36 Mechanics of Materials 2 $2.3 Pinned-pinned Fixed-fixed Ends fixed in direction but not in position P 4m1 Fixed-free Fixed-pinned 2L7 777 70P历 R:E红 f07L)2 22虹 L Fig.2.6."Equivalent length"of struts with different end conditions.In each case is the length of a single bow. 2.3.Comparison of Euler theory with experimental results (see Fig.2.7) Between L/k =40 and L/k 100 neither the Euler results nor the yield stress are close to the experimental values,each suggesting a critical load which is in excess of that which is actually required for failure-a very unsafe situation!Other formulae have therefore been derived to attempt to obtain closer agreement between the actual failing load and the predicted value in this particular range of slenderness ratio. (a)Straight-line formula P dyA[1 n(L/k)] (2.8) the value of n depending on the material used and the end condition. (b)Johnson parabolic formula P=o,A[1-b(L/k)2] (2.9) the value of b depending also on the end condition.36 Mechanics of Materials 2 $2.3 Pinned - pinned P pe*+[ T 1 fixed-free IP fixed- fixed IP f ixed-pinned P b7 L Ends fixed in &reclan but not in position Fig. 2.6. “Equivalent length” of struts with different end conditions. In each case 1 is the length of a single bow. 23. Comparison of Euler theory with experimental results (see Fig. 2.7) Between L/k = 40 and L/k = 100 neither the Euler results nor the yield stress are close to the experimental values, each suggesting a critical load which is in excess of that which is actually required for failure-a very unsafe situation! Other formulae have therefore been derived to attempt to obtain closer agreement between the actual failing load and the predicted value in this particular range of slenderness ratio. (a) Straight-line formula P = cYA[1 - n(L/k)] the value of n depending on the material used and the end condition. (b) Johnson parabolic formula P = uyA[l - b(L/k)’] the value of b depending also on the end condition. (2.9)