Struts 29 Perry-Robertson Formula Na=loy+(n+1)0.] 2 V+g+- where n is a constant depending on the material. For a brittle material n=0.015L/k For a ductile material n=0.3 100k These values will be modified for eccentric loading conditions.The Perry-Robertson formula is the basis of BS 449 as shown in 82.7. Struts with initial curvature Maximum deflection max= Pe Co L(Pe-P) P Maximum stress omax PPe Coh (P。-P)I where Co is the initial central deflection and h is the distance of the highest strained fibre from the neutral axis (N.A.). Smith-Southwell formula for eccentrically loaded struts With pinned ends the maximum stress reached in the strut is given by a=l+尝c5/(品) 0 m=l+装√( where e is the eccentricity of loading,h is the distance of the highest strained fibre from the N.A.,k is the minimum radius of gyration of the cross-section,and o is the applied load/cross-sectional area. Since the required allowable stress o cannot be obtained directly from this equation a solution is obtained graphically or by trial and error. With other end conditions the value L in the above formula should be replaced by the appropriate equivalent strut length (see $2.2).Struts Perry-Robertson Formula 29 where q is a constant depending on the material. For a brittle material q = 0.015L/k For a ductile material 2 t) = 0.3 (&) These values will be modified for eccentric loading conditions. The Perry-Robertson formula is the basis of BS 449 as shown in $2.7. Struts with initial curvature Maximum deflection 6,, = Maximum stress amax = - f where CO is the initial central deflection and h is the distance of the highest strained fibre from the neutral axis (N.A.). Smith-Southwell formula for eccentrically loaded struts With pinned ends the maximum stress reached in the strut is given by a,,, = 0 [ 1 + - : sec - :/(&I] or where e is the eccentricity of loading, h is the distance of the highest strained fibre from the N.A., k is the minimum radius of gyration of the cross-section, and o is the applied loadkross-sectional area. Since the required allowable stress a cannot be obtained directly from this equation a solution is obtained graphically or by trial and error. With other end conditions the value L in the above formula should be replaced by the appropriate equivalent strut length (see 52.2)