5.5 . variation of material strength . two alloys of widely different strengths from he30-wp were selected in order to study the effect of material properties on strut behaviour . the alloys were ne6-m and he15-wp , which have 0.1 % proof stresses of approximately 10 tons &amp;sol; in2 and 28 tons &amp;sol; in2 respectively . the specimens were fabricated from 3 in x 2 1/4 in x 0.15 in ( 76.2 x 57.15 x 3.81 mm ) A.D.A unequal bulb angle section , and were of the same design as for the first series of A.D.A specimens shown in fig 13 . as material failure might be expected to have the greatest influence on strut behaviour in the lower slenderness ratios , these specimens were made in a limited range of slenderness ratios only : 30 to 60 for the he15-wp and 30-90 for the ne6-m . the overall picture of failure behaviour was similar to that for the previous sets of specimens - torsion-flexure . failure of the higher strength material specimens was generally of an elastic buckling nature , with torsional and flexural deflections starting near the ultimate load and growing very rapidly to large magnitudes , when no further increase in load could be sustained . on unloading , there was almost complete recovery , showing that the buckling was largely elastic . an exception was one of the L/k = 40 specimens where the torsional deflection was increased so much that local collapse occurred in the lower third of the specimen . the lower strength specimens generally failed quite suddenly , with very little deflection visible beforehand . failure was of the torsion-flexure form , with flexure more predominant than in the tests previously described , coupled in all cases below L/k = 50 with local failure of the outstanding bulbed edge of the individual angle member . there was scarcely any recovery on unloading , showing that the distortion had given rise to large areas of plasticity . the forms of specimens of the two materials after failure for slenderness ratios 30 , 40 and 50 are shown in fig 33 , where the large permanent set of the ne6-m specimens can be clearly seen , and compared with the almost complete recovery of the he15-wp ones . the right-hand specimen of the middle pair is the exceptional case of local collapse in the he15-wp series referred to above . fig 34 shows the L/k = 90 specimen in ne6-m after failure . the results of this series of tests are given in table 16 and fig 35 shows the strengths of the two series of specimens compared with those for the he30-wp . it will be noticed that the results for ne6-m are presented in two parts : this is because a second batch of material for these specimens had an appreciably higher strength than the first . 5.6 . determination of material properties . tension specimens were taken from each different batch of section . in some cases machined round specimens of 0.282 in ( 7.16 mm ) diameter were made from the corner of the section or from the bulbed edge , in others standard flat specimens were made from the longer leg of the section . strains were measured with a 1 in ( 25.4 mm ) gauge length Robertson optical extensometer on the round specimens , and with a Gerard extensometer on the flat ones . to make a satisfactory compression test , the length of the specimen should not exceed about 2 1/2 times its diameter ; therefore the length of compression specimens taken from small structural sections must be small . as the greatest diameter of specimen that could be obtained from the 3 in x 2 1/4 in ( 76.2 x 57.15 mm ) A.D.A section was about 3/8 in ( 9.5 mm ) the length was limited to 1 in ( 25.4 mm ) . a jig was made in which the specimen was clamped and both ends could be ground at one setting , so that they were finished accurately flat and parallel . strains were measured by a pair of Martens extensometers having a gauge length of 0.6 in ( 15.24 mm ) . the test was carried out in parallel platen apparatus to ensure , as far as possible , that compression took place without bending . the results are summarised in table 17 . it will be noticed that where test pieces were taken from both the bulb and corner and from the flat part of the section , the material in the flat part of the section had an appreciably lower tensile proof strength . the Young &apos;s moduli are generally of the order of 5 % higher in compression than in tension . observations of this nature have been recorded before with aluminium alloy but no satisfactory explanation seems to have been offered . 6 . analysis of results . the analysis of the results falls naturally into three categories : the comparison of values of failing stress predicted analytically with those obtained experimentally : a similar comparison of the results obtained from standard design methods ; and a study of the behaviour of double angle struts having different cross-sectional profiles . 6.1 . prediction of failure . the prediction of the elastic buckling load of members where there is interaction between the flexural and torsional modes has been fully dealt with by Timoshenko and many other authors . for members having one axis of symmetry , the critical load is given by the smallest root of the equation : &amp;formula; where p1 , p2 , p3 , are respectively the critical stresses for flexural buckling about the principal axis x-x at right angles to the axis of symmetry , flexural buckling about the axis of symmetry a-a , and torsional buckling . the value of r is given by &amp;formula; where a is the distance between the shear centre and the centroid , and kx and ka are the respective principal radii of gyration . the exact analysis of the buckling of built-up members such as those considered here is extremely complex , but provided the individual members are fastened together at a sufficient number of points it is justifiable , as a first approximation , to treat the members as being homogeneous . in the case of the struts used in this investigation the bending stiffnesses about the two principal axes are approximately equal ; therefore , as the member is effectively fixed-ended for buckling about the x-x axis , p1 will always be greatly in excess of the actual buckling stress , and may be disregarded . the stiffness for bending about the axis of symmetry is taken as the reduced value calculated in 4.1 . the value of the torsional stiffness used in calculating the torsional buckling load is obtained for the various slenderness ratios by multiplying by the appropriate factor b from table 11 . the warping stiffness of the angle sections themselves , which is very low , has very little effect on the torsional buckling load and is neglected in the calculation . thus the torsional buckling stress &amp;formula; , where gj is the free-ended torsional stiffness of the composite member , and Ip is the polar second moment of area of the cross-section about the shear centre . the values obtained for the buckling stresses are shown below in table 18 . fig 36 shows these values graphically , curve ( 1 ) , and those for the he30-wp struts ( 2 ) . the immediate observation is that the experimental failing stress curve lies well below the theoretical one , the discrepancy being most marked in the lower slenderness ratios . the most obvious explanation for this is the reduction of the effective stiffness due to inadequate rigidity of the fastenings , discussed in 4.1 . if the experimental results were re-plotted on a basis of slenderness ratios calculated from actual stiffness , then the curve would be moved to the right . some confirmation of this explanation is given by the results for the few tests with the knife-edge along the x-x axis , in which the effects of the fastenings on flexural buckling might be expected to be much smaller , which lie much nearer to the theoretical curve . it is interesting to re-calculate the torsion-flexure buckling stress values when the flexural buckling stress is derived from that obtained by taking the measured bending stiffness , the torsional stiffness remaining as before . these values are plotted in curve ( 3 ) , fig 36 , which lies much closer to the experimental values of curve ( 2 ) than does the original theoretical torsion-flexure curve . on the other hand , it might be argued that compression should tend to reduce the effects of bolt clearances and that the discrepancy between the experimental and theoretical values might be due to plasticity of the material at the higher stresses . from the compression stress-strain curve of the he30-wp material used , values of the tangent modulus may be deduced , and the Engesser plastic flexural buckling curve can be constructed , curve ( 4 ) , as a continuation of the Euler curve for the elastic range . this curve diverges rapidly from the Euler and elastic torsion-flexure curves as the slenderness ratio diminishes . the limit of proportionality of the he30-wp was just below 8 tons &amp;sol; in2 ( 12.7 kg &amp;sol; mm2 ) , and it might be expected that after the critical stress of this value , which occurs at about L/k = 70 , the true torsion-flexure buckling curve would begin to diverge from the elastic one . there is no direct method of constructing the plastic torsion-flexure buckling curve . however , by assuming that the critical load for the torsional mode does not change , which is reasonable if the shear modulus remains nearly constant , it is possible to devise a method of successive approximation . taking for the flexural buckling stress , p2 , the value obtained for flexural plastic buckling , a new value can be obtained for the torsion-flexure buckling stress p . from the compression stress-strain curve the value of the tangent modulus Et at the stress p is obtained . using this value of Et in the Engesser equation , &amp;formula; , the buckling stress of a strut of the same slenderness ratio can be calculated . this value will generally be found to differ from the value chosen for p2 . another value is now chosen for p2 , and the process repeated until a value is obtained , for the plastic torsion-flexure buckling stress , at which the value for the tangent modulus corresponds to plastic flexural buckling at the chosen value of p2 . the values obtained by this method are shown in fig 36 , curve ( 5 ) , where it will be seen that , except for slenderness ratios below 40 , the curve lies above the experimental one - between those obtained from the elastic torsion-flexure equation using modified flexural stiffness and the ordinary elastic torsion-flexure equation . it may be concluded that both plasticity and loss of expected stiffness contribute to the divergence of the experimental from the predicted values . confirmation of this is obtained by examination of the results for he15-wp and ne6-m materials ; the elastic limit of he15-wp is about 23 tons &amp;sol; in2 so that , as the critical stress for elastic torsion-flexural buckling at L/k = 30 is 23.1 tons &amp;sol; in2 , it might be expected that plasticity would have scarcely any influence on failure in the range of slenderness ratios used in the tests . fig 37 shows that the experimental values are in reasonable agreement with the values obtained from the elastic torsion-flexure equation with modified flexural stiffness . the small discrepancy at the lower slenderness ratios could be attributed to an over-estimation of the torsional stiffness . the ne6-m alloy , with an elastic limit of between 4 and 5 tons &amp;sol; in2 , gives the opposite picture in that plasticity affects failure over the whole range of slenderness ratios considered . the plastic torsion-flexure curve , in fig 37 , lies well below the elastic values and a little above the experimental ones . this seems to indicate that , although plasticity is the dominating factor affecting failure , the reduced flexural stiffness contributes to the difference between experimental and predicted values , and the best prediction might be obtained from the plastic torsion-flexure approach using the reduced , experimental flexural stiffnesses . the results of this calculation for he30-wp and ne6-m are shown in fig 38 , where it will be seen that good agreement is obtained except at the lowest slenderness ratio where the stiffnesses have probably been over estimated . 6.2 . design methods . as the mode of failure at all slenderness ratios up to 150 was torsion-flexure it is evident that direct design from the Perry-Robertson strut curve is unsatisfactory . forms of compression instability , other than purely flexural , may be dealt with by the equivalent slenderness ratio ( e.s.r ) method . 