$2.4 Struts 37 Neither of the above formulae proved to be very successful,and they were replaced by: (c)Rankine-Gordon formula 11.1 PR=P.+Pe (2.10) where Pe is the Euler buckling load and Pe is the crushing(compressive yield)load =oA. This formula has been widely used and is discussed fully in $2.5. 2.4.Euler "validity limit" From the graph of Fig.2.7 and the comments above,it is evident that the Euler theory is unsafe for small L/k ratios.It is useful,therefore,to determine the limiting value of L/k below which the Euler theory should not be applied;this is termed the validity limit. Euler curve For structural steel,curves coincide at L/k.B0 6 Yieid or collapse stress ssaus ayor de Experimem al results Curves coincide at L/k:120 50 100 150 Slenderness rotio L/k Fig.2.7.Comparison of experimental results with Euler curve. The validity limit is taken to be the point where the Euler oe equals the yield or crushing stress oy,i.e.the point where the strut load P=A Now the Euler load can be written in the form CTEl-CTEAR Pe=C"L2 L where C is a constant depending on the end condition of the strut. Therefore in the limiting condition A=CTEAk2 L2$2.4 Struts 37 Neither of the above formulae proved to be very successful, and they were replaced by: (c) Rankine-Gordon formula (2.10) where P, is the Euler buckling load and P, is the crushing (compressive yield) load = a,A. This formula has been widely used and is discussed fully in $2.5. 2.4. Euler "validity limit" From the graph of Fig. 2.7 and the comments above, it is evident that the Euler theory is unsafe for small L/k ratios. It is useful, therefore, to determine the limiting value of L/k below which the Euler theory should not be applied; this is termed the validity limit. Eukr curve Yield or colbpse stress Curves coincide at L/k*120 1 50 100 150 Slenderness ratio L/k Fig. 2.7. Comparison of experimental results with Euler curve. The validity limit is taken to be the point where the Euler a, equals the yield or crushing stress ay, i.e. the point where the strut load P = ayA Now the Euler load can be written in the form where C is a constant depending on the end condition of the strut. Therefore in the limiting condition n2EAk2 L2 aVA = C------