$2.7 Struts 41 2.7.British Standard procedure (BS 449) With a load factor N applied,the Perry-Robertson equation becomes N。=+(+1)ol -++-} (2.18) 2 With values for steel of ay =225 MN/m2,E 200 GN/m2,N =1.7 and n =0.3(L/100k)2, the above equation gives the graph shown in Fig.2.9.This graph then indicates the basis of design using BS449:1959 (amended 1964).Allowable values are provided in the standard, however,in tabular form. 150 100 50F 40 80 20 160200240 Slenderness rotio L/k Fig.2.9.Graph of allowable stress as given in BS 449:1964(in tabulated form)against slenderness ratio. If,however,design is based on the safety factor method instead of the load factor method, then N is omitted and ov/n replaces o,in the formula,where n is the safety factor. 2.8.Struts with initial curvature In $2.6 the Perry-Robertson equation was derived on the assumption that strut imperfec- tions could be allowed for by giving the strut an initial curvature.This proof applies equally well,of course,for struts which have genuine initial curvatures and,provided the curvature is small,the precise shape of the curve has little effect on the end result. Thus for an initial curvature with a central deflection Co. maximum deflection c-[ (2.19) (oe-) maximum B.M.=Pe、 C0= (2.20) P,「 Poe hCo and$2.7 Struts 41 2.7. British Standard procedure (BS 449) With a load factor N applied, the Perry -Robertson equation becomes With values for steel of (T, = 225 MN/m2, E = 200 GN/m2, N = 1.7 and 9 = 0.3(L/100k)2, the above equation gives-the graph shown in Fig. 2.9. This graph then indicates the basis of design using BS449: 1959 (amended 1964). Allowable values are provided in the standard, however. in tabular form. t I I I I I I I 40 80 I20 160 200 240 Slenderness ratio L/k Fig. 2.9. Graph of allowable stress as given in BS 449: 1964 (in tabulated form) against slenderness ratio. If, however, design is based on the safety factor method instead of the load factor method, then N is omitted and a,/n replaces (T~ in the formula, where n is the safety factor. 2.8. Struts with initial curvature In 02.6 the Peny-Robertson equation was derived on the assumption that strut imperfec￾tions could be allowed for by giving the strut an initial curvature. This proof applies equally well, of course, for struts which have genuine initial curvatures and, provided the curvature is small, the precise shape of the curve has little effect on the end result. Thus for an initial curvature with a central deflection Co, maximum deflection = (2.19) maximum B.M. = P (2.20) and P omax = A - f [ ~- ((T~~o)] '7 -