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By L. I. Sedov, J. R. M. Radok

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The load may start to either increase or decrease soon after the first significant lateral deflections near the critical load take place. In these cases of postcritical reserve or postcritical loss of carrying capacity, which are especially marked for plates and shells (Chap. 7), the Southwell plot deviates from the straight line quite significantly at the upper right end of the plot. Such deviations make the Southwell plot useless for plates. A modification of the Southwell plot that can take these postcritical deflections approximately into account was proposed by Spencer and Walker (1975) (see Eq.

This last equation is now used in the current AISC (1978, -1986) and ACI (1977) codes for columns braced against lateral sway. 18 Equivalent-moment factor Cm for beam with unequal end moments. (After C. 4 applies for a range of values Mtf M2 in which the initial double curvature of the beam reverses on approach to critical load to a single curvature (Fig. 15b). In that case the concept of magnification factor does not give a good approximation. For the relatively infrequent cases when primary bending moments M 0(x) are caused by a lateral load on the column, the AISC and ACI codes prescribe Cm=l.

They are of two kinds, kinematic and static. 7 Effective length L of columns with various end restraints. and w = 0 at x = 0. The remaining boundary condition is static: M = 0 or Elw" = 0 or w" = 0 at x = 0 (axial coordinate xis measured from the free end; see Fig. 7). 1) Ak cos kl - Bk sin kl + C = 0 This is a system of four linear homogeneous algebraic equations for the unknowns A, B, C, and D. This system, representing an algebraic eigenvalue problem, can have a nonzero solution only when the determinant of the equation system vanishes.

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A course in continuum mechanics, vol. 1: Basic equations and analytical techniques by L. I. Sedov, J. R. M. Radok

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