A king post truss of 8 m span is loaded as shown in Fig.33. Find the forces in each member of the truss and tabulate the results. Fig.33
Question
A king post truss of 8 m span is loaded as shown in Fig.33. Find the forces in each member of the truss and tabulate the results.
Fig.33
Solution
To solve for the forces in each member of the king post truss with an 8 m span, we'll follow the structured approach outlined below.
1. Break Down the Problem
- Identify the geometry of the truss and the locations of applied loads.
- Determine the support reactions due to the applied loads.
- Use methods such as the method of joints or method of sections to find the force in each member.
2. Relevant Concepts
- Equilibrium of Forces: The sum of vertical forces and the sum of horizontal forces must equal zero.
- Moment Equilibrium: The sum of moments around any point must equal zero.
- Truss Member Force Calculation: Assuming members are pin-jointed, we can analyze one joint at a time.
3. Analysis and Detail
Assuming a simple case where we have joint loads (like P at the center) and that the truss is symmetric, the following would apply:
-
Calculate Support Reactions:
- Let and be the reactions at supports A and B respectively.
- Using the equilibrium equations: From these, you can solve for and .
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Force Distribution in Members:
-
Start at joint A: is the force in the member AC.
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Move to joint C: where is the angle between member BC and the horizontal.
-
-
Continue analyzing other joints (D, B, etc.) using similar equilibrium equations until all member forces are calculated.
4. Verify and Summarize
- Check calculations for consistency (do the forces balance out when summing at each joint?).
- Present the forces in a tabular format once calculations are verified.
Final Answer
Here’s an example of how the forces might be presented, assuming values from calculation:
Member | Force (kN) |
---|---|
AC | |
AD | |
BC | |
BD |
Note that exact force values depend on the specific loading and geometry detailed in Fig. 33, which was not provided. To perform these calculations, you would need to substitute values into the equations based on that diagram.
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