Question

1.2 (20 Marks) A beam of rectangular cross section (width b and height h) supports a uniformly distributed load along its entire length L. The allowable stresses in bending and shear are all and Tallow, respectively. a) If the beam is simply supported, what is the span length Lo below which the shear stress governs the allowable load and above which the bending stress governs? b) If the beam is supported as a cantilever, what is the length Lo below which the shear stress governs the allowable load and above which the bending stress governs?

Answer 1

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Anste ه) ---- WN i immmmmmmmmmaa R- since, simple supported. RA + Rp - we EMA = - RB XL = WL x H - L- le force Boll. = Bending moment. Sef. = Shear PA = Rp = WL I Bima At any section xx, (sty = – Wt twee. (s. 7) max = why And sit =0 @ x=4 - Bime will be ma . At any section xx (BM), = With - WX2 4 Bima will be maximum @ x=²

& max = ? allow = 3x tang - * Callow - 3 with W= 1bh calonat a 543 from froom 0 0 16 xall розL 3L 4662 x Gallow เo) Gollow Tallow uif LLLO If L LO & - Callow Carrow governs goverens allowable load. allowable load.

R = WL = (s.to) max And MA = wLX - _ _ W12 = (B.M. Now, cay = (st) mass - w ► los estado y Tennes 0 from abh & & Callow - bh 2 x farow h (Gallow ) 30 Ti - z rallow) . If If L<to l>Lo allow Sallow goverens allowable load, goverens allowable load

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