JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II STRUCTURAL ANALYSIS I Previous Question Paper (November/December - 2020 - R15)

The tension coefficient method is an efficient approach for analyzing statically determinate trusses. For a member connecting joints A and B, the tension coefficient t_AB is defined as the force in the member divided by its length L_AB. The equilibrium equations at any joint are given by:

To solve for all member forces, follow these steps:

1. Calculate the support reactions using global equilibrium equations (Σ F_x = 0, Σ F_y = 0, Σ M = 0).
2. Establish a coordinate system for all joints (x_i, y_i).
3. Write the equilibrium equations for each joint in terms of tension coefficients t_ij, where t_ij = F_ij / L_ij.
4. Solve the resulting system of linear equations to find all t_ij values.
5. Determine the force in each member by multiplying the tension coefficient by the corresponding member length: F_ij = t_ij × L_ij.
6. A positive result indicates tension, while a negative result indicates compression.

By systematically applying these equations to each joint, the internal forces are determined directly without the need for resolving forces into trigonometric components at every step.

To determine the forces in all members of a truss using the method of sections, follow these systematic steps:

1. Calculate Support Reactions: Apply the equations of static equilibrium (ΣFx = 0, ΣFy = 0, ΣM = 0) to the entire truss to find the external reactions at the supports.
2. Select a Section: Pass an imaginary cutting plane through the truss such that it cuts through no more than three members whose internal forces are unknown. The section should divide the truss into two distinct parts.
3. Isolate a Part: Choose one of the two parts of the truss and draw its free-body diagram. Include all external loads, support reactions, and the internal forces of the cut members.
4. Assume Force Directions: Assume the internal forces in the cut members are in tension (pulling away from the joint). If the resulting calculation yields a negative value, the member is actually in compression.
5. Apply Equilibrium Equations: Use the three equations of equilibrium on the isolated section:
   • ΣFx = 0
   • ΣFy = 0
   • ΣM = 0 (Choosing a point where two of the unknown forces intersect simplifies the calculation significantly).
6. Repeat: If the truss is complex, repeat the process by taking different sections until all member forces are determined.

By applying these steps, the internal axial forces in the members are solved algebraically. Ensure that the chosen section cuts through members that allow for the sequential calculation of unknowns.