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Therefore length of beam over which yielding has occurred

(d) For W = 1500 N the beam is completely elastic and the maximum deflection, at the centre, is given by the standard form of eqn. (5.15)^:

WL3 1500 x 23 x 12

With W = 1650 N and the beam partially plastic, deflections are calculated on the basis of the elastic core only,

Example 32

(a) Determine the "shape factor" of a T-section beam of dimensions 100 mm x 150 mm x 12 mm as shown in Fig. 3.38.

(b) A cantilever is to be constructed from a beam with the above section and is designed to carry a uniformly distributed load over its complete length of 2 m. Determine the maximum u.d.l. that the cantilever can carry if yielding is permitted over the lower part of the web to a depth of 25 mm. The yield stress of the material of the cantilever is 225 MN/m2.

Solution (a)

Shape factor =

fully plastic moment maximum elastic moment

To determine the maximum moment carried by the beam while completely elastic we must first determine the position of the N.A. Take moments of area about the top edge (see Fig. 3.38):

(100 x 12 x 6)+ (138 x 12 x 81) = [(100 x 12) + (138 x 12)] y 7200 + 134136 = (1200 + 1656) y y = 49.5 mm

88 x 37.53"1

= +[121.29+ 121.81 — 46.4] 10 = 6.56 x 10"6 m4

10"12 m4

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