ARR No. UkF2k NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT OWONALLy ISSUED June lykk as Advance Restricted Report LUF2^ THE DETERMINATION OF EFFECTIVE COLUMN LENGTH FROM STRAIN MEASUREMENTS By Evan H. Schuette and J. Albert Roy Langley Memorial Aeronautical Laboratory Langley Field, Va. „-.."^.~"'"*" V... ... ...«=■■';, . ,, .- i^ WJEW-s-to WASHINGTON NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were pre- viously held under a security status but are now unclassified. Some of these reports were not tech- nically edited. All have been reproduced without change in order to expedite general distribution. L - I98 \ Digitized by the Internet Archive in 2011 with funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/determinatioOlang II*, b^ x l o &> 3/6 " /ver 7 NACA ARR No. LJ+F21+ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS ADVANCE RESTRICTED REPORT THE DETERMINATION OF EFFECTIVE COLUMN LENGTH FROM STRAIN MEASUREMENTS By Evan H. Schuette and J. Albert Roy SUMMARY A method is presented for the experimental deter- mination of the effective length of a column for which the end conditions are unknown by establishing the points of zero curvature from readings of strain gages dis- tributed along the length of the column. Tests of four columns of different cross sections indicated that the proposed method gives satisfactory results even when there is considerable scatter in the strain-gage readings. INTRODUCTION A suitable method is needed for experimentally evaluating the effective length from column tests in which the end conditions are unknown. One such method consists in establishing the deflection curve from meas- urements of lateral deflections and estimating from this curve the locations of the inflection points. The prin- cipal objection to this method is that the determination of inflection points from an experimentally established curve is an inherently inaccurate procedure. A more accurate method of establishing the inflection points consists in measuring the curvature rather than the deflection and establishing from such measurements the points of zero curvature, which define the inflection points. The present report shows how strain measurements can be used to indicate curvature and thus to establish the effective column length. Four columns of different cross sections were tested to provide an experimental check of the method. 2 NACA ARR No. Li+P2lf SYMBOLS L actual length of column, inches L, effective length of column, inches strains at two points in cross section e l' € 2 distance between points in cross section for which strains e n and £p are taken, meas- ured perpendicular to neutral axis, inches radius of curvature, inches METHOD OF MEASURING CURVATURE AND DETERMINING EFFECTIVE COLUMN LENGTH If it is assumed that sections remain plane after bending, the curvature 1/r of a column at a given cross section is related to the difference in strain at two points on the particular cross section according to the equation r d This equation indicates a convenient experimental method for determining curvature from strain measurements taken along the length of the column. The method consists in attaching a number of strain gages on opposite sides of the column along its length and recording the dif- ferences in strain on the two sidee. It is then necessary only to plot the curvature - or, if d is constant, the strain difference € i ~ e P " a S a i riS t distance along the length of the column and to determine the points of zero curvature . SPECIMENS AND TEST EQUIPMENT In order to check experimentally the practicability of the strain-measurement method for determining effective NACA ARR No. Ll±F2k length, columns of four different types of cross section were tested. A rectangular bar was tested with strain gages placed opposite each other on the wider sides. The cross sections and the locations of the resistance-type wire, strain gages for the Z-sectlon column, the skin-and- ;iffener column, and the hat-stiffened panel column are 3hown In figures 1, 2, and 3> respectively The wire strain gages were attached along ' the length of each column at small intervals. The approximate distance d between strain gages at a particular cross section, measured perpendicular to the neutral axis, was: Column d (in.) Ear o< . 2 '-' action a ' J , Ln -aud-stiffener 3.0 H s. t - s T- i f f e ne d p a ne 1 • 9 The over-all accuracy within 2 percent. of the strain measurements was The specimens were tested flat-ended in hydraulic testing machines having accuracies within three-quarters of 1 percent for the range of load used. figure I). shows the Z-sectlon column under load. RESULTS AND DISCUSSION The re suits of figures . The curvature f the St rain for the g a£ ainst dls tance se veral lo? ds ne 11 nes repre sent (f igs. 9 to 12) ac tual leng til, pl otted aga Inst of the tests are presented in two sets first set (figs. 5 to 8) shows the columns, as given by the differences ages at each cross section, plotted along the length of the coluniri for ar the maximum load. The b 1 :. ontal m zero •rain difference. 'V. a 00116. set .'3 the ratio of effective ] < ■• ,h to btained from the first set of figures, load. Except for the Z-section column, the values plotted in figures 5 to 3 represent the increase of curvature 1| NACA ARR No. li>F2i| caused by loads in excess of a particular initial lead ar the maximum. The use of a fairly high initial load in the calculation of strain differences had the effect of eliminating a large part of the scatter in the test data. It was believed that this procedure would not affect the accuracy of the results, because the strain differences at the particular initial load were quite small in comparison wi th the differences that were recorded at leads near the maximum. For the Z-section (fig. 6), however, a somewhat more satisfactory plot was obtained when the strain increments were taken from zero load, because large strain differences were recorded as soon as loading was started. A part of the scatter in the plot for the skin-and- stiffener column (i*ig. 7) results from the fact that slightly different curvatures were measured on the right and left sides of the column. Near the bottom of the column, especially on the left side, some of the scatter is thought to be due also to local buckling of the skin. All strain gages were placed on the stiffener, but it is probable that the effect of the buckles in the skin carried over to some extent into the stiffener and influ- enced the strain readings. In the plot for the hat-stiffened panel (fig. 8) the effects of any possible differences in curvature between the two stiff eners to which strain gages were attached were eliminated by using averages of the corre- sponding gage readings on the two stiff eners. Figures 5 to 8 establish the effective lengths for several loads below the maximum. In order to extrapolate from these values to the maximum load, the ratio of effective length to actual length is plotted against load in figures 9 to 12. In the extrapolation, greater weight was given to the values obtained at the higher loads. This procedure seemed justified because the absolute scatter in the curvature plots was approximately the same for ail loads and thus relatively less important in comparison with the greater curvatures that existed at higher loads. Theoretical considerations, moreover, lead to the conclusion that the 3hape of the elastic curve for maximum load is more and more accurately approximated as the maximum load is approached, and the effective length thus approaches a definite value. NAGA ARR No. LJ+P2l> It will be noted that, for all except the Z-section column, a reasonable extrapolation to maximum load was accomplished by drawing a horizontal line through the test points. This fact is of particular interest in the case of the skin-and-stif f ener column (figs. 7 an ^ H)> for which quite consistent results were obtained even though considerable scatter was evident in the curvature plot. For the Z-section column (fig. 10), the extra- polation was accomplished by drawing a curve through the points for high loads in such a manner that the tangent to the curve was horizontal at the maximum load. Because of the presence of ineffective widths of skin, it was impossible to check the loads obtained from the skin-and-stiff ener column and the hat-stiffened panel against the values given by the Euler column formula. Such a check was made for the other two columns, however, and the results are given in the following table: Column Exp e r ime n t a 1 maximum load (lb) Euler load based on experi- mental L e (lb) Bar Z-section 50,000 2,800 1+7,800 2,930 The calculated values of Euler load, based on the experi- mentally determined effective length, are within 5 percent of the test values. LIMITATIONS OF THE METHOD The method presented for the determination of effec- tive column length from strain measurements is not applicable in all cases. If there is local buckling of the column, the strain measurements will be adversely affected. Whether the results are completely invalidated will depend on the extent to which the local buckling takes place at the points where the strain gages are located. In the tests of the skin-and-stif f ener column reported herein the local buckling did not carry over into the sides of the stiff ener, where the strain gages were located, in a sufficient degree to invalidate 6 NACA ARR No. LI4P2I4. \ completely the results obtained but the effects of the buckling were evident in the strain measurements. Another limitation is imposed by the size of the column being tested. It is evident that the accuracy of the results depends to some extent on the distance d between strain gages. If the column cross section is such that this distance must be small, the accuracy of the results will be imoaired, especially if there is a variation in strain across the width of the strain gages. CONCLUDING REMARKS The test data presented indicate that the proposed strain-measurement method for the experimental deter- mination of the effective length of a column for which the end conditions are unknown gives satisfactory results even when there is considerable scatter in the strain- gage readings. Langley Memorial Aeronautical Laboratory National Advisory Committee for Aeronautics Langley Field, ya. NACA ARR No. L4F24 Fig. 1 Strain gage fr JJ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS Figure I. - Cross Section of Z- section column. NACA ARR No. L4F24 Fig. 2 S= a Strain gage £ A NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS Figure 2.~ Cross section of skin- and -stiffener column. NACA ARR No. L4F24 Fig. 3 f N k-J L^! L S^J. NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS Figure 3- Cross sect/on of hat- Stiffened panel column. \ NACA ARR No. L4F24 Fig. 4 Figure 4.- Z-section column under load. \ NACA ARR No. L4F24 Fig. 5a Bottom NATIONAL ADVISORY COMMITTEE FOR AEROMUTICS T 0002 Curvature, ± 1/in. Distance along column, in. Figure 5r Curvature of rectangular bar. \ NACA ARR No. L4F24 Fig. 5b Bottom V NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS Distance along column, in. T.OOOZ Curvature, 1/in. Figure Or Continued. NACA ARR No. L4F24 Fig. 5c Top Botfom Load- 49.5 kips NATIONAL ADVISORY COMMITTEE TOR AERONAUTICS Distance along column, in. T. 0002 Curva ture, ± 1/in. Figure 5.- Concluded. NACA ARR No. L4F24 Fig. 6a Top Bottom ^ Distance along column, in. Curvature , NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS Figure 6 . ~ Curvature of Zsection column. NACA ARR No. L4F24 Fig. 6b Bottom NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS .0002 Curvature, 1/in. Distance along column, in. Figure 6r Continued. \ NACA ARR No. L4F24 Fig. 6c Bottom NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS .0002 Curvature, l/in. Distance along column, in. Figure 6. - Concluded . NACA ARR No. L4F24 Fig. 7 Top g^ Load '= 27.0 kips ^ Bottom Distance along column, in. NATIONAL ADVISORY COMMITTEE Km AERONAUTICS .00005 Curvature, 1/in. © Right side o Left side Figure 7. - Curvature of skin- and- stiffener column. NACA ARR No. L4F24 Fig. 7b Top Bottom 1 10 Distance along column, in Figure 7. - Concluded. NATIONAL ADVISORY / COMMITTEE FOR AERONAUTICS oooo5 Curvature, 1/in. a Right side <> Left side NACA ARR No. L4F24 Fig. 8a Top Bottom Load - 113 kips \ \ ^-^ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS T oooz Curvature, ■*■ 1/in. Distance along column, in. Figure 8~ Curvature of hat- stiffened panel column. \ NACA ARR No. L4F24 Fig. 8b Bottom Load -122. kips \ / \ / \ / \ / \ / 125 Distance along column , in. NATIONAL ADVISORY I COMMITTEE FOR AERONAUTICS \ / \^y T.0002 Curvature, l/in. Figure dr Conclu de d. \ NACA ARR No. L4F24 Fig. 9 .6 L 45 46 O O (|) o . o Max/mum bad L L NATIONAL COMMITTEE FOU ADVISORY AERONAUTICS 47 43 Load, kips 49 SO Figure 9. - Ratio of effective length to actual length for rectangular bar. NACA ARR No. L4F24 Fig. 10 .3 L .z ~5 e> Wax/mum load T L L e NATIONAL ADtlSORY COMMITTEE FOR AIRONAUTICS 2.3 2.4- 2.S 2.6 2.7 2<8 29 Load, A/ps Figure 10. - Ratio of effec five length to ocfual length for Z- section column. \ NACA ARR No. L4F24 Fig. 11 .3 L L ./ 26 27 < > > <) — Q o o p Max> mum loat 1— * ' — — t L L e ■ L_ NATIONAL m ISORY it l_ ^ 5MMITTEE FOR At RONAUTICS 2Q 29 30 Load, kips 3/ 32 Figure. //.-Ratio of effective /ength to actual /ength for skin - and- <3+/fTon*r column. NACA ARR No. L4F24 Fig. 12 L .2 Maximum load -O a LJ r L L e NATIONAL ACVISORY COMMITTEE FOR AERONAUTICS HO //4 118 I2Z Load, kips /26 /SO Fiqure 12.- Ratio of effective length to actuat length for ha t - stiffened panel column. UNIVERSITY OF FLORIDA 3 1262 08106 499 9 UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 1 20 MARSTON SCIENCE LIBRARY P.O. BOX 11 7011 GAINESVILLE, FL 32611-7011 USA