Calculate the vertical displacement at d and the

Question

Problem-1

Pin-connected truss structure is shown in Fig.1. The concentrated forces are applied at E (10,000 lb) and F (15,000 lb). Point A is connected to a solid foundation and B is supported by a roller. Young's modulus E = 10x10⁶ lb/in². As shown in the figure, the total height and length of the structure are 6 ft and 16 ft, respectively.

1) Solve the reaction forces (A_x,A_y, B_x, B_y ) at Pont A and B

1-2) Calculate the deflections (δ₁, δ₂, ......δ₉) for all the truss members (indicate if each truss is tensile (+) or compressive (-) with sign

1-3) By applying the virtual forces of P and Q in energy method, calculate the vertical displacement at D and the horizontal displacement at B

Free-Body Diagram should be recalculated with P and Q. Then, contrary to 1-1), an internal force at each member (Fi) is the function of P and/or Q. The horizontal reaction force R3 must be also considered due to Q (Please refer the below figure). For δ at D, Calculate

Then, apply for P=0. For δ_H at B, Calculate Then, apply for Q=0.

1-4) Now B point is fully supported as shown in the below figure (no movement). Find out the horizontal reaction force of Q and the vertical deflection at D by using Energy method