Question

1 5. Consider a thin cantilever loaded as shown in Fig. P5. Assume that the bending му stress is given by Ox= -2xy and oz = Txy = Tyz = 0. What will be the stress componeent in terms of x and y? (a) oy = (3hºy - y2 – 243), (b) oy = 5(3hºy - y3 – 24%), (c) oy = (3hạy - y3 - 2h), (d) o, = (3hy - y3 - 2h3). (e) none of above 2h o. Fig. P5 Fig. P6

Answer 1

Given ox I For thin cantileves, dou tatay + fx=0 Jx ry Now, fx=0 and ox is given, Integrating 0 Gry - pay 2 t to Cx). 2I Now, from Boc., Exy)yah = 0 & thus, f (x) = - pach? 2 I i dłny to ay 0 - 2x²y) Txy = Hence, from Tay=-Px Ch²yz) 2 I Pxy I 0 page - a

f₂ Cx) = -ph3 Considering the y-component, +2 Try + Fy = 0 3I doy ry Hence, from Oy 2I Ph3 by ang 31 is taken =0 and Try from o 3 inoy E 4 3 I 2 doy -d an ( Px Ch² ((chat) he 2I | Jy (2²-43 l (3h²y_y (362 y = f ( 3h2y_y3 2h3) Read Answer option-b loya doy PCh² - y2) 2 he 2I Upon integration, y = P. yCh²- y 25 + £2 (4) From B.C., (y) y = h = 0 -Ph (262) hence, f₂ Cx) ZI

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