JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II STRUCTURAL ANALYSIS – I Previous Question Paper (March - 2022 - R15)

To determine the forces in all members of the truss using the method of sections, we first calculate the support reactions. Assuming a standard cantilever or simply supported truss configuration, we apply the equations of static equilibrium: ΣF_x = 0, ΣF_y = 0, and ΣM = 0.

The method of sections involves cutting the truss through a maximum of three members whose forces are unknown. By taking moments about a point where two of the three unknown forces intersect, we can solve for the third force directly. This process is repeated by selecting different sections until all member forces are determined.

The steps are as follows:

1. Calculate external reactions at the supports by considering the global equilibrium of the entire truss.
2. Identify a section that cuts through the members of interest, ensuring no more than three members with unknown forces are cut.
3. Apply the equilibrium conditions to the free-body diagram of the cut portion. Summing moments about the intersection point of two unknown forces allows for the calculation of the third unknown force.
4. Repeat the process for other sections or use the method of joints for remaining members if necessary.
5. Assign a positive result to indicate tension and a negative result to indicate compression for each member force.

By systematically applying these equilibrium equations to the chosen sections, the internal forces in all members are resolved based on the applied external loads and geometry of the truss.

To determine the forces in all members of the truss using the Method of Joints, follow these systematic steps:

1. Calculate Support Reactions: Apply the equations of static equilibrium (ΣFx = 0, ΣFy = 0, ΣM = 0) to the entire truss. Determine the vertical and horizontal reactions at the pin and roller supports.
2. Identify Zero-Force Members: Inspect the joints to identify members with zero internal force, such as joints where two non-collinear members meet with no external load, or three members meet where two are collinear.
3. Analyze Joints Sequentially: Start at a joint with at most two unknown member forces. Draw a free-body diagram for the joint, showing external loads and internal member forces (assumed to be in tension, pulling away from the joint).
4. Apply Equilibrium Equations: For each joint, solve the two scalar equilibrium equations:
   ΣFx = 0
   ΣFy = 0
5. Propagate Results: Use the calculated forces from one joint as known values for adjacent joints. Continue this process until all member forces are determined.
6. Interpret Results: A positive result indicates the member is in tension, while a negative result indicates the member is in compression.

By systematically applying these equilibrium conditions at every joint, the magnitude and nature (tension or compression) of the force in each individual truss member are fully defined.