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The maximum u.d.l. which can be carried by the cantilever is then

Example 33

(a) A steel beam of rectangular section, 80 mm deep by 30 mm wide, is simply supported over a span of 1.4 m and carries a u.d.l. w. If the yield stress of the material is 240 MN/m2, determine the value of w when yielding of the beam material has penetrated to a depth of 20 mm from each surface of the beam.

(b) What will be the magnitudes of the residual stresses which remain when load is removed?

(c) What external moment must be applied to the unloaded beam in order to return it to its undeformed (straight) position?

Solution

(a) From eqn. (3.2) the partially plastic moment carried by a rectangular section is given by

Thus, for the simply supported beam carrying a u.d.l., the maximum B.M. will be at the centre of the span and given by wL2 Bo,, , -) BMmix = — = -^[3D2 - d ]

(b) From the above working

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