Question

Figure 4.14The uniform 1-ton (2000 lb) beam DD roller pinned to the truss structure at point B in Figure P4.147. Find the reactions onto the structure at A and C. 5 ft 125 Roller 4 ft 4 ft 395îtugu, 4 ft A c 733 7 lb. Figure P4.147
the ans at the back of the book, I have written with pen. please help!!

Answer 1

AT A At c. - Axens fa FCA R 600d. Z or 5 O AY At B 6000

Solution :- Weight of beam BD, W = 2000 lb (given): RB is the reaction at B. from given figure tano = 5 O = 22.620 .ssum ram BD Assume free body diagram for BD Emo=0 -Re) () (W6050) 5) = 0 RB = 2000 cos 22.62 ) RB = 923.08 167

consider equilibrium position at B : E Fx = 0 FBC GoS60°- FRA COS60° + Rosin 0 - 0 FBA - fec - 923.08 sin 22.62° COS 60° FBA - FBC = 710,06 { fy=0 Ff8c-sin 60° -fra sin 60° - RBcos 0 = 0 IFBA + FBC - 923:08COS 22.62% Sin 600 FBA + FBC - - 983-89 — ☺: By solving equations © and @); we get | FB4 = - 136.915 lb IFBC = - 846.975 1b 1:. Force member AB is FBA = 136.915 16 i force in member BC is foc = 846.9751610)

Consider the equilibrium position at C:. Efre = 0 - FCA - FBC Cos60º = 0 IFCA = 846.975 cos 60°. FCA = 423 - 49 lb. !. force in member CA is fca = 423:49 16 (O) {fy=0 cyt FBC sin 60° = 0 ily = 846.975 Sin 60° ly = 733.5 lb. :. Reaction at Cis (y = 733.5 16 a

consider the equilibrium position At A? {fx=0 - Are + FBA COS60° + FCA = 0 Ax = - 136.91500360° +423.49 Axa: 35503 lb Horizontal reaction at A is Ax=355.03 lb Efy = 0 Ay + FBA sin 60° -O Ay = 136.915 sin 60 ° Ay = 118:57 16 I Vertical reaction at A is Ay = 118.57 16

The problem is solved by assuming thereactions in x,y plane. kindly note that.

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