JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year STRUCTURAL ANALYSIS I Previous Question Paper (August/September 2022 - R15)

To determine the forces in members BC, CG, and EF of a pin-jointed truss, we employ the Method of Sections. This method involves cutting the truss through the members of interest and applying the conditions of static equilibrium to one of the resulting segments.

1. Global Equilibrium: First, calculate the support reactions at the external supports (typically pins or rollers) by applying the equations of static equilibrium for the entire truss: ΣF_x = 0, ΣF_y = 0, and ΣM = 0.

2. Section Selection: Pass a section line through members BC, CG, and EF. This section divides the truss into two parts. Choose the part that is simpler to analyze or has fewer external forces.

3. Equilibrium of the Section: Apply the three equations of equilibrium to the chosen segment:

4. Calculation: By taking moments about a point where two of the unknown member forces intersect, the third unknown force can be determined directly. Repeat this process for the other members. Tension is indicated by a positive result, while compression is indicated by a negative result.

5. Verification: Ensure that the internal forces calculated satisfy the equilibrium of the joints connected to these members to verify the accuracy of the section analysis.

To determine the forces in each member of the truss using the Method of Joints, follow these steps:

1. Calculate Support Reactions: Determine the external reactions at the supports by applying the equations of static equilibrium: ∑F_x = 0, ∑F_y = 0, and ∑M = 0.
2. Identify Zero-Force Members: Inspect the joints to identify members with zero internal force, typically where two non-collinear members meet at an unloaded joint or where three members meet at a joint with two being collinear and no external load applied.
3. Select a Joint: Start at a joint with at most two unknown member forces.
4. Apply Equilibrium Equations: At the chosen joint, resolve all forces into horizontal and vertical components. Apply ∑F_x = 0 and ∑F_y = 0 to solve for the two unknown member forces.
5. Proceed to Adjacent Joints: Move to the next joint where there are now only two unknown forces, using the values calculated from previous joints.
6. Determine Nature of Force: If the calculated value is positive, the member is in tension; if negative, the member is in compression.

Repeat this process until the forces in all members are determined. Ensure that the final joint satisfies equilibrium as a check for the calculations.