Determine the force in each member of the truss shown by the method.
Understand the Problem
The question is asking to determine the forces in each member of a truss structure using a specific method, likely involving static equilibrium analysis and possibly the method of joints or sections.
Answer
The forces in the truss members must be calculated using equilibrium equations, which yield member forces depending on the analysis at each joint. For detailed values, specific calculations need to be performed based on the information provided.
Answer for screen readers
The forces in the members of the truss structure will vary depending on calculations from the method of joints and support reactions.
Steps to Solve
- Identify Support Reactions
First, determine the reactions at supports A and G. Use static equilibrium equations:
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Sum of vertical forces ($\Sigma F_y = 0$): $$ R_A + R_G - 40 - 40 - 80 = 0 $$
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Sum of moments about point A ($\Sigma M_A = 0$): $$ R_G \cdot 24 - 80 \cdot 4 - 40 \cdot 10 = 0 $$
- Calculate Support Reactions
Solve the equations from step 1 to find values for $R_A$ and $R_G$.
- Apply the Method of Joints
Start analyzing the joints to find the forces in each member.
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Begin with joint A:
- The only supporting forces at A are $R_A$ (from above) and the forces in members AB and AH.
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Use the equilibrium equations at joint A: $$ \Sigma F_x = 0 \quad (F_{AB} = 0) $$ $$ \Sigma F_y = 0 \quad (R_A - F_{AH} = 0) $$
- Continue to Other Joints
Proceed to analyze each joint in the truss, such as:
- Joint B
- Joint C
- Joint D
- Joint E
- Joint F
- Joint G
At each joint, resolve forces into horizontal and vertical components, applying the equilibrium equations.
- Record the Forces in Each Member
As you calculate the forces in members, keep a record indicating whether each member is in tension or compression.
The forces in the members of the truss structure will vary depending on calculations from the method of joints and support reactions.
More Information
In truss analysis, the method of joints is a systematic way to find the internal forces by solving equilibrium equations at various joints. The forces can result in either tension (pulling away from the joint) or compression (pushing towards the joint).
Tips
- Forgetting to account for all external loads when calculating support reactions.
- Not considering the geometry of the truss, which can lead to incorrect force components.
- Failing to apply the equilibrium conditions correctly at each joint.
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