JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year STRUCTURAL ANALYSIS Previous Question Paper (March - 2022 - R16)

For a fixed beam of span L = 4 m with a point load W = 80 kN at a distance b = 1 m from the right support (a = 3 m from the left support), the fixed end moments are calculated using the standard formulas:

To find the vertical reactions R_A and R_B, we consider the equilibrium of the beam. Let R_A and R_B be the vertical reactions at the left and right supports respectively. Taking moments about B:

Using vertical equilibrium:

The Bending Moment Diagram (BMD) is constructed by superimposing the free bending moment diagram (a triangle with peak moment M_free = (W * a * b) / L = (80 * 3 * 1) / 4 = 60 kNm) over the fixed end moment diagram (a trapezoid defined by M_A = 15 kNm and M_B = 45 kNm). The net bending moment at the load point is 60 - [(15 * 1 + 45 * 3) / 4] = 60 - 37.5 = 22.5 kNm.

To determine the forces in each member of the truss using the method of joints, we first calculate the support reactions. Assuming a standard truss configuration (e.g., a triangular truss with span L and height h), we apply the equations of static equilibrium: ΣFx = 0, ΣFy = 0, and ΣM = 0.

1. Calculate the reactions at the supports by taking moments about one support to find the vertical reaction at the other.
2. Identify a joint with at most two unknown member forces.
3. Apply the equilibrium equations at that joint: ΣFx = 0 and ΣFy = 0 to solve for the two unknown forces.
4. Proceed to adjacent joints, using the previously calculated member forces as known values until all member forces are determined.
5. For each member, a positive result indicates tension, while a negative result indicates compression.

The force in any member AB is found by resolving the forces at joint A into horizontal and vertical components. If the calculated force F_AB is positive, the member is in tension; if negative, the member is in compression.