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QuestionMathematics
** 2.** [10pts - Question 3.19 - Textbook] Determine the force in members AE, BE, and BC of the truss using the method of Sections. Indicate if the members are in tension or compression. (Some answers: BE = 27.5 k (C))
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Step 1:I'll solve this truss problem step by step using the method of sections:
Step 2:: Identify the Approach
The method of sections involves cutting the truss through the members we want to analyze and using equilibrium conditions to determine the forces.
Step 3:: Draw the Free Body Diagram
- Apply equilibrium conditions: $$\sum F_x = 0$$, $$\sum F_y = 0$$, $$\sum M = 0
- We'll cut the truss through members AE, BE, and BC - We'll use the left portion of the truss for our analysis
Step 4:: Calculate Reactions at Support
- At pin A: Vertical reaction $$R_A = 30 \text{ k}
- Horizontal reaction H_A = 0
Step 5:: Analyze Member BE
- Cut through BE and adjacent members - Apply moment equilibrium about point E - Use known loads and distances
Step 6:: Moment Equation for Member BE
F_{BE} = 30 \text{ k (Compression)}
30(4) - F_{BE}(4) = 0
Step 7:: Analyze Member AE
F_{AE} = \frac{30}{\sin(45°)} = 42.4 \text{ k (Tension)}}
- Resolve forces in x and y directions
Step 8:: Analyze Member BC
- $$F_{BC} = 22.5 \text{ k (Compression)}}
- Use remaining equilibrium conditions
Final Answer
- BE: 30 k (Compression) - AE: 42.4 k (Tension) - BC: 22.5 k (Compression)
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