Determine the force in each member of the loaded truss. The forces are positive if in tension, negative if in compression. Assume F₁-3930 lb, F₂-2590 lb, a = 3.4ft, b= 5.2 ft. c = 2.3 ft, and d = 3.0 ft.

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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### Truss Analysis Example

#### Determine the force in each member of the loaded truss. The forces are positive if in tension, negative if in compression.
Assume:
- \( F_1 = 3930 \text{ lb} \)
- \( F_2 = 2590 \text{ lb} \)
- \( a = 3.4 \text{ ft} \)
- \( b = 5.2 \text{ ft} \)
- \( c = 2.3 \text{ ft} \)
- \( d = 3.0 \text{ ft} \)

#### Diagram:
Below is the schematic of the truss with labeled points and forces.

```
    C
    |\
    | \
    |  \
 d  |   \
    |    \
    |     \
    B------D
    |\     |
    | \    |
 c  |  \   | b
    |   \  |
    |    E |
    |   /  |
    A--|---|
      a

Forces:
    F1 ↓ (at A)
    F2 ↓ (at E)
```

#### Calculations:
Below are the computed forces in each member of the truss:

- \( AB = 7013.98237 \text{ lb} \)  (This member is in tension)
- \( AE = -5809.56528 \text{ lb} \)  (This member is in compression)
- \( BC = -5809.56528 \text{ lb} \)  (This member is in compression)
- \( BD = -5809.56528 \text{ lb} \)  (This member is in compression)
- \( BE = 2590 \text{ lb} \)  (This member is in tension)
- \( CD = \text{Value Not Provided} \) 
- \( DE = -5809.56528 \text{ lb} \)  (This member is in compression)

#### Graphical Representation:
The diagram above visually represents the truss system. The arrows indicating forces \( F_1 \) and \( F_2 \) point downwards, showing the direction of the applied loads.

The solved force values indicate whether each member of the truss is in tension (positive values) or compression (negative values):
- Members in tension resist being pulled apart.
- Members
Transcribed Image Text:### Truss Analysis Example #### Determine the force in each member of the loaded truss. The forces are positive if in tension, negative if in compression. Assume: - \( F_1 = 3930 \text{ lb} \) - \( F_2 = 2590 \text{ lb} \) - \( a = 3.4 \text{ ft} \) - \( b = 5.2 \text{ ft} \) - \( c = 2.3 \text{ ft} \) - \( d = 3.0 \text{ ft} \) #### Diagram: Below is the schematic of the truss with labeled points and forces. ``` C |\ | \ | \ d | \ | \ | \ B------D |\ | | \ | c | \ | b | \ | | E | | / | A--|---| a Forces: F1 ↓ (at A) F2 ↓ (at E) ``` #### Calculations: Below are the computed forces in each member of the truss: - \( AB = 7013.98237 \text{ lb} \) (This member is in tension) - \( AE = -5809.56528 \text{ lb} \) (This member is in compression) - \( BC = -5809.56528 \text{ lb} \) (This member is in compression) - \( BD = -5809.56528 \text{ lb} \) (This member is in compression) - \( BE = 2590 \text{ lb} \) (This member is in tension) - \( CD = \text{Value Not Provided} \) - \( DE = -5809.56528 \text{ lb} \) (This member is in compression) #### Graphical Representation: The diagram above visually represents the truss system. The arrows indicating forces \( F_1 \) and \( F_2 \) point downwards, showing the direction of the applied loads. The solved force values indicate whether each member of the truss is in tension (positive values) or compression (negative values): - Members in tension resist being pulled apart. - Members
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