H

In this case the shear centre S is positioned on the Cx axis so that >>s = 0 and Eq. (6.92) applies. The distance x of the centroid of area C from the web of the section is found by taking first moments of area about the web. Thus which gives

The position of the shear centre S is found using the method of Example 9.5; this gives xs = —76.2 mm. The remaining section properties are found by the methods specified in Example 6.1 and are listed below

PCR(,,) = 4.63 x 105 N, Pcu,,) = 8.08 x 105 N, PCR{0) = 1.97 x 105 N Expanding Eq. (6.92)

Rearranging Eq. (i)

P2( 1 - Axi/I0) - P(PCR(a,v) + pcm) + PCr(xx)Pcr{0) = 0 (»)

Substituting the values of the constant terms in Eq. (ii) we obtain

The roots of Eq. (iii) give two values of critical load, the lowest of which is

It can be seen that this value of flexural-torsional buckling load is lower than any of the uncoupled buckling loads Pcr(xv), PcR(vy) or Pcr(o)- The reduction is due to the interaction of the bending and torsional buckling modes and illustrates the cautionary remarks made in the introduction to Section 6.10.

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