Determine the force in members BC, CH, GH, and CG of the truss and state if the members are in tension or compression.
The Correct Answer and Explanation is :
To determine the force in members BC, CH, GH, and CG of the truss and whether they are in tension or compression, follow these steps:
Step-by-Step Solution:
- Determine the Reactions at the Supports:
Begin by calculating the reactions at the supports using equilibrium equations. For a planar structure in static equilibrium:
- ( \Sigma F_x = 0 )
- ( \Sigma F_y = 0 )
- ( \Sigma M = 0 ) (taking moments about any point to solve for unknown forces).
- Apply the Method of Joints:
The method of joints involves solving for the forces in the truss members by considering equilibrium at each joint (node) of the truss.
- Start at a joint where there are two unknown forces and solve for them using the equations of equilibrium.
- Continue this process for other joints until the forces in all members are found. For the given truss, begin at a joint where the number of unknown forces is minimal. At each joint, apply the equilibrium equations in both the x and y directions.
- Method of Sections (Optional):
Alternatively, the method of sections involves cutting through the truss and solving for the forces in the members that are cut. You’ll take the section to expose the internal forces of the members you’re interested in (BC, CH, GH, and CG) and apply equilibrium equations. - Analyze the Force Results:
After solving for the forces, determine whether each member is in tension or compression:
- If the force is pulling away from the joint (tensile force), the member is in tension.
- If the force is pushing toward the joint (compressive force), the member is in compression.
Conclusion:
Once you solve for the forces in BC, CH, GH, and CG, analyze their direction to determine if the members are in tension or compression. Remember that the direction of the force will tell you whether the member is being stretched (tension) or compressed (compression).
If you can share the specific values or layout of the truss, I can guide you through the calculations with more detail.