Question

25 points For the beam shown below: (i) Determine the reactions RA and RD. (ii) Sketch the (a) shear, and (b) bending moment diagrams under the free body diagram. (iii) What is (a) the maximum moment on the beam and (b) its location. M=4500 lbft 3000 lb 3ft 1

Answer 1

3ooout m= 4500 It ft C - 6ft 3 ft TRD Force balance in the vertical offreation - RAT RD = 3000 lb Moment balance about A Positive ROX 12 - 4500 - 3000x 3=0 RD = 1125 lb so Ro = 3000 - Rp Color = (3000-1125) = 1875 It for Shear force d&agram - I Positive I Negative B 키Va I from A to

= - 1875 at (x) = -(RA) B To Do from 3000 lb RA ula) . 3ft. = -(RA-3000) - (1975-3000) = 1125 lb 1125 Shear Force (16) Deestance - -1875t For from bending moment diagram I to B Possitive 2 Negative = I-RA ) - 1875 m(x) from B to 3000lt. B A h - 3 ft m(x) = -(-RO (3+2) + 3000x] -5625 - 1875 et 3000x - - 1125x + 5625

From D to a 3oooub 95oolb-fa 2 - 3 ft x 6 fit m(x) = -1875 (stre) + 3000 (6 t ) - 4500] -- - 16875-1875 et 18000+3000x - 4500] = (-1125x +3375) - 5625 73375 Bending F moment (lb-ft Y ton Dyston ce ift) -1125 - - - - - (iii) on beam = 5625 lb-fat. maximum at a moment point B