Question

For the beam shown, a) Draw the bending moment diagram, b) Determine the maximum normal stress due to bending. 300 N 400 N/m D B С Hinge 200 N.m 2.00 m 2.00 m 2.00 m 300 mm 750 mm N A x = 292 mm 560 mm NA: Neutral Axis

Answer 1

J.M.D. Given 3ooEN 400 N/m 200 Nm t 2m - t - 2m 300mm A 750mm 560mm- BMD - ? 292 6 Max Nonmall stress due to bending - Since 615 is Hinge 400N/m Moment About C=0 2m- No X2 + 400 X2X1 Tvo Vc Vo=400 N +Vet Vo = 400 x2 Vc = 40082 - 400 = 400 N Zoon D Never 200 Nm -2m € Vc = 400 N VA VA= 300 of you Too N EM =) MA + VAX 4 - 300 x 2 + 200 =0 MA = -2400 Nm le [MA = 2400 Nm G

Now Zoon 400Nm 2400 Nm Iz am +200Nm ID 1400 Toon Sign for BMD clo tre BMD In CD Parabola Mx = + 4000n - 400 x 2² At n=2m . Me=0 Nm In BD straight line n=4m My = 4000 - 400 x 2x (no) MB = 400x4 - 400 x 2 x (41) = - 800 Nm at B there is a jump of 2000m 200 Nm + 800 1000Nm 1 2400 Nm 문 Mmax x Imax

Momax = 2400 Nm Yman 750-292 = 458 mm - 0.458 m I= d? (9²+ 4a6t6² 36 (ato) I= 7503 (30027 4x300 x 5604 560²) 36 (3004 560) I= 0.014656 m4 Imax = 0,458 2400 0.014656 Umax = 14996.86 N. ma