Question

Consider the simply supported beam and loaded as shown in the M figure. Perform the following: 1. Determine the support reactions. 2. Plot SFD and BMD 3. if L=9 m, the beam will fail when the maximum shear force is Vmax= 5 kN or the maximum bending moment is Mmax=22 kN.m. Determine the largest couple moment Mo the beam will support.

Answer 1

) . Mo po A RB RA k Nir =0 EMA a hinge, since 'A is - = Mo RB X L Mo =) RB )) Σ V = 0 Mo - =0 RA RA TRB L RA --Mo L so support geactions are 8 RB Mo L CS Scanned with CamScanner

A Mo B I mo Mo L L K L So Shear force Diagram SFD Mo mo Mo L B A Bending moment at a = from end 'A' 2 Mo Bm = Mo x x -mo x t a mo L Mo BM -Mo 2 Kat Bending moment at mas from end 'B' Bm= Mo XX Mo Mo 2 Х & ÅNEN 1 J M 2 mo BM= ܐ 2 SO BMD re Mo 2 Đ B 0 мо 2 cs Scanned with CamScanner

5 KN (3) given, L = 9m maximum Shear force (Vomax) or maximum bending moment = 22 kn m So first considens maximum Shear force 9n Shear force diagramo, maximum shear force, Vanax Mo L Vmax Mo ㄷ 5 KN Mo 5XL =5X9 KNM Mo 45 KNm comsideriong maximum beording moment go besding moment Diagram, Mo maximusos beording moment, Bmax BM, max Mo 2 = 22 KNM Mo = 44 KNM so for beam not to fail maximum Couple mo homent allowed , mo = 44 knon. canned with CamScanner