2) Each of the five struts below consists of an aluminum tube that has a 32-mm outer diameter and a 4-mm wall thickness. Using E=70 GPa and a safety factor of SF=2.3, determine the critical force, Po, for each support condition below. 2.0 m (1) (2) (3) € (5)

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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The image presents a problem involving five different aluminum struts, each with a tube configuration characterized by an outer diameter of 32 mm and a wall thickness of 4 mm. These struts are composed of aluminum with a modulus of elasticity, \(E\), of 70 GPa. The task is to determine the critical force, \(P_0\), for each of the support conditions depicted in the diagram. A safety factor of 2.3 is to be used in the calculations.

### Diagram Description:

1. **Strut (1):** 
   - Features a fixed support at the base and a free end at the top. 
   - The critical force, \(P_0\), is applied downward at the free end.
   - The length of the strut is 2.0 meters.

2. **Strut (2):** 
   - Both ends are hinged, allowing rotation but no lateral movement. 
   - The critical force, \(P_0\), is applied vertically downward at the top.

3. **Strut (3):** 
   - Has a fixed support at the base and a hinge at the top, allowing rotation of the upper end. 
   - The critical force, \(P_0\), is applied downward along the strut's axis.

4. **Strut (4):** 
   - Both ends are fixed, preventing rotation and lateral movement. 
   - The critical force, \(P_0\), is applied at the top, compressing the strut.

5. **Strut (5):** 
   - Similar to strut (3), it has a fixed base and a roller support at the top, allowing lateral movement but no rotational movement.
   - The load, \(P_0\), is applied vertically downward.

Each strut configuration will have unique equations to determine the critical buckling load, taking into account the length, elasticity, and boundary conditions specified.
Transcribed Image Text:The image presents a problem involving five different aluminum struts, each with a tube configuration characterized by an outer diameter of 32 mm and a wall thickness of 4 mm. These struts are composed of aluminum with a modulus of elasticity, \(E\), of 70 GPa. The task is to determine the critical force, \(P_0\), for each of the support conditions depicted in the diagram. A safety factor of 2.3 is to be used in the calculations. ### Diagram Description: 1. **Strut (1):** - Features a fixed support at the base and a free end at the top. - The critical force, \(P_0\), is applied downward at the free end. - The length of the strut is 2.0 meters. 2. **Strut (2):** - Both ends are hinged, allowing rotation but no lateral movement. - The critical force, \(P_0\), is applied vertically downward at the top. 3. **Strut (3):** - Has a fixed support at the base and a hinge at the top, allowing rotation of the upper end. - The critical force, \(P_0\), is applied downward along the strut's axis. 4. **Strut (4):** - Both ends are fixed, preventing rotation and lateral movement. - The critical force, \(P_0\), is applied at the top, compressing the strut. 5. **Strut (5):** - Similar to strut (3), it has a fixed base and a roller support at the top, allowing lateral movement but no rotational movement. - The load, \(P_0\), is applied vertically downward. Each strut configuration will have unique equations to determine the critical buckling load, taking into account the length, elasticity, and boundary conditions specified.
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