed with great simplicity in the determination of the bending moment 62 MITERING LOCK GATES. in the unit strip. To illustrate, let us suppose that the frames of the leaf are to be proportioned by the rule of Par. 27. To find the forces w n (s n — p u ) we have only to find by Par. 12 the loads m n s n due to the depth, to cal- ( H W \ culate the value of S ( -=- — q~tj2~ ) and multiply by m n for the loads m n p n , and to subtract the latter from the former for the loads on the verticals : or, more simply, let Fig. 15a represent the vertical strip of unit's width of a leaf of which the line A B is the inside of the sheathing and let L P be the level of the lower pool. Lay off from A B on L P the distance x c, to represent to some suitable scale the pressure per square unit at and below L P, and draw the lines A c and c d, the latter parallel to A B. Draw the (XT 7.3 \ to the scale used in laying off x c, and drop ordinates u iv, o q, etc., from the middle points of the frames to the lines A c d and E F. The difference in length of these ordinates will be the resultant horizontal force transmitted to the vertical strip by each square unit of sheathing supported by the hori- zontal frame in question; and when multiplied by the width of the sup- ported sheathing will give the total force, or the quantity m (s — p). Thus the load on the vertical at the frame next to the bottom, Fig. 15a will be given by the distance v w multiplied by m n ; at the frame next to the top it will be a & multiplied by i l~ — i / or its equivalent, — k I. When the ordinate of the broken line A c d is greater than that of the line E F, i. e., when s n is greater than p m the resultant thrust on the vertical acts downstream; when the reverse is the case, it acts upstream. Having thus found the horizontal forces tending to bend the vertical strip, draw, as in Fig. 15&, a line a b parallel to A B to represent the vertical section, and lay off on it to some suitable scale of distances the points of application of the forces, and draw through these points perpendicular to a b the lines 1-2, 2-3, 3-4, etc., to represent the forces. Draw, as in Fig. 15c, a line perpendicular to a b and lay off on it, in order, to some suitable scale of intensities the forces 9-8, 8-7, 7-6, etc., forming the force polygon. The closing force 1-9 will be the total reaction at the sill and should be /H 2 h 3 h 2 \ equal to 8 ( -~- + s^ct — a ) , vide Par. 18. It should be remembered that, since the force 9-8, Fig. 156, is applied at the sill, it serves only to generate and neutralize a portion of the reaction, and has no further influence on the polar and equilibrium polygons. Par. 149. Taking the pole o, Fig. 15c, at some suitable distance from the force polygon, and, for convenience, on a horizontal through l, complete the polar VERTICAL FRAMING. 63 A^ a 7. s t m Tl /7 ^^— 1c ' Fiq.l5*\ \ 1 ^ 1 ' X 1 — i i i i i E^ 9 i ^< v If i \ \ ! ^\ 1 1 i -h ! ! 1 1 >- L - J, ^ .9 ] i, - k i k < , , i ^^' Fig. 15* w-r Ji i 2 ■ < 3 4 5 y' 6 7 8 9 FiqA5 c - Vif"=4S. 64 METERING LOCK GATES. and equilibrium polygons by drawing the strings and links parallel each to each. The point of greatest bending moment is seen at once to be at g, Fig. 156, while its amount will be given by the ordinate g g' to the scale of distances, multiplied by the pole distance 01, Fig. 15c, to the scale of inten- sities. The convenience of the method lies in the fact that it shows at once the position of the point of maximum moment. Having determined it. position, the amount may be found analytically if desired. Par. i5o. Each vertical strip one unit wide is exposed to the moment found as above. The combined vertical system will, therefore, have to resist the product of this moment by the length of the leaf. The frames and sheath- ing should be so proportioned that the fiber stress developed in the verticals shall be the same as that in the horizontals. The rigidity of the system should then be calculated to see that it falls within the limit of safety, as it will generally be found to do. The above method does not require a close calculation of the ratio between the rigidities and avoids the difficulty inci- dent to such comparison when the horizontals are curved. ( Vide Par. 7.) Par. i5i. The theoretically best disposition of frames is to have the horizontals proportioned to bear the load due to the depth and to have absolutely no vertical rigidity, since the frames so constructed are suited at the same time for the loads which come upon them when the fitting is perfect and when it is imperfect. It is, however, impossible to build the leaf without vertical rigidity, and so soon as this is allowed to enter the structure it becomes nec- essary to strengthen the upper frames to provide against the loads due to it. If we admit the necessity of providing against the stresses endured both when the leaf rests against the sill and when it does not, the simplest and best method for leaves of ordinary relation of length to height is to proportion the horizontals by the rule in Par. 27 and the verticals bv the method of Par. 146. If we assume that the leaf will at all times be in per- fect bearing, the vertical system may be first assumed and the horizontals proportioned to the loads which it will throw upon them, employing for the calculation the method of M. Lavoinne, of M. Galliot, or a variation of the process given in Par. 15. When the leaf is very high and short, it may be constructed without verticals intermediate between the quoin and miter posts. In this case the influence of the vertical rigidity would be small, and the frames should be constructed according to the law of varia- tion with the depth, giving to the upper ones a slightly increased strength, determined by M. Galliot's formula or otherwise. Par. 15a. When it is desired to design a vertical system capable of resisting the bending moment determined as in Par. 147, it will be convenient to assume VERTICAL FRAMING. 65 the sheathing as suited to the local water pressure, and to calculate its S I moment of resistance — when working at the allowable fiber stress S; to subtract this from the bending moment thrown on the whole leaf by the forces in action, and to provide vertical frames having a combined moment of resistance equal to the remainder. In wooden leaves the sheath- ing and frames work independently of each other. In metal leaves a strip of plating may be considered as acting with the vertical. The width of this strip should be the same as that considered to act with the flanges of the horizontals, vide Par. 121. It should, of course, be left out of consideration in the calculation of the moment of resistance of the portion of the sheath- ing which acts independently. The number and spacing of the verticals which are to have the deter- Par. 153. mined moment of resistance are largely matters of judgment. In general it is well to employ enough to justify approximately the assumption that the rigidity is uniformly distributed through the leaf, i. e., at least three intermediate between the quoin and miter posts. When one or two are used it will be well to make the horizontal frames near the top strong enough to stand the total load applied by the vertical system, under the assumption that that load is concentrated at the joints with the verticals. In small metal leaves it has been recommended to so space the verticals as to divide the sheathing into squares, since the plating is then in the best condition to resist local pressure. In most cases the spacing will be regulated by the size of the panels into which it is desired to divide the leaf for bracing against its own weight. A type of leaf has been recently coming into favor in France, in which p j a l ^; 8 I ^* , h the load of the water is transmitted by the sheathing to a system of verti- ti" gle hor,zo, ' cals which are supported by the miter sill at the bottom and by an extremely strong frame at the top of the leaf. No intermediate horizontals are used, except such as are needed for bulkheads to the air-chambers, and these are too weak to carry any load. The stress in the horizontal depends upon the type adopted and may be found from the formulae of Chapters II and III. The advantage claimed for the design is that a large portion of the pressure, reaching sometimes two-thirds of the whole, is borne by the miter sill. When the length of the leaf is much greater than its height, a saving in weight may result from the adoption of this type of girder gates, since the short vertical girders may be lighter than the long horizontal frames which would be used in an ordinary leaf to carry the part of the load now borne by the sill. In any case, the division of the leaf into vertical instead of horizontal compartments greatly facilitates examination and repair. 2623— No. 26 9 66 MITERING LOCK GATES. M. Collignou is believed to have first suggested this form of leaf, in 1863. Since that time several examples have been constructed, notably those at Dunkerque, by M. Guillain, and those at Havre, by MM. Widmer and Desprez. The latter will be found on Plate 2. Par. 155. In all these leaves the heavy top frame is practically a straight-backed girder. There would seem to be no good reason why it should not be used in the arched form in cases where the curvature is not considered too great an obstacle; the advantages of the arch would then be combined with those of the vertical framing and a light leaf of ready inspection would be secured. In point of weight the leaf with many horizontal arches might still be superior, since the vertical girders might weigh more than the longer, but not so heavy, horizontal arches. The saving due to the vertical transmission of the load is not apparent in all cases where it has been applied; for instance, the leaves at the Havre dock are probably heavier than they would be if built on the arched system; but the advantage of ready accessibility and of less curved metal work may justify greater weight in certain situations. Par. 156. The construction of the verticals needs no extended description. For ofvertioais. wooden leaves with open built horizontals, they are frequently also open built, consisting of two parallel vertical timbers clamping between them the lower chords of the horizontal frames. When the horizontals are solid, the verticals may also be solid and fastened to the downstream side of the leaf or open and embracing the horizontals between their timbers. In riveted metal leaves the verticals are similar to the horizontals, being solid or open built plate girders, fastened to the sheathing and hori- zontals by angle bars. In leaves with rolled metal frames, the vertical frames may conveniently be made solid and riveted to the downstream flange of the horizontals. CHAPTER VI. SHEATHING. Par. 157. Local streas. In large metallic gates with a number of horizontal frames the sheath- ing has a complex function. It transmits the pressure to the framework of the leaf, and in so doing endures a local fiber stress; it acts more or less as a flange to the main frames and endures thereby a general fiber stress; and it acts as part of the bracing against vertical forces. The maximum stresses endured in the last manner do not come on the sheathing at the same time as the others and will not in ordinary cases govern the design. The plates must be proportioned to bear the sum of the first two stresses. In earlier structures it was customary to space the horizontal frames Par. i»§ closely and to use a sheathing of such thickness as to require no interme- diate support. This necessitated very thick plates and cramped interior space ; in the gates of the old Victoria Docks, for instance, the lowest frames are but 1' 11" apart, and the corresponding strake of sheathing is §" thick. It is now more usual, in double sheathed structures, to keep the main horizontal frames at a distance of not less than 30" apart, to use a thinner plate not exceeding §", and, when the pressure requires it, to supply the necessary support by intercostal frames or ribs, running either parallel or perpendicular to the main frames. When the intercostals are parallel to the main frames, the sheathing, if plane, is in the condition of a beam fastened at its extremities. If the distance apart of the supports be taken as 2 a, the maximum bending moment in a strip one unit wide will occur at the point of support and will be equal to ts p' « 2 , p' being the local pressure per square unit. The fiber stress due to the local pressure endured by a plate of which the thickness is h, will therefore be s/= M2 = 2p_a>; (32) this should be added to the unit stress due to the action as part of the flanges of the frame to obtain the maximum stress per unit of section. The plate has undoubtedly a greater resisting power than is indicated by the 67 68 MITERING LOCK GATES. above formula or by any other which regards it purely as a beam. After slight bending it will carry its load by tension, rather than by transverse strength. As it is desirable to avoid this bending as much as possible, it is usual to design the plating as a beam, obtaining in this way a somewhat indefinite reserve of strength. In spite of this, the plating is usually the first part to give way. Par. 1*9. When the intercostals are placed at right angles to the main frames P anef 8 tansular the skin becomes divided into rectangles fixed at the four edges, and is in a much more favorable condition. The formulae for the stress in such plates have been deduced by Prof. Grashof, and are given in convenient form in the Appendix of Lanza's Mechanics, as follows: Par. 160. 1 2 ¥ a 2 p' ) Ee x _ ii 1 • 1 i i "Wooden leaf be in one 01 two conditions, viz : it will be either too heavy at low water for varying lift. or too buoyant at high water. It should be so constructed as to be suited to the most common level, and provision should be made for working at very low or very high stages, either by giving the necessary excess of strength to the anchorage, in the one case, or by providing additional weight, in the other, the weight being detachable so that it may be removed as the water sinks. In extreme cases an excess of weight at low stages may be taken up by a roller. A sudden increase of upward pressure caused by variation of level in Par. 17§. the upper pool when the gates are closed must be guarded against either by a suitable reduction in the exposed area of the bottom, as indicated in Par 96, or by providing additional weights, as above indicated. If the leaf be of sufficient size to justify the expense of an air chamber the difficulties incident to changes in level may be avoided, as in the case of metal leaves. A metal leaf may be made without difficulty to suit a varying lift, if Par. 179. it be possible to buoy it up enough at low water. The air chamber must varying im. for have its roof below or just above the lowest working level and may require a great depth between sheathings, to furnish the necessary displacement. Should this depth prove excessive, the air chamber may be made large enough to partially relieve the anchorage at low water, or the difficulty may be met squarely by leaving the chamber out altogether and trusting to the anchorage to support the leaf while working at the lowest stages. The latter method finds favor with certain engineers, who consider that the strain and wear on the fastenings is less objectionable than the difficulty of con- structing and maintaining an intact air chamber.* This point will be treated more at length when the choice of type is discussed. *It is intended to take the whole weight of the gates of the Cascade loots on the anchorage and to swing them without an air chamber. Each leaf is designed to weigh 130 tons in air. 76 MITERING LOOK GATES. Par. 18©. Par. 181. The extra weight at low water may be taken up by a roller. The slow- ness of manoeuvring a leaf thus supported, as well as the expense, makes this method less desirable than either of the others. When it is desired that the manoeuvring preponderance be large, advan- tage may be gained by making the depth between sheathings so great that the required buoyancy at ordinary stages will be given by a chamber lim- ited to less than the full length of the leaf, and by placing this chamber as far away from the quoin point as possible. To illustrate, let Fig. 18 repre- sent an elevation of the leaf and let o o' be the ordinary working level. If the desired manoeuvring weight is attained by the use of an air chamber abed removed as far as possible from the quoin post Q Q' it becomes at once evident that the buoyant effort P of the air chamber will have a greater lever arm about Q' than will the weight of the leaf, and that the strain on the anchorage Fig.18. will be relieved more than by the same buoyant effort acting nearer the quoin, while the resultant vertical pressure R on the pivot will remain the same. This effect may be still further increased by impounding the water in the upper part of the leaf near the quoin to supply ballast. The resultant R of the combined weight W and the buoyancy P may be brought near the quoin and a leaf obtained of any desired manoeuvring weight and stability against shocks, and with small strain on the collar and anchorage. The method requires a considerable depth between skins, and is not always applicable. It has been used for harbor gates only and would be very difficult of execution in wooden structures. When the air chamber is used provision must be made for easy access to it at all stages of water at which the gates are worked. This must be done either by placing its roof above the manoeuvring level and piercing it with man holes having detachable water-tight covers, or by connecting it with the top of the leaf by water-tight chimneys of sufficient size to admit a man. The first method will answer only where the level of the lower pool is practically constant. Sometimes in harbor gates provision is made by valves for impounding the water in the upper part of the gate to increase the stability in times of danger from wave shocks. VERTICAL STRAINS. 77 The stresses produced by the weight of the leaf must be taken up by Par. i§2. bracing designed to carry the load to the points of support. In small weight. wooden leaves a diagonal strut is used, extending from the foot of the quoin to the head of the miter post. This strut is cut where it crosses the frames and securely connected with the latter. Iron brackets are also used to con- nect the upper and lower horizontal frames with the quoin and miter posts. In large leaves the compression braces are formed by the vertical Par. 183. frames which divide the leaf into panels. The tension members are formed in wooden leaves by diagonal iron straps and in iron leaves by the sheath- ing itself; diagonals are used to replace the omitted plating in single-sheathed leaves of great size. The horizontal stresses induced by the braces must be taken up by the horizontal frames of the leaf. The top and bottom frames will take the greater part and may have their dimensions fixed rather from these stresses than from those due to the water pressure. When the leaf has a roller the weight must be carried by the bracing Par. 184. to the pivot and roller, and the horizontal stress to the collar. The division of the load is more or less uncertain, and will depend upon the degree to which the turnbuckles of the anchor bars are tightened up. The bracing should tnerefore be strong enough to carry the weight to the pivot and roller, supposing the collar free from stress. Where there is no roller the bracing must be designed to carry the weight to the pivot and the horizon- tal stress to the collar. All the parts strained by the weight must be calculated for the most Par. 185. unfavorable position of the leaf, preferably for its weight in air, since it is often swung for some time before water is admitted, and since it may be necessary to pump the lock dry. Where parts are strained by the weight and by the water pressure Par. 186. simultaneously they should be calculated for the sum of the two stresses. Ordinarily the upward pressure on the bottom of the leaf is sufficient to take off most of the stress due to the weight at the time when the water pressure is in action. When a roller is used its axis should lie on the horizontal projection of Par. 187. a straight line passing through the center of the pivot and the line of action of the manoeuvring the weight of the leaf. The tread should be slightly conical, the circumference of one end bearing to that of the other the same ratio as the radii of the paths passed over when the leaf is swung. The weight is usually applied by means of a strong adjustable vertical post which rests its lower end on the axis of the roller, extends the whole height of the leaf, and is provided at the upper end by a system of screws or 78 MITEEING LOCK GATES. levers by which it may be raised or depressed and a less or greater share of the weight thrown on the roller, while the stresses on the pivot and col- lar are correspondingly changed. The diameter of the roller varies from a few inches to 2 feet, the largest sizes giving the best results. Par. 188. The use of the roller carries with it many disadvantages. The added expense is great, the division of the weight is uncertain,* and the operation of opening and closing the gate is rendered slower. Per contra, the anchor- age may be much relieved and the manoeuvring weight much increased where great stability against wave shocks is necessary. There seems to be no insuperable difficulty in swinging even very heavy gates from the pivot and collar. The wooden leaves of the lock of 1881 at Sault Ste. Marie, Mich., are supported without rollers by an ordinary anchorage and cast- iron pivot. Each leaf weighs 76 tons in air and has often thrown this full weight on its fastenings, as the lock pit is pumped dry twice annually. Unless the leaf is to remain long unsupported, no attention is paid to block- ing up the bottom to relieve the fastenings. The gates have been in con- stant use for ten years without any general repairs and without showing any signs of structural weakness. In the great majority of cases the ma- noeuvring weight can readily be reduced much below 76 tons, no matter how much the leaf may weigh in air; and if at any time the full weight in air is to be thrown on the fastenings, the miter posts may be blocked up by a diver before pumping out the lock, should this be deemed necessary. It would therefore seem that there is no absolute necessity for the use of the roller and that in most, if not all, cases it may be omitted. The weight of authority seems to indicate that it is an objectionable feature, only to be tolerated when unavoidable. Par. 189. The construction of the quoin post is of importance. Its duty is not Quom post, only to carry the whole or a part of the weight of the leaf, but also to transmit to the masonry the thrust delivered to it by the horizontals and sheathing. In wooden leaves it is usually made either of one timber, or of several so framed as to form one single post. In metal leaves it has fre- quently, in the past, been made 'of timber or cast iron. The present practice is to make it wholly of rolled metal, either building it of plates and angles in the larger structures or using a simple rolled beam in the smaller ones. Par. 190. Frequently the post is made circular in horizontal section, on the side which is in contact with the masonry, the other side being of some form * In the proceedings of the Institute of Civil Engineers, session of 1878-'79, the ease is mentioned of a gate of the old north lock of the Bristol dock, which on removal was found to be carrying it« roller clear of the track and appeared to have done so for many years without the fact being sus- pected. VERTICAL STRAINS. suitable for easy connection with the horizontals. The center of figure of the circular portion coincides with the center of figure of the hollow quoin when the leaf is closed. The axes of the pivot and gudgeon are placed on the same vertical line, and somewhat eccentrically, so that there is no fric- tion in opening and closing the leaf. The construction for the best position of the center of rotation is given by Debauve as follows: Let R R' and Q Q', Fig. Wd, be the positions occupied by the axis of the leaf when closed and when open. Through their point of intersection, O, draw O A, bisecting the angle Q' R, which is the supplement of the angle of revolution of the leaf. On the bisectrix select some point, as G, on 79 the upstream side of R R' ; this point should, if possible, be in the vertical plane parallel to R R' and through the center of gravity of the leaf. From G drop perpendiculars G S, G P to Q Q' and R R'. The point P will be the center of the circular portion of the hollow quoin and post. The point S will be the position of the center of the post when the leaf is open. The point G will be the center of revolution. The circular quoin post is objectionable in giving a rounded bearing Par. 191. against the masonry. The surface of contact should theoretically be plane and perpendicular to the line of the reaction. The form to give such a sur- face may be found in some such way as follows for girder leaves : 80 MITERING LOCK GATES. Let c d, Fig. Ida, be the line of direction of the reaction found, as in Par. 38, and let a b be the downstream side of the leaf when shut. Through the point of intersection o draw op, perpendicular to d c and of a length Fig. 19^ equal to the desired extent of the surface of contact. Draw p q perpen- dicular to o p. The center of rotation of the leaf should be on the line -p q, or at some point on the upstream side of it.* The back of the post may * If possible, the center of rotation should be in a vertical plane parallel to the downstream surface, and passing through the center of gravity of the leaf. VERTICAL STRAINS. 81 be finished in any way, provided that the radius 5 t of the curve tangent to the surface of contact at p is less than the distance r p of the center of rota- tion from the same point. Care must be taken to so shape the hollow quoin that the post will not strike in turning, and to round off the angle at o for the same purpose. By the above construction the surface of contact will be placed as far Par. 192. downstream as possible and will have the proper direction. For an arched leaf it is desirable to have this surface symmetrical with respect to the median line. To find the center of rotation in this case some construction similar to that in Fig. 1 96 may be used. Let c d be the median line of the leaf. Draw s t perpendicular to c d at its extremity, and bisected by it, making the length s t equal to the width of the desired contact. Draw s o perpen- dicular .to s t at s. Any point r on this line, or on the upstream side of it, will answer for the center of rotation. Both in this case and in the preced- ing one, Fig. 19a, it is better to put the center on the perpendicular rather than on the upstream side of it, as it will be easier to conceal the post in the recess when the leaf is open. The portion of the post above the center of rotation may be finished in any way such as to avoid striking at s when rotated around r. A simple way is to make it a circular arc tangent to s t at s in plan, the point r being farther from s than the center o of the arc. In shaping the post the following points should be observed, viz: To Par. 193. make the surface as small as is consistent with safety against crushing ; to place it perpendicular to the line of thrust ; to place it as far downstream as possible in a girder leaf and symmetrically on each side of the median line in an arched leaf; to so place the axis of rotation that there shall be no friction in turning, and that the post shall be concealed when the leaf is open ; to make a water-tight joint with the masonry ; and to avoid exces- sive depth in the quoin. The surface of contact is rarely reduced to the amount just sufficient Par. 194. to transmit the pressure, although advantage would result from so doing, since thereby the line of pressure would be kept in practically the same position all the time. The designer should always endeavor to restrict it to the lower half in girders and to the middle third in arched frames, for the reasons given in Pars. 58 and 103. When the frame is large this ratio of contact to depth may be much reduced. The function of the quoin post as a weight-carrier requires a sufficient p a r. 195. sectional area to support its share when the leaf is swinging in air. In designing it, the fact should be kept in view that the force is applied eccen- trically along a vertical through the center of the pivot, and that, conse- quently, more material will be required than for an axial force. 2623— No. 26 11 82 MITEKING LOOK GATES. Par. 196. Ill metal leaves the duties of carrying weight and transmitting pressure are sometimes separated, the post being made of some simple section adapted to the vertical stress and armed at intervals with shoes to trans- mit the pressure to the masonry. The horizontal section of the shoe is determined in the same manner as that of the post when the latter transmits the pressure. Thus Fig. 19c would be the shape of a shoe to replace the the post of Fig. Idb. Between consecutive shoes the post itself is not in contact with the masonry, and must, therefore, have a sufficient transverse strength to bear the thrust of the intermediate horizontals and sheathing. This method of construction was adopted in the gate of the Charenton Lock, PI. vn, and has been applied to very large structures — as, for instance, the gates of the Bassin Bellot at Havre, which closely resemble in other respects those of the Transatlantic Docks, PI. 2, and were built a year or two later. The quoin posts in these are vertical plates perpendicular to the axis of the leaf and connected to the sheathing by angle bars ; in short, nothing but vertical frames closing one end of the leaf. They do not fit the hollow quoin, but are centered at two points between the foot and head by cast-iron shoes. As the top frame is constructed to take the whole pressure {vide Par. 154), these intermediate shoes exert but little force against the masonry. Par. 197. The manifest advantage inherent in the above construction is the avoidance of sharply curved wrought metal work, which is always expen- sive and sometimes difficult of execution. Another means of avoiding it would be to construct the quoin post, as before, in the form of a simple vertical diaphragm closing the end of the leaf, and to rivet to it on the outside a rolled metal buffer of suitable section, to transmit the pressure to the masonry. This buffer may be a simple rolled I beam or a box built up from plates and angles, as shown in horizontal section in Fig. 20, which represents a study for the quoin post of a leaf in which the reaction is parallel to the line A B. Par. 198. Iii localities where the gates must be worked in continuous cold weather, some caution must be used in adopting a form of post which does not ap- proximately tit the hollow quoin, as the formation of ice in the interval when the leaf is open may cause inconvenience. The surface of contact of a wooden post should form a tight joint with the masonry. In metal work a timber cushion is generally applied on the downstream side, as shown in Figs. \% and 20. The surface in which this cushion touches the masonry should be nearly parallel to the line of the reaction to avoid the danger of splitting either the wood or the corner of the masonry. Par. 199. VEETICAL STKAINS. 83 Timber posts are sometimes built up by shaping the ends of the hori- Par. 200. zontal frames to transmit the pressure directly, and laying them immedi- ately in contact with each other, or separated by short blocks of timber. In this construction there is no post, properly so called, the compression due to the weight of the leaf being resisted by the frames and blocks in contact with each other, and bolted together. This construction is suitable where there are so many horizontals that it is difficult to frame them into the continuous post without cutting away too much of the latter. In the improvement of the Great Kanawha River some large gates of this type have been built. As stated in Par. 216, gusset plates may be used in the quoin and miter Par. 201.. posts between the horizontals to transmit the pressure to the intermediate sheathing. Fig. 19e shows this construction. The footstep is generally a casting either of steel or iron, very solidly Par. 202. connected with the bottom of the quoin post. Great care must be taken to Foot8tep Pivot. 84 MITEEING LOOK GATES. so unite the parts that the stress due to the weight shall fall as uniformly as possible on the cross section of the post. When the latter is hollow, the footstep is usually united to the lowest horizontal frame below the post, and between the frame and the one next above suitable provision is made inside to distribute the weight to the plating. Too much solidity can hardly be given to this part of the structure. Par. s©3. The pivot is sometimes of forged metal shrunk into a cast bed plate, which gives sufficient bearing on the lock floor. For all except the largest gates it has generally been considered more advantageous to cast the pivot and bed plate in one piece. The form is cylindrical, terminating on top in the segment of a sphere. Various devices have been resorted to with a view to diminishing the friction and wear in the footstep. A bushing of brass or bronze has frequently been used where electric action is not to be feared. If the manoeuvring weight be kept within even moderate limits, there would seem to be no necessity for any such precaution. The diameter of the pivot varies in accordance with the size of the leaf a maximum of 15A inches being reached in some of the largest examples. In almost all cases the cylinder projects upward from the floor rather than downward from the leaf, the socket being placed in the footstep; although in some instances, as at the Transatlantic Docks at Havre, the reverse is the case. The former practice is preferable, since it avoids the danger of obstructions falling between the surfaces of the pivot and socket. The socket receiving the projecting cylinder of the pivot is usually conical, being larger at the base than at the top. It terminates in the seg- ment of a sphere which bears against the corresponding surface of the piv< >t. The concave segment may have a slightly larger radius than the convex one. The area of contact of the socket and pivot should be sufficient to preclude all danger of crushing under the weight of the leaf. When the leaf is swinging freely the quoin post is unsupported by the hollow quoin; there is, in consequence, a horizontal thrust delivered to the pivot equal to the horizontal pull on the collar, viz, equal to -y^ , in which It W is the greatest weight of the leaf, g the distance from the pivot to the vertical through the center of gravity, and h the height between pivot and collar. This thrust is applied to the pivot at or near its top and produces a bending moment equal to the intensity multiplied by the lever arm,* viz, by the distance from the top of the pivot to the bed plate. The cylindrical Par. 204. Par. 905. • The bendi D g moment may therefore be written, M = W gj , in which I is the distance which the pivot projects above the tied plate. VEETICAL STKAESTS. 85 part must be proportioned to resist this bending and the accompanying shear. The formula for flexure as applied to circular bars is P =-tt—j in which P is the maximum fiber stress per unit of area produced by a moment m in a pin of which the area is A and the diameter d. The value of P should be small, as the stress may be applied in different directions and while the leaf is in motion; particularly in the case of cast pivots should the unit stress be small. Advantage will result from making the cylindrical part of the pivot Par. 206. short, since the lever arm of the horizontal thrust is thereby diminished. Enough projection should be allowed to preclude the possibility of the leaf being lifted off its bearing by shock or flotation. From 3 to 6 inches will usually be found sufficient. Unless extremely short, the pivot will be safe against shear when it will resist the bending; if not, it should, of course be made so. The actual cross-section of the pivot and the area of contact must, of course, be large through to prevent danger of crushing. The upper gudgeon is a pin made of steel or iron, forged when practi- Par. aov. cable, fastened to the leaf at the top of the quoin post, and held by the col- g eon Pper fe "" ! lar. For large leaves it is ordinarily fixed in a bed plate, frequently a cast- ing, with which it is assembled hot, and which is firmly fastened to the top of the quoin post and the upper frame. For small leaves the gudgeon and bed have been generally cast in one piece. The horizontal pull on the gudgeon is the same in intensity as the Par. ao§. thrust on the pivot, and the design should be governed by the same prin- ciples in both cases. "When the stress is great a very large pin may be required, the diameter ranging as high as 14" in certain cases. A less cumbrous and more secure fastening may be devised for large Par. 209. iron leaves, by which the diameter of the gudgeon may be materially re- duced, if both ends of the pin be supported by the leaf and the collar be applied midway between the supports. The pin will be of form suitable for forging, being a detachable cylinder, and the bending moment will be much lessened. In the large iron gates at St. Nazaire the ends of the detachable pin rest in castings bolted to the first and second frames where they project into the quoin post, and the collar embraces it midway between them. A detail which is apparently preferable in certain cases is to rest the lower end of the pin in a socket prepared on the upper frame, the pin passing through the plates of the latter, and to hold the upper end in a transom bolted or riveted to the plates of the post or sheathing, which are 86 MITERING LOOK GATES. Par. 21©. Par. 211. Collar. Par. 212. Par. 213. Par. 214. prolonged above the upper frame. The two arrangements are sketched in Fig. 21. The bending moment of the pull may thus be reduced to about half what it is when the pin is secured at only one end, and an unmanageable diameter may often be avoided. Care must be taken to so reenforce the plates of the upper frame and transom as to give a sufficient bearing area for the pin. This may be done by riveting additional plates to them or by using castings as sockets. The collar consists usually of a strap which passes around the gudgeon and is held to the masonry by the anchor bars. In small leaves, the strap is simply a prolongation of the bars and is joined to the latter by turn- buckles, pins, or other suitable connections. When the weight of the leaf is great, a more elaborate attachment is necessary. The collar and the portion of the anchor bars which project from the masonry are subject Fig 21. to a greater or less bending action in certain cases. To take this up, a headpiece or anchor box may be introduced between the collar and anchor bars. Various forms have been used; a few are shown in the plates. The collar may be in one piece or in several parts, with pin connec- tions. The latter may be more convenient in some cases. The use of cast iron in the collar should be avoided as a matter of course. In the headpiece it has been frequently used, but is not to be recommended, at least one case of failure being recorded. Cast steel suit- ably strengthened by rolled plates should answer the purpose in compli- cated designs. In simpler ones built-up forms of rolled or forged metal would be preferable. The anchor bars may be double or multiple. They should, if possible, be so placed as to include within their splay all possible positions of the line of directions of the horizontal force exerted by the leaf. A large excess of strength should be provided, as the parts can not be inspected when once in position. VERTICAL STRAINS. 87 The miter post has but little stress except that which is thrown on it Par. 215. Miter post. by the duty of distributing the compression to the horizontal frames. In wooden leaves it is generally a simple or solid built post, so chamfered as to keep the center of pressure within the desired limits. In metal leaves it may be a simple vertical diaphragm riveted to the sheathing ; or it may result from curving the plating around the ends of the horizontal frames. Both forms must be provided with some attachment for the cushion. When it is desired to have the sheathing carry its share of the general Par. 216. stress it is advisable to introduce in the quoin and miter posts gusset plates intermediate between the main horizontal frames, as shown in Fig. 19e. In timber leaves the miter post as well as the quoin post may be built Par. 217. up out of the ends of the superposed frames with intermediate blocking when necessary. The surface of contact of the two leaves must form a water-tight joint ; Par. 218. must be a plane surface lying on the axis of the lock; must be as small as is consistent with proper transmission of the pressure, ami must be in the best position, i. e., as far downstream as possible in girders, and symmetrical with respect to the median line in arched frames. These conditions are practically the same as in the case of the quoin post, and need no further discussion. The limits allowed for the position of the centers of pressure should be the same at both ends of the leaf. In timber leaves the material of the posts will serve to render the joint Par. 219. water tight. In metal leaves a wooden cushion applied to the shutting sur- face of the two miter posts has very generally been used to prevent leak- age. This cushion is so placed as to keep the line of pressure from passing outside the desired limits. In a few modern structures the wooden cushion has been abandoned and a metal shutting surface adopted. As already stated, the upper and lower horizontal frames may differ Par. 220. slightly from the others in scantling by being designed to resist the hori- zontal strains due to the weight of the leaf. In addition to this the upper member may be used as a foot walk, or may have to support a bridge. In either case it should have a thicker web plate than the other frames near * the top of the leaf. The lower frame may form the bottom of an air cham- ber, in which case its web will have to be proportioned to resist the local water pressure and may require stiffening. In most cases of metal leaves the shutting surface against the miter Par. 221. sill is made water tight by the use of a wooden cushion applied to the leaf near the lowest frame. The position of this cushion will depend upon the necessity of reducing the upward pressure, as shown in Par. 171. 88 MITEBING LOCK GATES. Par. 22a. Accident al blowa. Piir. 223. Otlier types. Par. 224. Portes valets. The stresses due to accidental blows, or wave shocks, are manifestly impossible of analysis, nor can the extreme case be provided against. It is, of course, not practicable to build a leaf strong enough to stand the blow which would be delivered by the bow of a boat at high speed. When the sheathing of the leaf has been made thick enough to resist punching by any ordinary blow, and the members have been solidly and carefully assembled, little remains to be done. The best course is to avoid accident by enforcing care on the part of the lock tenders and vessel men. It may be stated that a well assembled gate leaf will sometimes develop a strength against shock which is simply surprising. (Vide Par. 237.) As has been stated in Par. 1, there are, in addition to the mitering type, the rolling or caisson gate and the gate turning about a horizontal axis. The former of these has been successfully applied at the Davis Island Dam and the latter in various locks, particularly as the upper gate or the guard gate. The stresses may be readily determined by applying the proper pi-inciples of loading and the ordinary theory of transverse stress. The rolling caisson requires a recess perpendicular in direction to the side wall of the lock, and equal in length to the caisson itself. It leaves practically the whole length of the lock chamber available for vessels. While gener- ally costing more than a set of mitering gates, it may be advisable in cer- tain cases where the span of the lock is great and the depth small, and where, in consequence, it would be difficult to swing the ordinary gate leaf from the quoin. Another form of gate has been suggested, viz, one mitering down- stream and carrying the load wholly by tension. This was discussed by Mr. E. S. Wheeler, C. E., with a view to its application to the new lock at St. Mary's Falls Canal. The gate itself was found in the design to be lighter than any other known form ; but the fastening in the hollow quoin VERTICAL STRAINS. 89 had to be very strong and hard to execute. In the future the constructive difficulties may be overcome and the principle successfully employed. So far as the writer knows this has never yet been done. It is not uncommon in harbor locks to provide what are called by the French fortes valets to hold in place such of the main gates as are exposed to the action of waves against their downstream surfaces. These additional gates are light open-built structures opening into the same recesses as the main gates, and behind the latter. They turn about axes placed at that part of the recess where the toe posts of the main leaves rest when open. When in use they abut against seats prepared for them on the upstream face of the main gates, as shown in Fig. 22. They hold the gates shut and prevent waves on the downstream side from opening them when the level on the two sides is nearly the same, and thus allowing them to slam together with violence under the head on the upstream side when the wave departs. 2623— No. 26 12 CHAPTER VIII. MANOEUVRING AND CHOICE OF TYPE. Par. 225. The means used to maneuver the leaves and valves of a lock may be steam power, hydraulic power, or hand power. The first is generally used in connection with the second, steam pumps forcing water into an Arm- strong accumulator, from which it is carried by pipes to the gate and valve engines, the latter being hydraulic cylinders, one stroke of which opens or closes the movable member.* Sometimes the pumps are driven by water- wheels or turbines, instead of by steam. Par. 226. To move the gates, one engine is provided for each leaf. Each engine P a?ata aulic ap consists usually of one double-acting cylinder, as shown in Figs. 23a and 23b, or of two single acting cylinders. The power is applied to the leaf directly through the plunger of the ram, or indirectly by chains or wire cables attached near the toe post. The best point in the height of the leaf to apply the force is about half way between the bottom and the usual working level of the water; but for convenience it is sometimes taken else- where. The engines are generally placed in chambers or shallow wells in the top of the lock wall; when the indirect method is used, a system of pul- leys is provided to lead the cables in the desired direction. Two arrange- ments have been frequently employed; in the first, Fig. 23a, each engine is attached to both leaves, a stroke in one direction closing one leaf, while the reversed stroke opens the other. Thus, the cylinder shown in the figure has just completed a stroke which closes the leaf X, while the engine on the other lock wall has closed the leaf Y. The reversed stroke of the cylinder shown will open the leaf Y, while at the same time it will slack off the cable r, enabling the other engine to open the leaf X. Since the engines are near the top of the wall and the power is applied to the leaf some distance down, it is necessary to lead the cables through vertical wells ir and w, bringing them out of the wall at the proper height by the pulleys b. When the power is suddenly applied to the leaf, structural stresses may be generated in the framework. These may be reduced to an inconsiderable amount by care iu manoeuvring. 90 MANCEUVEING AND CHOICE OF TYPE. 91 To avoid the use of the wells in the masonry the second method was Par. 227. devised, and is sketched in Fig. 236. Here each engine is attached to one leaf only. The cables are led to the gates by pulleys near the top of the wall, and are then carried to the point of application of the power by pul- leys on the leaf itself. The end of the cable is made fast to the lock wall on one side and to the floor on the other. The pulley at the point where the cable leaves the gate is articulated, having both horizontal and vertical rotation. The first part of the cable from the wall to the point b, Fig. 23b, is horizontal. At b it becomes vertical until it reaches the proper height. When it does so it leaves the leaf by the articulated pulley and goes to its fixed point in the masonry One stroke of the engine opens the leaf. The reverse stroke closes the same leaf. This method was applied to the gates of the Bassin Bellot, the engines there having each two single-acting cyl- inders instead of one double-acting one, as shown in the sketch. 92 Par. 228. Hand power METERING LOCK GATES. The direct application of the power has been infrequently employed. It will be described in Chapter IX as used in the Barry dock, in Wales, where it has given great satisfaction. When hand power is used it may be applied by means of the well- known horizontal balance beam, by cables and capstans, or even by a rack pivoted on the leaf and engaging a pinion fixed to the top of the lock wall. Instead of the rack, a toothed arc has been used, firmly fast- ened to the leaf, and having its center on the axis of rotation. When hydraulic apparatus is used, means should always be provided for working the gates by hand in case of failure of the machinery. Par. 229. Drawings of the hydraulic apparatus used in working the gates, at St. Mary's Falls Canal, will be found in the book of detailed drawings of that work published by the United States Engineer Department. The machinery is of the type sketched in Fig. 2* a, and cost $59,000. A descrip- tion, with clear drawings, of the hydraulic apparatus used at the Bassin MANOEUVRING AND CHOICE OF TYPE. 93 Bellot will be found in the Annales des Ponts et Chaussees for 1889. It is much more elaborate than that on the older American work and cost about $92,000. The water is admitted into and discharged from the lock by valves. Par. 230. These are usually placed in the gates in small structures, and in culverts in large ones. The culverts may either be in the walls or under the floor. The latter method was tried by Gren. Weitzel in the lock of 1881 at St. Mary's Falls Canal, and has given eminently satisfactory results in service. v When the valves are placed in the gates they are usually worked by hand from the top of the leaf. The openings are at as low a level as possible to get the greatest head of water. The valves are opened and closed by means of a vertical rod extending to the top of the leaf and terminating in a rack which engages in a pinion attached to the footbridge and turned by a lever or crank. The apparatus is too simple to require extended descrip- tion. V alves Closing culverts in the masonry are usually worked by hydraulic cylinders fixed near them. The cylinders draw their power from the gen- eral accumulator, and each works one valve, opening it by one stroke and closing it by reversal. The French favor sliding valves or gridiron valves. In this country balanced valves are much used. Cylindrical valves have been frequently applied in recent structures. It is well to provide great strength in the valve, valve seat or frame, and the engine, as the parts can not be inspected nor repaired without interruption of traffic. When large balanced or turning valves are used the trunnions should be forged, if pos- sible. Experience at St. Mary's Falls Canal has shown the danger of trusting to cast metal in this important part. There are other means of applying the power both to gates and valves. Par. aai. The writer has tried to indicate the methods most commonly used, and must leave the others unnoticed. In the previous chapters the construction of recognized forms of miter- Par. 23a. ing gates has been briefly discussed. The selection of the type for any Ch01060ft yp e - particular service now requires remark. The questions for settlement are — First, what material to use. Second, in what form to dispose it. The materials which are or have been used for gate construction are Par. 233. cast iron, wrought iron, mild steel and timber. Of these we may drop cast iron at once. Large leaves, as those at Montrose and Sevastopol,* have had their entire framework built of it, and in more modern structures the quoin posts have often been so constructed, but the present facilities for * Built 1843 and 1846. Materials. 94 MITEKLNG LOCK GATES. working rolled metal have to a large extent taken away from cast iron the only advantage it ever possessed, viz, economy in complicated shapes, while its disadvantages of weight and untrustworthiness remain as salient as ever. We may safely say that no engineer will now design a complete leaf of this material, and that even in the quoin post its use will in the future be restricted to the seat for the gudgeon and the footstep. Structural iron and steel may be considered together, as the present prices of the materials in this country are practically the same. The work- manship of the steel leaf will perhaps be the more expensive, but the in- creased allowable fiber stress should about balance that. There is no expe- rience as to the relative durability of the two in gate construction. We may assume them as the same. But few leaves have yet been built of steel, and for guidance we must have recourse to other structures. Reasoning from the experience in shipbuilding, it would appear that steel is to be pre- ferred to wrought iron. In comparison with timber they may be consid- ered together. Par. 234. The first cost of a rolled metal gate of small size is materially greater origmai cost. ^ ian t na t £ a timber one, probably 50 to 75 per cent more in most places. As the leaf grows in size the difference diminishes until, when the greatest dimension is from 35 to 40 feet, the cost is approximately the same, while for larger structures the advantage is with the metal. The exact point at which the first cost of the two is the same will depend, of course, upon the local facilities for obtaining and working the materials. At Dunkerque, France, gates 27 feet high and 38 feet long were found to cost practically the same amount whether of timber or iron, while at Havre one leaf of the metal gate, PI. 2, built in 1886, cost 155,000 francs, including the cost of gal- vanizing the metal and of tearing down and rebuilding a part of the lock wall. One of the leaves of the wooden gates which these replaced (and which were built in 1861-62) cost 201,000 francs, including its proportion of certain incidental expenses. For leaves of this great size advantage in first cost is seen to lie with the metal. Par. 235. Experience has shown that a timber leaf may be expected to last from fifteen to twenty-five years, if well constructed and well cared for. During this time it will require a certain amount of repair and an annual examina- tion, with possible repainting or tarring. The durability of a good metal gate can not be accurately stated. The iron gates of Limerick floating dock, built in 1852, were replaced by new steel ones about thirty-five years later, chiefly on account of the failure of the air chamber. The iron gates built at Bremerhaven and Geestemiinde in 1850, 1862, and 1872 are Duration. MANOEUVRING AND CHOICE OF TYPE. 95 still* in service and in excellent condition. In 1866-67 two pairs of gates were built at Boulogne, the more exposed pair of iron, the inner pair of wood. The iron ones were found easy to keep in order, and at the end of twenty years' service contrasted favorably with the wooden ones, which were in very bad shape. While, therefore, the data are insufficient to de- termine accurately the probable life of the iron gate, it may be safely reck- oned as about double that of the wooden one. Indeed, with proper original construction and careful annual examination and repainting when neces- sary, it would seem difficult to set a limit to the endurance.f The metal leaf generally costs less to maintain than does the wooden one. If we assume the life of the wooden leaf at twenty years and that of the iron one at forty years and if we allow an annual loss of 6 per cent simple interest on the cost when first built and when renewed, we shall find that the iron leaf costing at the outset 1.6 times as much as the wooden one is, in the end, slightly the better investment of the two. / - The weight of the structure enters the problem as affecting the anchor- Par. 236. age and the rapidity of maneuver. In large leaves the metal ones may be eig made lighter, but the difference is not so great as would be expected, and in certain individual cases has been found to be in favor of the timber struc- ture. For example, at Dunkerque, it was found that a wooden leaf with 877 square feet of exposed surface weighed 50 tons, while an iron one with 984 square feet weighed 49 tons. On the other hand, the wooden leaf at Havre weighed 149 tons, while the larger iron one built to replace it weighed 175 tons, though costing much less than its predecessor.}: Estimates will generally show but little difference in weight for the two structures ; there- fore, in so far as it affects the anchorage, which should be strong enough to carry the leaf in air, the weight gives to neither material a marked advan- tage. The difficulty in maneuvering and the strain on the fastenings which are incident to a great weight may be avoided in the metal leaf by the use of an air chamber. This device would much increase the cost if applied to a wooden leaf. In so far, therefore, as the weight affects the working of the leaf, the metal structure has the advantage of the wooden one, though * In the spring of 1892. t As additional data, we have the following : Victoria dock gates : built in 1857 ; arched, iron ; still in daily use; have been extensively repaired. Victoria dock extension gates: built in 1878; single- sheathed, arched, iron; still in use. South West India dock gates : built in 1866: pointed, arch ; iron; in daily use. iThe area of the wooden leaf was 1,820 square feet. That of the iron leaf is 1,966. 9(3 MITERING LOCK GATES. Par. 237. Solidity. Par. 338. Conclusions. Par. 239 this advantage is often foregone by engineers who fear difficulty in keeping the air chamber water-tight. In the matter of resistance to shocks the advantage is supposed to rest with the timber leaf. It will certainly develop a marvelous elasticity some- times, as when in 1886 a heavy steam barge ran into the downstream face of the lower gates at St. Mary's Falls Canal and forced them open against a head of 18 inches of water in the lock. Although apparently severely strained, the gates were found to work perfectly after tightening up a few turnbuckles, and are still in service, five years later. Metal leaves have also been known to resist well a sudden shock. The great iron gates of the Transatlantic Dock were tremendously strained soon after being put in place, being opened by waves from the outside while there was still some head in the inner harbor, and kept slamming open and shut with great violence until the upper gudgeon of one leaf was broken. At the next high water the leaf fell over into the lock pit, but sustained no injuries of consequence. A- few rivets were started, but the seam was readily tightened. In certain localities facilities for repairing even such slight injuries to metal structures might not be available, while a wooden leaf may always be patched up unless very badly damaged. From the foregoing considerations we may say that, if the metal leaf does not cost originally more than about half as much again as the wooden one, it will be more economical. If economical and if the conditions are such as to make its repair easy in case of ordinary injuries, such as starting a seam or punching a hole in the sheathing, then it is to be preferred. The point at which the first costs will bear the above ratio must be decided by estimate, due regard being had to the local facilities for obtaining and work- ing the two materials. Taking into consideration the growing scarcity of timber of large dimensions and the spread throughout the country of iron ship-building establishments suitable to perform the work of gate construc- tion, it seems probable that leaves of more than 20 feet in greatest dimension will in the future be more economically constructed in metal. French engi- neers have used metal for much smaller ones; on the other hand, the English are now constructing timber gates 45 feet high and closing an opening of 80 feet. These are on the Manchester Canal, are built of green heart, and are said to weigh the enormous amount of 260 tons per leaf, vide "Special Consular Reports of Canals and Irrigation in Foreign Countries." If timber be used, white oak is the best for fresh water, and next to that, probably yellow pine or some wood resembling it. In salt water, where the teredo works, greenheart is said to give better results than any other. MANOEUVRING AND CHOICE OF TYPE. 97 In harbor locks it has been the practice in France to galvanize the Par. 240. plates and angles of metal leaves to avoid electrical action. This process increases the cost, but probably no more than the means necessary in sim- ilar localities to increase the durability of a timber structure. In this country, where fresh-water locks alone demand attention at present, no such precaution has been found necessary. Having chosen the material, it remains to determine in what form to Par - ***• dispose of it. The points for consideration are — Whether to make the leaf arched, straight-backed, or bowstring; Whether to use an air chamber; Whether to use a roller; Whether to use the vertically framed type of Par. 154. No engineer can say, ex cathedra, that any one type is always the best. **»»■. 24a. In one locality and for one kind of work a certain form will be found suit- able, while it may not be for another place or another duty. Thus, for a harbor gate exposed to wave shocks and manoeuvred but four times a day, a very heavy structure would have great advantages and small drawbacks, while, in the still waters of a busy canal, lightness and ease of manipulation would be worth purchasing at the price of increased original cost. The best that can be done is to enumerate and roughly reason upon certain of the properties of the different forms, leaving the final decision to be made with due reference to local circumstances. Taking, first, metal leaves, we note that the arched leaf will cost the Par - 243> most per pound on account of the curved work. That the amount of this increased cost depends upon local facilities for working metal and is modi- fied by the fact that nearly all large girder leaves require a considerable amount of curved work, particularly near the posts. That the bowstring type exacts nearly as much curved work as the arched type. That in practice the arched leaf is lighter than the straight leaf about as 60 to 100.* That the arched leaf requires a deep gate recess. That the girder is better suited than the arch to resist shocks or the moving loads of waves. That the use of an air chamber diminishes the maneuvering weight and the habitual strain on the fastenings, but increases the original cost, increases the weight in air, and makes examination and repair more difficult. That the use of a roller relieves the collar to an uncertain extent, increases the expense, and increases the time required to work the leaf. That the vertically framed leaf is heavier than the horizontally framed one, unless the height is considerably less than the length ; f at the same time it is easy of construction and repair. * Theoretically the arched leaf weighs less than one-half as much as the straight one. t The two leaves will be equal in weight when the height is about two-thirds of the length. 2623— No. 26 13 Par. !»45. 98 MITERING LOCK GATES. Par. 844. With respect to the form, it is plain that, if the material in the leaf were only that theoretically required to resist the stresses, the arched form would be cheaper than the girder form so soon as the saving of 40 per cent of material should balance the extra cost of the curved work. When there is a large amount of the latter to be done it can be let at a relatively less mcreased cost than can a small amount. Roughly speaking, it is probable that a 60-foot span can be closed just as cheaply by an arched as by a girder leaf of metal. For larger spans the arch will probably have the advantage ; for smaller ones, probably straight-backed or broken-backed girders will be best. The bowstring type combines the extra cost of the curved work with the extra weight of the girder. There seems to be no economic reason for employing it at all. It finds application, however, in the frequent cases where metal leaves are built to replace worn-out wooden ones, and where, in consequence, the shape of the leaf is already more or less fixed by the existing masonry. With respect to the use of a double skin there is a difference of opin- ion and of practice. Small leaves, as might be expected, are almost always made with a single skin. When the leaves become so heavy that the con- stant strain on the fastenings is too large, an air chamber is necessary. The soon; others say, not within practicable sizes of leaves. The air chamber question is, just when does that happen 1 .Some engineers say, very would undoubtedly be more frequently used were it not for the fear of difficulty in keeping it intact. This difficulty has been found to exist in some cases, particularly in England; and on the other hand many leaves with air chambers have been found very easy of maintenance and manipu- lation. With the present advanced knowledge of metal work there ought to be no trouble in building a chamber so tight that an occasional pumping will keep it dry. The interior examination is more difficult and the original cost, and weight somewhat greater than in the single-sheathed leaf, but the manoeuvring weight is reduced and the working made easy. The ques- tion of the relative weight to be given to these advantages and defects must be decided by the designer in individual cases. Other things being equal, the use of the air chamber would seem judicious for metal leaves weighing more than 50 tons when the full benefit of the flotation can be obtained; vide Par. 179. An objection has been raised against the arched leaves to which no reference has yet been made, namely, that from their form they are exposed to damage from vessels striking them near the quoin or miter posts while the gates are open and in their recesses. The writer believes this to have MANCEUVEING AND CHOICE OF TYPE. 99 no foundation in practice. All leaves are liable to be struck, and should have suitable fenders on the downstream side, but the form of the arched gates does not render them more liable to injury than the straight leaves. The question of the roller has already been alluded to, Par. 187 et seq. In extreme instances it may do more good than harm. Ordinarily the reverse is the case. The vertically-framed type has some undeniably great merits. It is Par. 246. easy to build and less inconvenient to examine and repaint internally than framed leaves. y ' any other double-skinned form. When its increased weight is not objec- tionable, or when from the form of the leaf it becomes nearly as light as the horizontally-framed type, it is to be recommended. It will probably grow in favor as it becomes more widely known. As already stated, it has as yet always been constructed in the form of a girder. There seems no reason why it should not be built as an arch. In the case of wooden leaves the conditions are somewhat different. Par. 247. Ordinarily, it will not be found advantageous to use timber for leaves above a certain size, say 20-25 feet in greatest dimensions. Should it be neces- sary, the very largest sizes, say from 40 to 55 feet in greatest dimension, will probably be most cheaply executed in the form of arches with straight tie beams, PI. in, or voussoir arches, PL v. The bowstring girder will replace the arch with very little additional weight. For smaller openings the bowstring girder, simple or trussed, or the straight-backed frame will be better. Ordinarily when the leaf is too large to be built of straight frames metal should be used. Some leaves have been built of both materials. Metal has been used Par, 248. for the frames and timber for the sheathing, and vice versa, and weak tim- ieaies mp031te ber frames have been strengthened by iron. Except in some combination like the trussed bowstring girder, where each material takes the stress to which it is best suited, these composite forms are but little used. Before dismissing the subject, it should be stated that the weight of the Par. 249. leaf is not altogether determined by the amount of material necessary to resist the water pressure. About 60 to 75 per cent of the contents of the leaf is so employed. The remainder is necessary to keep this directly use- ful part in place. The skill of the designer has great room to show itself in saving as much as possible from this extra material without lessening the structural solidity of the leaf. Engineers working with widely different models will frequently arrive at about the same result as to economy. We might almost say that the details and joints have as much influence on the value of the design as has the type chosen. CHAPTER IX. EXAMPLES. Par. 25©. I n the plates will be found a few examples of gates constructed in France, England, and the United States. The ones chosen are intended to illustrate the different types of leaves, and have been taken principally from foreign practice, as the results of our experience in this country are usually more readily accessible. The dimensions have been reduced to feet and inches and the weights to tons of 2,000 pounds each. IRON GATES OF THE HARBOR LOCK, AT BOULOGNE, FRANCE. Par. 251. (Plate and description adapted from M. Debauve's Navigation Fluviale Boulogne, pi.,. e t Maritime.) The gates were built in 1866, and are of wrought-iron. The frame- work- consists of — Two vertical plates forming the quoin and miter posts and armed with green-heart cushions ; Eleven horizontal frames; Three intermediate vertical frames. The upstream sheathing is curved, the downstream straight. The space between horizontals is 37£", except between the first and second, where it is 43$", and between the two lowest, where it is 35.4". The water has free access to the upper part of the leaf; the lower part, below the eighth horizontal, counting from the bottom, is an air chamber kept dry by pumps and entered through manholes. Each horizontal consists of a web plate 0.39" thick; four angle bars, 3|" x 3J" x 0.41" ; two flange plates, 6.7" x 0.374", riveted to the angles on the inside of the sheathing, and two cover plates of the same dimensions on the outside of the sheathing. The upper and lower horizontal are mod- ified as their position requires; the lower one is stiffened against the local pressure by angle bars and gusset plates. The plates of the quoin and miter posts are 0.63" thick. The quoin post is stiffened at the bottom, where it rests on the pivot by a triangular vertical gusset plate, the plane of which is parallel to the downstream 100 EXAMPLES. 101 sheathing. This plate bears against the web of the lowest horizontal, and is fastened to this as well as to the quoin-post plate by angle bars. It forms a bracket extending through the two lowest compartments, and is shown in horizontal section in Fig. 5, PL i. The construction of the verticals is sufficiently explained by the plate. The sheathing varies from 0.63" thick at the bottom to 0.315" at the top. It is without intercostal framing, except in the lowest compartment. It is applied in horizontal strakes with single-riveted butt joints. The roller is adjustable and has a long axis. The pivot is of steel, 7.97" in diameter, projecting the same distance above the lock floor. The upper gudgeon is 11.9" in diameter, and is held by a forged collar. The gates are manoeuvred by a capstan with hand power. The clear span of the lock is 68.9 feet and the angle a is 22°. Each leaf weighs 77 tons in air and cost about 75,00') francs, including the portes valets and the maneuvering apparatus. Wooden gates constructed at the same time and of the same size cost per leaf about 6,000 francs less, with an increase in weight of 17 tons. In 1888 the iron gates were still in excellent condition. The leaf is 38' 9" long and 32' 2" high, exclusive of the footbridge. IRON GATES OF TRANSATLANTIC DOCK AT HAVRE. (Plate and description adapted from article by MM. Widmer and Des- Par. 252. prez in the Annales des Ponts et Chaussees for 1887.) hsvto.pi.u. The gates are of the vertically framed type and made of wrought iron, galvanized. The upper and lower frames are girders, the backs being broken lines of three segments each, connected by short curves. The framework of each leaf consists of a quadrilateral composed of the upper frame, the lower frame, the hollow quoin-post, the hollow miter- post, and nine intermediate verticals, equally spaced between quoin and miter posts; Two horizontal bulkheads, dividing the leaf into chambers; Intercostal frames to stiffen the sheathing. The leaf is provided with oak cushions to form contact with the oppo site leaf, the sill, and the masonry. It has also horizontal oak fenders ol the downstream face for protection against blows. The arrangement of the air and water chambers is shown in the plate. Access to them is obtained through the quoin and miter posts,* and circu- * An arrangement found faulty and abandoned in the gates of the Bassin Bellot, constructed two years later. 102 METERING LOOK GATES. lation inside is effected through manholes in the verticals. The roof of the air chamber is below the lowest manoeuvring level, and the strain on the fastenings is therefore nearly constant. The water in the upper part of the leaf may be retained or discharged through valves at low water. The air chamber is kept dry by a movable pump, and the water ballast may be discharged by a pulsometer. The upper frame is of the form and dimensions shown in Figs. 3 and 4, PL II. The web plate is 0.59" thick near the middle and strongly reenforced at the ends to resist the shear. The four angle bars are 5.9" x 5.9" x 0.59". The upstream flange consists of six plates of varying lengths, so arranged that the metal in the flange is proportioned to the strain. Each of these plates is 39.4" wide and 0.47" thick. The flange, being so wide, is stayed by vertical stiffeners to prevent wrinkling at the edge. The downstream flange is a single plate 15.7" wide and 0.39" thick, enlarging at the ends to a width of 39.4" and a thickness of 0.99". The upper frame is armed at the ends with cast-steel shoes to receive the thrust of the other leaf and to transmit it to the masonry. These shoes are omitted in Fig. 4 of the plate. The upper frame is calculated to carry the load transmitted by the verticals, vide Pai\ 154. This load is taken as one-third the total water pressure, the support of the lower pool being neglected. The vertical frames have a web plate 59" wide and 0.39" thick; four angle bars, 3.5" x 3.5" x 0.47"; and two flanges, each consisting of two plates 0.47" thick. One of these plates is 13.4" wide and extends the whole length of the vertical; the other is 24.8' long, and occupies that part of the frame where the bending moment is the greatest. The second plate is 8.4" wide. The first plate, being wider, projects beyond the second on each side; to the inside of this projection the sheathing is riveted in vertical strakes. Each vertical is calculated to bear the load of water on the strip of sheath- ing extending half way to the adjacent frames. The intercostals are "]_ bars, built up of two angles 2 4" x 2.4" x 0.24", and one plate 8" x 0.20". They are placed horizontally, fastened at their ends to the verticals by short pieces of angle iron. They are spaced at varying intervals, being 16" between centers at the bottom of the leaf, and are calculated to carry the load resting on the strip of sheathing supported by them, being regarded as beams supported at the ends. The sheathing is 0.32" thick at, the top, 0.39" at the middle, and 0.47" at the bottom. It is calculated to carry its load as a beam fixed on its sup- port at the intercostals. EXAMPLES. 103 The upper gudgeon was made originally of cast steel 11.8" in diameter. After the accident alluded to in Par. 237, the forms of the gudgeon and pivot shown in the plate were substituted for the original ones. The cylin- drical parts of the new design are of forged iron, assembled by shrinkage with the shoe and footstep. The pivot projects downward from the leaf, instead of upward from the lock floor. The lowest frame has no particular transverse stress, being supported by the miter sill. It is made strong enough to support the local pressure and not to crush either the metal or the sill when the load comes on the verticals. The weight of each leaf is 175 tons, and the cost 155,000 francs. The greatest stress allowed on the iron is 10,000 pounds per square inch. The clear opening of the lock is 1 00 feet, and the dimensions of the leaf 56' 7" x 34' 9", exclusive of the cross walk. The angle a is 19° 53.' No rollers are used. These gates were built to take the place of the wooden ones shown in PI. Ill, after the latter had worn out in service. Two years after the construction of the gates just described, a pair very Par. 253. similar in general features were built for the new Bassin Bellot, at Havre. No S piate. e ' The length of each leaf is 53' 4", and the height exclusive of cross walk is 35' 9". The leaves are of the vertically framed type, and differ from the new ones of the Transatlantic Docks, principally in having a simple verti- cal diaphragm for a quoin post, this diaphragm being armed at two points between the head and foot, with castings to center it in the hollow quoin. The air chamber is kept dry by the use of a double system of pipes. Through one set compressed air is admitted, forcing the leakage out through the other set. Entrance to the air chamber is effected through water-tight chimneys extending from the bulkhead to the top of the leaf. This method was substituted for the entrance through the quoin and miter posts, on account of the experience gained in the service of the Transatlantic Dock gates, where it has been found difficult to keep the posts from leaking. No rollers are used. Each leaf weighs 171 tons and cost about 130,000 francs. The ma- terial is wrought iron. Hydraulic power is supplied to work the gates. The clear opening of the entrance is 98J feet. A description of the work will be found in the Annales des Ponts et Chausse'es for 1889. OLD WOODEN GATE OF TRANSATLANTIC DOCK AT HAVRE. (Description and plate adapted from Debauve Navigation Fluviale et Par. 254. -. r -,• \ Havre. PI. n Maritime.) 104 MITERING LOCE GATES These gates belonged to the arched type with straight tie beam. When closed, the upstream surfaces formed a continuous circular arc from quoin to quoin. Each leaf was 56' 7" long and 32'- 2" high. The depth from upstream to downstream face was 6' 3" at the middle. The framework of the leaf consisted of a quoin and miter post with several horizontal frames, and intermediate verticals. A double brace extended from the top of the quoin to the bottom of the miter post. The weight was carried by the pivot and two adjustable rollers. Each horizontal frame was built up of six pieces of red German pine; of these, two were straight and formed the chord bar, and four were steamed and bent to form the arch. The lower 18 horizontals were superposed, making that part of the leaf a solid mass. The remaining horizontals were consolidated in two groups, the intervals between groups being preserved by galvanized iron bracing. The quoin and miter posts were built up of oak timbers. The inter- mediate verticals passed through the intervals between the arch and chord bars of the horizontals. The pivot and socket were of bronze, the pivot projecting downward from the leaf. The gates were worked by hand through chains and capstans. The manoeuvring was slow and took a large number of men. Each leaf cost about 201,000 francs and weighed 149 tons. The gates were built in 1861-62, and were replaced by those shown in PL ii in 1886-87. The indications of wearing out were a considerable deformation by drooping at the nose, decay of the quoin post, leakage, and yielding of the topmost group of horizontals, indicating possibly that the vertical framing was too strong for the arrangement of horizontals adopted. Par. 255. IRON GATES OF THE TYNE DOCKS AT SOUTH SHIELDS, ENGLAND. (Description and plate adapted from article of T. E. Harrison, C. E. pi.Tv." " s " Proceedings Institute of Civil Engineers for 1859, Vol. XV11.) These are among the earliest examples of wrought-iron gates. They are of the arched type and close an opening of 80 feet in the clear ; the angle a is 30°. Each leaf is 27 feet high at the miter post, and its chord is 46 feet 4|" long. There are ten horizontal and two intermediate vertical frames. The bottom of the leaf is curved in elevation as well as in plan, the pivot being set 3 feet 6" above the lowest part of the floor of the lock. An adjustable roller with long axis is used. The gates were built about 1858 and may be worked by hand or hydraulic power. The original ones were renewed in 1873. The short life was partially attributed to the dis- charge of acids from neighboring chemical works. EXAMPLES. 105 IRON GATES OF THE BARRY DOCK IN WALES, ON THE NORTH SHORE OF THE BRISTOL CHANNEL. (Description and plate adapted from article by John Robinson, C. E. Par • a56 - Proceedings Institute of Civil Engineers, Vol. CI, 1890.) Plv - These gates are of wrought iron, were built about 1889, and close a clear opening of 80 feet, with a value of a of 26° 30'. The sill is curved in elevation, as in the Tyne Docks, the pivot being at a higher level than the bottom of the miter post. The extreme depth from the latter part of the leaf to the ordinary level of spring-tide high water is 40 feet, nearly. The quoin post, imter post, and sill have green-heart cushions. Each leaf is divided into fifteen water-tight compartments and contains twelve horizontal frames, five of which are water-tight. These, with the verticals, are shown in Fig. 4, PI. v, by heavy lines. Both upstream and downstream sheathing are curved in plan ; the latter slightly, the former sharply. The depth between skins is 2 feet at the posts and 8 feet at the middle. A shaft, or chimney, communicates with the air chamber. The sheathing varies in thickness, as shown in Fig. 5 of the plate. An adjustable roller is provided to take part of the weight. Each leaf weighs about 254 tons, including the cast iron and timber which enter its structure. The buoyancy of the air chamber is nearly sufficient to overcome this weight when the gates are worked. The manoeuvring apparatus is especially noteworthy. It consists of a direct-acting hydraulic ram, the cylinder of which is mounted on vertical trunnions, on a frame which pivots on horizontal trunnions in bearings fixed to the masonry, thus permitting oscillation in both directions. The cylinder for the outer gates is of cast steel, with an interior diameter of 2 feet 5§ inches. The plunger is of cast iron 1 foot 9 inches in diameter, with a stroke of 25 feet 9 inches. It is made fast to the upstream face of the leaf near the top. A single stroke of the ram opens or closes the leaf, which is held firmly during the operation, and afterwards. The working of the appa- ratus has given great satisfaction and has attracted much favorable comment. It takes one minute to open or close the gates. Fig. 7 of the plate will give an idea of the mechanism. Valves are provided through the gates to empty the large interior basin when the latter is used as a lock. Ordinarily the gates are used only at high tide. 2623— No. 26 14 106 METERING LOCK GATES. TIMBER GATES OF THE AVONMOUTH DOCK AT BRISTOL, ENGLAND. Par. 25*. (Description and plate adapted from article by J. F. Bateman, C. E., in Do A ck.° pT°v uth Proceedings Institute of Civil Engineers, Vol. LV, for 1878-79.) These gates are of the arched type and close a clear opening of 70 feet, with a value of a of about 25°. The quoin and miter posts are of oak in the inner and of greenheart in the outer gates. The horizontals and intermediate verticals are of pitch pine and Memel fir. For the outer gates a system of construction was adopted which is shown in PI. v, Figs. 1-3. The horizontals are made in segments, each consisting of three pieces, the outer one only being dressed to the curve of the leaf. These pieces are framed at their ends into continuous vertical posts, the structure being united compactly by straps, bolts, and horizontal waling pieces of less curvature on the downstream face. The leaf is thus built up of sections or voussoirs, each about one-fourth of its total length. No long timbers are required except for the verticals. The gates are 45 feet high. When they are closed the upstream faces form a continuous cylindrical surface, with a radius of 50 feet, extending from one hollow quoin to the other. Each leaf weighs 115 tons and has two rollers; the one adjustable, the other fixed. The latter was not contemplated in the original design, but was added under the toe post at the time of construction, to assist in balancing the leaf. The gates were built about 1877. In 1892 they were still in service and in good con- dition, having cost very little for repair. TIMBER GATES OF THE LOCK OF 1881, ST. MARY'S FALLS CANAL, MICHIGAN. Par. 25§. (Description from records of United States Engineer's office at Detroit, oaniu! pi y vi Falls Mich. Plate adapted from detailed drawing of work published by the Engineer Department, U. S. Army.) These gates close a clear opening of 60 feet, with an average lift of 18 feet and a depth in the locks of about 17 feet over the miter sill at the lower water level. They are of the trussed bowstring type (Par. 112). The plate shows the south leaf of the lower gates. Each leaf of these consists of a quoin post, a miter post, three intermediate vertical frames, and seventeen horizontal frames, spaced and proportioned nearly in accord- ance with the pressure due to the depth. The sheathing is three-inch Nor- way pine plank spiked to the horizontals. The timber of the framing is white oak. The value of a is 26£°. Each horizontal frame consists of an upper chord bent into a circular arc, a straight chord bar, and iron truss rods. The latter are fastened to EXAMPLES. 107 the quoin and miter posts in the intervals between the horizontals, but form part of the latter in reality. The upper or first frame is untrussed; the second and the lowest frame have each but one set of truss rods; the remaining ones have two sets each. For convenience in shaping it, the curved chord consists of three pieces, each extending the full length of the leaf. When closed the backs of the leaves form a pointed arch instead of a continuous one, as in the case of the old wooden gates at Havre. The quoin and miter posts consist of several timbers, each extending the whole height of the leaf. In the plate they are shown as solid instead of built-up posts. The intermediate verticals consist each of two timbers, clamping between them the straight chord bars of the horizontal frames. The assemblage of the different parts is assured by a thorough system of straps and bolts. The bracing against vertical strains is shown in the plate. Each of the long braces from the quoin to the miter post is double, being applied on the upstream side beneath the sheathing as well as on the downstream side. The braces and truss rods are adjustable by means of closed turn- buckles or sleeve nuts. At first many of these burst in the cold weather, water having found its way into them. This trouble was obviated by drilling holes in the middle part of the sleeve. The gates have proved serviceable and are easily maintained. They have successfully resisted shocks, among them at least one which would have annihilated a structure assembled in anything short of the most solid manner. (See Par. 237.) The upper eight frames and two of the lower ones are provided with fender strips which serve to receive the blows and to keep the truss rods from catching against the projecting parts of vessels. The gates are manoeuvred by hydraulic power, auxiliary hand appa- ratus being provided for emergencies. Each leaf cost about $8,000 and weighs 76 tons in air. The fastenings are often called upon to bear this weight, as the lock is pumped dry twice annually for inspection. The lock was opened to traffic in 1881. CHAEENTON LOCK ON ST. MAURICE CANAL, FRANCE. (Plate and description adapted from Debauve, Navigation Fluviale et Par. 259. Maritime, and from de Lagrene - , Navigation interieure.) umiZk. The frames of the leaf are riveted I-girders, fastened to the posts by bent plates. Rolled beams were contemplated, but could not be procured of the desired dimension at the time of the construction in 1865. The 108 MITEKING LOCK GATES. sheathing is 0.157" thick and is applied only on the upstream side. No diagonal braces are used. A vertical T-iron frame is fastened to the downstream face near the middle, and two vertical strips are applied near the posts. The thrust is delivered to the masonry by castings fastened to the quoin post at the top, bottom, and at two intermediate points. Wooden cushions form the contacts at the posts and sill. The leaf is 25' 6" high and 14' 6" long. It weighs 8.8 tons and cost about 6,800 francs. Par. 26©. As additional examples reference is made to the lock gates in use on the Great Kanawha River at Lock No. 7, and to those on the Illinois River at Kampsville Lock. Drawings of both of these structures have been issued by the Engineer Department. A description of the " Iron lock gates for the harbors of the Weser River, Germany," will be found in a pamphlet bearing the above title, and translated by the late Gen. Weitzel, Corps of Engineers. A description of one of the iron lock gates constructed at St. Nazaire, France, will be found in the Scientific American Supplement of March 17, 1883. APPENDIX I. CALCULATION FOR FRAMING. To illustrate the principles contained in Chapters i, n, and v, let it be required to make the preliminary design for the framework of a girder leaf ntended to close an opening of 97 feet between bearings in hollow quoins. Let the depth over the sill in the lower pool be 22.5 feet, and the lift 20 feet. Let the material selected be mild steel, the allowable stresses being 12,000 pounds and 10,000 pounds per square inch in tension and compres- sion, respectively; and suppose the girder type to have been adopted. If the intervals between the frames be taken as 30", the load per linear foot of the frame would be 2 J x 6 (H — K) for the part of the leaf from the bottom to the surface of the lower pool. From the latter level it will be 2 J x 6 (H — y) until the point is reached when (H — y) becomes equal to ( -q~ — q~TT2 ); for the rest of the way the load is 2£ f -5- — -otTz )■ 109 110 MITERIKG LOCK GATES. Table A. 1. 2. 3. 4. Load due to depth. m n s„. Load due to verticals. m n p n . Load on ver- ticals, mn (s„-p„). Max. load on horizontals. H x 62* x 7 ^ 49 945 + 896 945 30" ft X 62i X ft 390 1890 + 1500 1890 50" • 30" m x 6 2 | x n 781 1890 + "°9 1890 50" 45" 30" n x 62^ x ft 1172 1890 + 718 1890 ft x 62^ x W 1563 1890 + 327 1890 ft X 62$ x W 1953 1890 - 63 '953 35" f3 X 62* x W 2344 1890 — 454 2344 ft X 62* x W 2735 1890 - 845 2735 30" ft X 62i x W 3125 1890 — 1235 3125 30" JS x 62^ x W 3125 1890 — '235 3125 5 j x 621 x W 3'25 1890 — 1235 3125 ft X 62* x W 3125 1890 — 1235 3125 ft X 62^ x W 3125 1890 — 1235 3125 ft X 62i x W 3 I2 5 1890 — 1235 3125 ft x 62^ x W 3125 1890 — 1235 3125 30" ft X 62i x W 3125 1890 — 1235 3"25 30" ft x 62^ x W 3>?5 1890 — I2 35 3'25 30" 30" ft x 62i x W 3125 1890 — 1235 3125 3°" p = 8545 From the data I ■-*- — ^jp ) = 12'. 1 Hence for 30" intervals the loads on the frames will be as tabulated in Table A. We may either preserve the uniform spacing and vary the scantling of the frames to suit the loads, or we may vary the spacing so as to throw uniform loads on the frames, which will then be of uniform scantling. Adopting the latter method, we shall find the spacing as given on the right of the table, and the loads very nearly 3,125 pounds per foot of each frame. 48 5 For preliminary calculation, we may take the value of 1 — — cos a 53.V, and the web thickness as iV'. With these values we have from Par. 73, D = 3125 X 53.5 2 ^ 8 X 10000 X 144 X^X A CALCULATION FOE FRAMING. Ill expressed in feet, or say 4.6'. The economic miter angle for this depth will be found from Table III or Tables I and II, according to the nature of the frame. Supposing it of constant flange section, we take Table III, Par. 72, and find for our ratio jy = ~a~s > a — say 25°. The true value of I is therefore 53'. 5. The miter cushions will be so shaped that the surface of contact can not lie more than 2 feet from the downstream surface.* The line of pressure will therefore be confined between the axis of the lower flange and the line 2 feet from the downstream surface. The maximum stress in the upstream flange is compressive, and occurs when the pressure is in its position farthest upstream. For this we have X — 2.6', A' zz 2.0' and from eq. (11) Kzz 321,105 pounds. The maximum tension in the lower flange occurs at the same time, and, from eq. (12) is T — 141,000 pounds. The maximum compression occurs in the lower flange when the line of pressure occupies its extreme downstream position. It is found by making A zz D in eq. (13) and is T k == 179,200 pounds. The compression flange must therefore contain 32.1 square inches and the tension flange 18.0 square inches. The shear on the web is equal to, say, 84,000 pounds near the end. A -re" web 4iV wide will need to be stiffened here to bear the shear. (Vide Appendix III.) A strip of sheathing, say, 14" wide, may be reckoned as acting with the flanges, since we shall have to use angle bars about 6" on each leg, in order to make up the large flange area required. The center of gravity of the combined flange area is at a point 35". 24 from the center of the lower flange. The moment of inertia of the flange area alone about its own center of gravity is 34,890; and about an axis through the line of pressure in its most dangerous upstream position is 41,220, expressed in inches. The unit vertical rigidity must not exceed H 4 -rj- — 0.4 times the unit horizontal rigidity in this part of the leaf; or, in other words, the horizontals are strong enough to stand a vertical system such that each member is as strong as one of the horizontals, i. e., has a moment of inertia about its own axis of 41,220, and in which the verticals are spacedf * The strictly correct value of a: may now be found from Eq. 14 by differentiation. It lies between 25° and 26°. Table III is not rigidly applicable, since the line of pressure in the example can not reach the middle line of the frame. pj ^ 3 t Since the horizontals are 50 inches apart at the point in the leaf where t> — oTST i 8 equal to H-j/. 112 MITERING LOCK GATES. 50" TyT, or say 10 feet apart. Any weaker system will be safe. To find the one which will work at the same fiber stress as the hori- zontal system, we must find the bending moment endured by the unit ver- tical strip. This we may do from the loads in the third column of Table A. Making a computation or a graphical construction based on these loads, we find that the maximum bending moment to which a strip 1 foot wide is subjected is 876,000 inch pounds, and occurs on the ninth horizontal from the bottom. The total vertical bending moment is therefore 876,000 X 53.5, or, say, 46,866,000 inch pounds. This will require a vertical system the moment of inertia of which about its own axis shall be sufficient to resist this bend- ing moment without developing a greater fiber stress- than 10,000 pounds per square inch, and from the usual formula of flexure we have, recollect- ing that the depth of the beam is 55", 10,000 I T = 27-5 X 46,866,000 Neglecting the transverse strength of the web, as we did in the case of the horizontals, I becomes 2 A X 27.5 2 , A being the combined areas of all the compression flanges of the verticals ; and, substituting and reducing, A =z — ^—^- • or, say, 86 square inches. The rigidity of a vertical strip 1 • u -a -n u i u Iv 4686.6 X 27.5 OA1 inch wide will be measured by v — ; or — -.« — => sa >Y> 201. 5o.5 X 12 56.5 X 12 At a point of the leaf 12.1 feet from the top the horizontal rigidity is meas- 41 220 ured by ' — 802. The system which works at the same fiber stress as the horizontals is therefore within the limit found by the test E T I V ,W . 201 ^W iXEflf Z 4 802 " I' which we have found to be 0.4. We may, therefore, use any number of verticals desired, provided that the aggregate of their compresssion or tension flanges does not have a greater area than 86 square inches. Five will be a convenient number to use inter- mediate between the quoin and miter posts. Each flange will then have an area of 17.2 square inches, which will be made up of the angle bars, the strip of sheathing, say 14" wide,* and a cover plate, if necessary. We have thus settled upon the number, size, and spacing of the hori- zontal and vertical frames with sufficient closeness for the preliminary * Depending upon the size of angle bars used. CALCULATION FOE FRAMING. 113 design, and may proceed to the more accurate work with the knowledge thus gained. The framework of a gate thus constructed would weigh, roughly speaking, as follows : Pounds. 16 horizontal frames 211,400 5 vertical frames 38, 500 Quoin and miter posts (estimated) 20, 000 269, 000 If the leaf were built of the arched form with a value of a — q> — 30°, the stress generated in uach frame would be, (eq. 26), K — p p. For a = cp - 30°, p = J-L - 55'.94. sin (p K = 3125 X 55.94, = 174,800 pounds, and by Par. 108 each frame must be constructed to carry four-thirds of this pressure, if the cushion be confined to the middle third of the abutting surface. Each frame must, therefore, have a sectional area of 23.4 square inches. With the same verticals as before, the framework of the arched leaf will weigh approximately Pounda. 16 horizontal arches at 4,568 pounds 73, 088 5 vertical frames 38, 500 Posts 20, 000 131, 588 or about half the weight of the girder framework. The finished leaf with sheathing and all the details will weigh from 50 to 60 per cent of the girder leaf. To compare the framework designed as above with a similar one designed by M. Galliot's method we may find the value of 9 from the ratio of the average horizontal to the average vertical rigidity. Since the rigidity of each horizontal frame is expressed by 41,220, and of each ver- tical frame by 2 X 17.2 X (27.5) 2 = 26133, we have ~ h J±X w =, say, ih Y 1 T H 6.36, and the quantity 0, Par. 29, equal to X .16.36 = 0.066. n 4 53.5X^/ 2 To assist in the calculation, we form the following table : 2623— No. 26 15 114 MITEEING LOOK GATES. 1. 2. 3- 4- 5- 6. / * S 8 <-> 1 X -^ 1 -1- 8. 9- 10. 11. 12. a. x £ 00 K tJJ en O X 12,000 or, say, 12.6. Referring to the handbook of a certain rolling mill, we find that this ratio of y to I is equaled or exceeded in the cases of the following beams and of all larger ones: 7" deck beam, 20 to 23J pounds per foot, y = 3£", I = 42.2 to 46.6 8" deck beam, 20 to 23^ pounds per foot, y = 4", I = 57.3 to 63.5 9" deck beam, 26 to 30 pounds per foot, y = 4£", I = 85.2 to 93.2 7" I beam, 15£ to 20 pounds per linear foot, y = 3£", I = 38.6 to 49.9 8" I beam, 18 to 22 pounds per linear foot, y = 4" , I = 57.8 to 71.9 9" I beam, 21 to 27 pounds per linear foot, y = 4 J", I = 84.3 to 110.6 The 7" deck beam may be dismissed at once, as it weighs practically the same as the 8" and has a less value of - . y Beginning with the largest size of the 8" deck beam, which has a total of inches, area of 7 square inches, we have in eq. (20), since A = - — 3 J square 3X3AX4X15X12 • 3 , , • , * A - - J -» sin a 4- cos a sin a — cos a -=i 2 X 63.5 from which we find by trial a — 14° 10'. Substituting this value and the other known quantities in the expression for the stress due to the bending moment alone, we have v C 2 v s' — ~- — TT^—f = 10,180 pounds per square inch. Hence R — s rr 12,000 — 8 cos 2 a I METAL FRAMES FOR STRAIGHT-BACKED LEAVES. 123 10,180 = 1,820 pounds per square inch, which is the fiber strength avail- able to resist the longitudinal compression in the upstream fibers. The total longitudinal compression - 1 . r -- is 13,800 pounds. The 2 sm a posts being so shaped that the line of thrust can not pass above the middle line, this thrust will act along that line when it produces its most dangerous effect on the upstream fibers, and in that position may be taken as uniformly distributed over the section. The area required to resist it I Q QAA with the available strength, 1,820 pounds per square inch, is ' = 7.58 1,820 square inches, which exceeds the limit to which the beam is rolled. Proceeding in a similar manner with the elements of the smallest size of the 9" deck beam, for which the area is 7.6 square inches, we find from eq. (20) a — 14° 50'. s' = 8,580 pounds per square inch. R — s' = 3,420 pounds per square inch, available to resist a total compression of 13,200 pounds, requiring an area smaller than any to which the beam is rolled. No deck beam will, therefore, exactly satisfy the conditions. The 9" beam may be used, reducing the value of a until in eq. (1 8) S becomes equal to 12,000 pounds; or, retaining a at 14° 50' and letting the beam work at less than 12,000 pounds per square inch; or, changing the frame spacing until p is so increased as to make the beam work at its full strength with the economic value of a. By the first method we find that a may be reduced to 6°, giving a frame weighing 392 pounds and working at 12,000 pounds per square inch. By the second the frame weighs 403 pounds and works at 10,339 pounds per square inch. By the third the frame weighs 403 pounds, works at 12,000 pounds per square inch, and carries a load of p zz 543 pounds per linear foot. If the frame spacing can be so changed as to throw that load on the horizontals this arrangement will be the most economical one of any involving the use of the deck beam. Taking now the I beams, dropping the 7" beam for reasons previously given, we find for the largest size of 8" beam, a — 14° 45', s' zz 9,044 pounds, R — s' — 2,956 pounds per square inch, requiring an area of 4.5 square inches to resist the compression, which is 13,260 pounds. This area is below the lowest limit to which the beam is rolled. Taking a value inter- mediate between the largest and smallest sizes of this beam we find by interpolation I zz 64.9, with an area of 5.9 square inches. For this beam we have a. — 14° 45', s' rz 10,000 pounds, R — s' zz 2,000 pounds, a total compression of 13,260 and a required area of 6.6 square inches, slightly 124 MITERING LOCK GATES. above the largest size to which the beam is rolled. The two last trials show that a beam intermediate between those tried will exactl" fulfill the condi- tions. Trying one midway between the two, we have by interpolation an area of 6.2 square inches, and I = 68.4 with a weight of 21 pounds per foot. For this we find a — 14° 45', s' — 9,505, R — s' = 2,495, and a required area of 5.3 square inches. A slightly smaller beam would exactly satisfy our conditions. This one does so very nearly, and may be taken. It will work at its economic angle of 14° 45' with a fiber stress of 11,645 pounds per square inch, and will weigh 326 pounds per frame. From the above it will be seen that when the values of I, y, and the area for the smallest size of any chart number give such a value of R — s' that the required area is smaller than the smallest size to which the beam is rolled, no further trial with that chart number need be made. Similarly, when the elements of the largest size of the particular chart number require a greater area than can be rolled, the beam may be dropped from consid- eration ; but when the elements of the largest size require too small an area, or those of the smallest size require too large an area, further trials with the same chart number should be made. In the above example the miter posts have been assumed of such shape that the line of pressure can not pass above the median line. If it can reach the lower flange of the beams, in its extreme downstream position, it fol- lows that near the ends, before the extension due to the bending moment relieves the compression due to the longitudinal thrust, the lower flange will have to carry practically all the thrust ±— cot a, which we have found to be 13,260 pounds. The area of the flange alone is 2 square inches, which is amply large enough to carry this stress. If a T beam were used there would be some danger in allowing the line of pressure to reach the down- stream edge of the post, and the surface of contact would have to be placed farther upstream, thus losing the advantage obtained by limiting the line of pressure to positions as far downstream as possible. APPENDIX V. SELECTION OF WOODEN FRAMES. To illustrate the selection of a suitable wooden frame, let it be required to find the size of timber for a frame to carry a pressure of 450 pounds per linear foot, the half span of the lock being 15 feet. The material is oak, ■with a working strength of 1,000 pounds per square inch. No greater depth than 12 inches is permissible. C* 1 ^ Passing at once to the greatest allowable depth we find that for -7 = — r the economic angle is 13° 30', by Table iv. Substituting proper values for the quantities in eq. (22) we find that S will be 1000 pounds for b — 7.94 inches, or, say, 8 inches. A frame 12" x 8" will therefore be the lightest possible within the assumed limit of depth. It will weigh about 617 pounds. If it were required to build the leaf out of smaller timbers, say, 12" x 7", the second column of Table iv would become useful. With the assumed value of p the unit stress in this case would necessarily exceed 1,000 pounds per square inch, and it would be advisable to use the frames at the angle which would try them the least, viz, at 15° 30'. A still better plan would be to alter the frame spacing until p should have such a value as to permit the frames to be used at. the economic angle 13° 30', without exceed- ing the allowable stress per square inch 125 INDEX A. Paragraph. Accident to St. Marys Falls Canal gate 237 Havre Gate 237 Louisville and Portland Canal 170 (loot note) Accidental shocks , 222 Air chamber 174 et seq., 245 Anchorage 211, 214 Arched frames. (See Horizontals.) leaf, weight of 243 and Appendix I Avonmouth Dock 257 Axis of rotation 190, 191 B. Barry Dock 256 Bassin Bellot 253 Bending moment in verticals 146-148 horizontals 40, 50 Boulogne Dock 251 Bracing 182,183 Buckled plates 168 C. Calculation for framing Appendices I, IV, and V Cascade Locks, proposed gates 134, 179 (foot note) Center of pressure, position of 45, 58, 95, 103, 106-109 Charenton Lock 259 Chevallier, experiments of 28 Choice of form 241 et seq. type 232 Collar 211 Composite leaves 130,248 Compression, longitudinal 37, 51 Comparison of riveted frames Appendix I Constant lift, effect of 171 et seq. Construction. (See Verticals and Horizontals.) Contact. (See Surface of contact.) Cost of different materials 234 Culverts 230 Cushion 199,219,221 127 128 INDEX. D. Paragraph. Depth, loading due to 12 Durability of different materials 235 Duty of sheathing 4, 157 framing 4 E. Elasticity of different materials against shock 237 Examples Chapter IX F. Filling and emptying. .. 230 Flanges, for arched frame 125 for girder frame 121 et seq. Footstep 202 Forces, straining 3 Form, choice of 241 et seq. Frame by Galliot's method Appendix I riveted, calculation for Appendix I rolled metal, calculation for Appendix IV timber, calculation for Appendix V spacing, influenced by load 131, 132 metal leaves 134 wooden leaves 135 Frames. (See Horizontals and Verticals.) Framework, methods of designing 27, 33, 94, 120, 139, et seq. Framing, calculation for Appendix I duty of 4 G. Galliot, formula for load 29 formula for sheathing 166 examples of use of formula Appendix I Gates, classification 1 nomenclature '. 2 tension 224 vertically framed 10, 154, 246 (See Leaf.) Girder frames. (See Horizontals.) leaf, weight of 243 and Appendix I Grashof, formula for sheathing 159 Gudgeon 207 et seq. Gusset plates 201-219 H. Hand apparatus for working gates 228 Havre gate , 252-254 accident to 237 Horizontal, lowest 183-220 upper 183-220 Horizontals : Bending moment in 40 et seq. Designing of 27, 33, 94, 120, 139, et seq. Forces on 37-38 Load on 5,9,12,13,27,29 INDEX. 129 Horizontals — Continued . Paragraph. Longitudinal compression 37 Maximum load 11 Rule for 27 Spacing - 131-158 Horizontals, arched metal : Center of pressure 103 Construction of 125 Minimum volume 101 Miter angle 101 Stresses 103-108 Surface of contact 108 Web '. 105 Weight Appendix 1 Horizontals, arched timber : Center of pressure 106-109 Construction of 129 Miter angle 101 Stress 107-109 Horizontals, bowstring, metal : Miter angle - Ill Stress - 110 Horizontals, bowstring, timber 112 Timber, construction 128 Trussed 112-114 Horizontals, broken backed 96 Horizontals, curved : Classification 97 Depth. 117 Designing - 120 Minimum volume ' 101 Miter angle 101 Horizontals, Gothic arch 116 Horizontals, mixed 130 Horizontals, riveted : Construction of - 121 Flanges 121-124 Web 74,105, 121, and Appendix III Horizontals, straight backed: Bending moment in 50 Designing of 94 Longitudinal compression - 51 Horizontals, straight backed, constant flange area : Depth - 73 Miter angle - 72 Stress 66, 68 Volume 70 Horizontals, straight backed, varying flange area : Depth 76 Designing of 94 Miter angle 60 Stress ---- 52-64 Volume 57 2623— No. 26 17 130 INDEX. Horizontals, straight backed, rolled metal: Paragraph. Construction 127 Designing of 94 Miter angle 83 Stress 80 Horizontals, straight backed, timber : Depth 92 Designing of - 94 Miter angle 92 Stress 88-89 Horizontals, timber, construction of 128-129 Hydraulic apparatus 226,227,229 Hydraulic apparatus, direct acting 256 I. Intercostal frames 134, 158 load on 164 L. Lavoinne, tables 28 Leaf for constant lift 171 varying lift 176 et seq. with single horizontal 10,154,246 Lift, constant 171 et seq. varying 176 et seq. Load due to depth 12 verticals 5, 13, 29 on horizontals 5, 9, 12, 29 maximum 27 verticals 146 Local load on sheathing . 158 Longitudinal compression 37, 51 Louisville and Portland Canal, accident to 170 (foot note.) Lowest horizontal 183-220 M. Manoeuvring - 225 et seq. Materials, comparison of 233 et seq. conclusions 238 Miter angle. (See Horizontals.) Mitering, conditions of 8 Miter post 215 surface of contact 218 N. Narrow leaves, designing of 33 Nomenclature 2 Notation 36, 49 P. Paneled sheathing 159 Pivot 203 et seq. Portes valets 224 Post. (Sec Quoin and miter.) Pressure. (See Load and upward pressure.) center of. ( See Center of pressure. ) INDEX. 131 Q- Par;igr;t]ili. Quoin post , 189 et seq. section of 195 shoes 196 surface of contact 191 et seq. R. Rigidity 7 vertical 5, 7, 35 limit of 142 et seq. Riveted frames 74, 105, 121, 124 example Appendix I and in. Rolled metal frame 79 et seq., 127 example Appendix I v. Roller 184-188 Rotation, axis of 190, 191 S. St. Mary's Falls Canal, accident to 237 present gates 188, 258 proposed gates 125, 134 Sheathing, action as part of flanges 121 et seq., 162 duty of - 4, 157 examples of 165 formula for 158, 159, 160, 166 paneled - 159 stresses in 158 et seq. thickness of 158,159,160,163,165,166,167 timber... 167 Sill, contact at 6,172,221 Shocks, accidental 222 Spacing of horizontals 131-158 verticals - - 158 Stresses in gudgeon 203 horizontals. (See Horizontals.) pivot 205 sheathing 158 et seq. verticals. (See Verticals.) due to weight 182 Surface of contact, arched frames 108, 109 girder frames 95 at posts 190 et seq., 218 sill 221 T. Thickness of sheathing. (See Sheathing. ) Timber. ( See Materials . ) frame. (See Horizontals. ) example of Appendix v. sheathing 167 Transatlantic dock 252, 254 Tyne docks 255 Type, choice of , 232 132 INDEX. u. Paragraph. Upper horizontal 183,220 Upward pressure 170,78 V. Valves 230 Varying lift, effect of 176 Vertical forces 169, 170, 178 section, equation of mean liber 23 strains Chapter vii. rigidity 5,7,35,142 Vertically framed leaf 10,154,246 Verticals, bending moment in . 146-148 construction of 156 discussion of Chapter v. duty of 4,138 loading due to 5, 13 et seq., 29 loads on 146 metal 156 timber 156 method of designing 139-151 and Appendix I. spacing of 153 stress in 146, 150 W. Web of riveted frames 74, 105, 121, and Appendix m. Weight of different materials _ 236 stress due to 182 et seq. Y. Yates, formula for sheathing 160 c