Question

2. (30 pts) The framework consists of three A-36 steel beams AB, CD, and BC. Each beam has a flexural rigidity EI (kip-ft?). The loading condition is shown in the figure below. (note: beams AB and CD are cantilevered beams subjected to uniform loads 5 kip/ft for 8 ft. Beam BC is a simple supported beam subjected to a force 15 kip in the middle of the beam). Appendix C of deflection charts is on the textbook. a) Calculate the support forces/moment at point D on beam DC. b) Draw shear and moment diagrams of beam DC. Indicate the max bending moment, max shear and their locations. c) Calculate the deflection at point C. (hint: from beam DC) d) Calculate the deflection at point G. (hint: combinations of two beams AB and BC) W=5 kip/ft 15 kip A W=5 kip/ft B D 8 ft 8 ft 8 ft 16 ft

Answer 1

Given member BC is simply supported beam- 15 kip B ВС 4 Re Ro Est 8ft Rct Ro 15 kip ( :: Efy =o) Take moment equilibrium about point 'c" EME RB+16 15*8 → Re = 7.5 kips Rc = 7.5 kips Rc=715 kips skip list Mp TI RD D ost

EFy = 0 RD 5+ 8 + 7.5 Rp (vertical reaction at support) 4715 kip, Take moment equilibrium about point D T Mo 7.5*16 t 5*8*8/2 Mo 120 + 160 » Mo 280 kataon kipn-ft 5 kiplift 75 + D 280 947.5 475 kip 7.5 kip, D shear force diagram monimum sheay force will OCCUY. At point D

D 60 kips-ft Hogging Bending moment diagram manimum bending moment occur at support Do from principle of virtual work 11 Sm M m M da ET virtual moment due to virtual external force apply unit load at point

(-x)+(-7.5x) dx + - 5+ (x-8)(2-8) du En 8 o sodel . Sosan e jaso sa curing -) = 1 ET [ (52) )** (2531)(1837) 8 X fis s=1 ET al 1280 + 8960 + 38400 + 15360 + (-53760) A = 10240 fte ЕТ due "Ğ only to load on t Deflection of point simply beam: Supported 3 3 PL 154 (16) A= 48E1 48 -1 -) 1280 ET

Both the enda of cantiliver beams cand B are | این deflected by same amount 10240 ET 4 i Total deflection of point 'G =deflection of can bliver + deflection of simply supported beam 102410 ET + 1280 El :: deflection of G 11520 ft Е1 plecne give rating