2.6. Perry-Robertson formula

The Perry-Robertson proof is based on the assumption that any imperfections in the strut, through faulty workmanship or material or eccentricity of loading, can be allowed for by giving the strut an initial curvature. For ease of calculation this is assumed to be a cosine curve, although the actual shape assumed has very little effect on the result.

Consider, therefore, the strut AB of Fig. 2.8, of length L and pin-jointed at the ends. The initial curvature yo at any distance x from the centre is then given by tlx

Fig. 2.8. Strut with initial curvature.

Fig. 2.8. Strut with initial curvature.

If a load P is now applied at the ends, this deflection will be increased to y + yo•

d2y P

dx2 EI


where A and B are the constants of integration. Now when x = ±L/2, y = 0

0 0

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