Question

A cantilever beam is shown in the figure below. Using the second-order integration method (moment-curvature equation): (a) Determine the equation of the deflection curve v(x) and draw the curve (6) Determine the deflection ve and the slope OB at B. Consider Young's Modulus E = 210x10° Pa. 2N А 200 mm B > 10 m 100 mm

Answer 1

Giren : faget E: 210 x 109 N / m² 3 bd? I Oolx 0.2 12 ma 12 15000 2N A Lama B MAY K lom Reaction : > EFxzo Ax=0 Ery=o Ay=en EMA » MA-2x10 = 0 MA = 200-m @ 2 N J? lay MA B Х we know that, Er dv B.M at Section xax dx² » EE d²y dx² Ay [x] - MA[x]" 2V EL = 2[x] - 90 [x] dx²

Page 2 antegrating on both sides worto x' then 0 Ed du du 2 [x] 20 [x] + a) 2 dv du is slope o at X=0, ie, slope is zero then , at support A, 오 ED (0) = 2[0]? 20[0] +ci 2 CE substitute ci value in equation @ then Ealo) [x]2-2000] Integaating on both gides the equation o w.antix then, EM) = 677* - 20 [4]" +42 -> at x=0, t.e., at support A, deflection (v) then, Ello) o-otc2 (=o substitute ce value in equation FI (VE co?- 20 x? I then 2 3

Page 3 Equation of deflection curve V(10) = é [ 10x2 - Deflection curve kelastic corre or deflection Curre Ne=? substitute X= lom in equation @ then 102 EL VB = 10 20 x 2 VB = (2000) (210 x 109 x 15000 VB 21000 am (ve sign indicates deflection is downwardy -0.048 mm Apa? substitute x=lom in equation then (10²_20xb) -! radians. (210X109x TSOOD 140000 OB =