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3.2 (B). A 50 mm x 20 mm rectangular-section beam is used simply supported over a span of 2 m. If the beam is used with its long edges vertical, determine the value of the central concentrated load which must be applied to produce initial yielding of the beam material.

If this load is then increased by 10% determine the depth to which yielding will take place at the centre of the beam span.

Over what length of beam has yielding taken place?

What are the maximum deflections for each load case? Take it, = 225 MN/ra2 and e = 206.8 GN/m2.

33 (B). A steel bar of rectangular section 72 mm x 30 mm is used as a simply supported beam on a span of 1.2 m and loaded at mid-span. If the yield stress is 280 MN/m2 and the long edges of the section are vertical, find the loading when yielding first occurs.

Assuming that a further increase in load causes yielding to spread inwards towards the neutral axis, with the stress in the yielded part remaining at 280 MN/m2, find the load required to cause yielding for a depth of 12 mm at the top and bottom of the section at mid-span, and find the length of beam over which yielding has occurred.

3A (B). A 300 mm x 125 mm I-beam has flanges 13 mm thick and web 8.5 mm thick. Calculate the shape factor and the moment of resistance in the fully plastic state. Take ay = 250 MN/m2 and /„ = 85 x 10 m .

35 (B). Find the shape factor for a 150 mm x 75 mm channel in pure bending with the plane of bending perpendicular to the web of the channel. The dimensions are shown in Fig. 3.46 and z = 21 x I0-6 m3.

150 mm

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