42 Mechanics of Materials 2 $2.9 P,「PPe1hCo (2.21) AL(P。-P)]I where h is the distance from the N.A.to the outside fibres of the strut. 2.9.Struts with eccentric load For eccentric loading at the ends of a strut Ayrton and Perry suggest that the Perry-Robertson formula can be modified by replacing Co by (Co +1.2e)where e is the eccentricity. Then =+12安 (2.22) and n'replaces n in the original Perry-Robertson equation. (a)Pinned ends-the Smith-Southwell formula For a more fundamental treatment consider the strut loaded as shown in Fig.2.10 carrying a load P at an eccentricity e on one principal axis.In this case there is strictly no 'buckling" load as previously described since the strut will bend immediately load is applied,bending taking place about the other principal axis. Fig.2.10.Strut with eccentric load (pinned ends) Applying a similar procedure to that used previously B.M.at C=-P(y+e) dy 2=-P(y+e) EI d2y dx2+n2(0+e)=042 Mechanics of Materials 2 52.9 (2.21) where h is the distance from the N.A. to the outside fibres of the strut. 2.9. Struts with eccentric load For eccentric loading at the ends of a strut Ayrton and Perry suggest that the Perry-Robertson formula can be modified by replacing CO by (CO + 1.2e) where e is the eccentricity. Then eh k2 17’ = 1 + 1.2- (2.22) and 17’ replaces q in the original Perry-Robertson equation. (a) Pinned ends - the Smith-Southwell formula For a more fundamental treatment consider the strut loaded as shown in Fig. 2.10 carrying a load P at an eccentricity e on one principal axis. In this case there is strictly no ‘buckling” load as previously described since the strut will bend immediately load is applied, bending taking place about the other principal axis. Fig. 2.10. Strut with eccentric load (pinned ends) Applying a similar procedure to that used previously B.M. at C = -P(y + e) d2 Y dx2 .. Et- = -P(y+e)