Question

6. For the following figure, determine A. The equations of the shear and bending-moment curves for the beam and loading shown B. The maximum absolute value of the bending moment in the beam. 2 :- - (1+3)

Answer 1

wa = Wo will + m2) В — L * Note: For ease the . of calculation, we can treat given variable load as two leado li) A uniform doad of intensity wo and 40) varaying load w(u) = For varying doad: & win) A ton² 2 Area of loadling n = now(n) 3 Won 3 L² h Centroid of loading (2) 4 Now calculate support reactions: MA L

Total loading Area of loading diagram 3 = Wolt wo 3 2² = woL t wol 3 W 4 WOL 3 ZFy Ay W – 0 Ay 4 wol 3 Centraid of EM R او بیا - MA - WOLI Z will x 3 x M اولا W L 2 3 wol² 4 A + 4 F1A = 0.75WL a). Equation for Shear force 0.75612 AS DIT V(") 17 M(M) n ful 4 wol 3 V (n) Wo.l - won 31² Scheeet

Equation for bending moment M(u) = w.Lin - Women Wome - 6-950,1 4 Won' 12 12 won² 4 woln - 3 3 wol² + 2 will be ( B ). Maximum of B.M absolute value support A at MA MA = Mmax to 3 3 wol² =0.75WL²