TABLE OF CONTENTS The solution M e for the critical moment M c of a perfectly straight simply supported I-beam with equal end moments given by Eq. (3.21) is only valid when the elastic critical stress ? e = M e/ S x is less than the stress required to cause first yield. In a short span steel beam, yielding occurs before the critical moment is reached, and significant portions of the beam are plastic or strain-hardened when buckling commences. The effective rigidities of these plastic and strain-hardened portions are reduced, and consequently, the critical moment is also reduced. There have been many investigations of plastic buckling, and most of these have been cited in recent studies by Trahair and Kitipornchai (1972), Nethercot (1972b, 1973e, 1974a, b, 1975a), and Fukumoto and Kubo (1972).
For beams with equal and opposite end moments ( ? = 1), the distribution of yield across the section does not vary along the beam, and when there are no residual stresses, the plastic critical moment M i can be calculated from a modified form of Eq. (3.21) as
| (3.77) |  |
in which the subscripted quantities ( ) r are the reduced rigidities which are effective at buckling. Estimates of these rigidities can be obtained by using the tangent moduli of elasticity which are appropriate to the varying stress levels throughout the section. Thus the values of E and G are used in...
