Question

Determine the equations for deflection (y) and slope (0) as a function of x for the beam below. What is the deflection at A and the slope at A when E = 200 GPa and I = 65.0 (109) mm“? 10 KN 10 kN m

Answer 1

Answer: low B RB 7 BOMB 2м At At the fixed and the Reactions are RB, MB and RB = 10 kn MB = 10x3 + 10 = 40 kNEM. a is taken from A to B so Moment equation for the Beam :- Mx= -106-10 { a = o to 3 to 3m} 3 So we know that E1.04 "Mr qu? -> EI 02y 어지고 Now -102-10 Integgeting both siete -100 -lon too an a) El. dy -10 22 » El dy = -52²-lonta qu Again integrating =) Eloy - 5 2 - 10 stere the = El.y - 23 -5 u²t qu the To find ei and C₂ we apply Bounc endary condition. so at a=3, y=0 and at u=3, dy have to 20 da

3 so EL. O = och} text axs - exter 20 at 2 = 3 =) olo =2tl28 again EIXO = -5832-108374 {ayo x=3} =0, at u=3 Yax o -45-30th -> c=75 so (2=90-7503 = C2 = -135 so Equation of deflectionly) yo o (3x+52°+752-185) equation of slope(0) o=dy -su-lon t7 Х du EI | Ary At point A:(2-0) EI so yo (0-0 to-1)-135 and ED - (inoxlok wak) x fox tex 1602 mt) EI 13000 KNima -135 =-0.01038 M =-10.38 mm so deflection at 1, YA = 13000 so ya = 10.38 mm in down word direction Ary Now Slope at A (A) (at u=o) 75 OA 3 " 75 13000 rdian EI =OA = 0.00577 erdian Supl