Please provide a detailed solution, showing steps. A structure of truss is loade

Question

Please provide a detailed solution, showing steps.

A structure of truss is loaded as shown in the Figure1 and is in equilibrium. The truss is supported by a pin joint at A and two cables BD and CE which are capable of supporting tension only. The structure is geometrically symmetrical about the y-axis. Members DS and DT and also AV and Aw have equal length (DS DT, AV = AW) and -68.. The weight of all members is neglected. Determine (In all c need to be shown) free body diagrams a. The reaction forces at the point A b. The internal force in the cables c. The internal force for members listed in the table (copy and complete the table). Hint:1. The columns AD and AE can be seen as a two-force member respectively 2. Only one of the cables is in tension. 4 x 2.5 m 13 KN D M 16 KN 13 KN 20 KN 20 KN 24 KN 1.2 m

Explanation / Answer

from the given data
let tension in the left cable be T1 and in the right one be T2
let reaction at A = Rx + Ry

then from force balance in both directions
Rx + (T2 - T1)cos(alpha) + 13,000 + 13000 + 16000 = 0
Ry - (T1 + T2)sin(alpha) - 64000 = 0
here alpha = 68 deg

from moment balance about A
(42000+ T2*cos(alpha) - T1cos(alpha))*sqroot(16^2 - 5^2) + (24000-20,000)*10 + (T2*sin(alpha)- T1sin(alpha))5 = 0

as only one of the wires is in tension, T2 = 0
(42000+ - T1cos(68))*15.198+ (24000-20,000)*10 + (- T1sin(68))5 = 0
hence the equations become

Rx -T1*0.374 + 42,000 = 0
Ry -T1*0.9271 - 64,000 = 0
-10.329T1 + 678316 = 0

hence
T1 = 65671.023 N
T2 = 0 N
Rx = -17,439.037 N
Ry = 124883.6054 N

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