Question

Q5: Using force method, determine the reactions of the supports for the beam shown in Figure (5). Then draw shear and bending moment diagrams for the beam. EI is constant. Use conjugate beam method to determine deflections.
I need it in 30min or 1 h

6 m 50 KN 200 kN.m 22 А В. С 9 m to 3m

Answer 1

Complete solution is given below.

1} DOI = hy-3 = 1 3. Assume reaction at b'as redundant. 27 primary structure (using principle of superposition) 200 kom At 50KN B 6m 3.De + 6 m 12m 6m 3 3 200 EL 300 EI onjugate beam MEI diagram 9-353- Coningate beam M diagram EL M = 200 KNM = 300 KNM M = 50x6 AB2 ABI= Bm @ B! in Conjugate bean BM @ 6' in Conjugate beam fax.2001 (1) (3 + 8x6 EL - {* xox one] (s+ 4 con AB2= 8100 El

AL = AB1 + 4B2 6300 ET + 8100 EI 14400 [AL] EI 37 Generate flexibility matrix > Apply on't load at B (Assume caction in the direction of loads) m = 1x9 = 9KNM A 3 9 I KN A 오 EI Conjugate beam diagram м de Bm @ 8!= {1x9x2] [3x9] 11 11 Jo 243 EI 243 12 [F] EI

47 Appley flexibility equation [P] {F}*' { [4) – [42]} Ro Mare - -/4400 11 El (243] [7 Ro 59.26 KN Acting down words Negative sign indicates opposite direction Ro= 59.26 KN * Acting upwards. Zfy = 0 Ay + RB so KK 9.26 KN AY MA = (58x 6)-( 59.26x9) + 200 MA • 33.34 kNm