4. Draw the free body diagram for each beam shown below. Discuss the constraints (proper, improper, partial, redundant) and whether it is statically determinant. Explain your answers. You should also consider stability (2 a. The beam below is fixed to the wall at A and rests on a roller at B. A JOKN.m A 5KN b. The beam below is supported by a pin at A and a roller at B. ION B b B F

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**Topic: Beam Diagrams and Static Determinacy**

**Exercise 4: Free Body Diagrams and Static Analysis**

Draw the free body diagram for each beam shown below. Discuss the constraints (proper, improper, partial, redundant) and determine whether it is statically determinate. Explain your answers, considering stability as well.

---

**a. Beam Fixed to Wall and Resting on Roller**

*Diagram Description:*

- The beam is fixed to the wall at point A and rests on a roller at point B.
- A moment of 10 kN·m is applied at point A.
- A vertical force of 5 kN is applied downward near point B.
- The fixed support at A can resist vertical, horizontal forces, and moments.
- The roller support at B allows horizontal movement but resists vertical forces.

*Analysis:*

- **Constraints:** Proper; the fixed support and roller provide the necessary reactions for equilibrium.
- **Static Determinacy:** Statically determinate; there are three equations of equilibrium and three unknowns (vertical reaction at B, and vertical and moment reaction at A).

---

**b. Beam Supported by Pin and Roller**

*Diagram Description:*

- The beam is supported by a pin at point A and a roller at point B.
- A vertical force of 10 N is applied downward in the middle of the beam.
- The pin support at A can resist both vertical and horizontal forces, but not moments.
- The roller support at B allows horizontal movement but resists vertical forces.

*Analysis:*

- **Constraints:** Proper; the pin allows rotation and prevents translation, while the roller allows horizontal movement and prevents vertical movement.
- **Static Determinacy:** Statically determinate; three equilibrium equations and three unknown reactions (vertical and horizontal at A, vertical at B).

---

Both configurations are crucial for understanding the basic principles of statics and structural analysis, focusing on determining reactions and ensuring stability.
Transcribed Image Text:**Topic: Beam Diagrams and Static Determinacy** **Exercise 4: Free Body Diagrams and Static Analysis** Draw the free body diagram for each beam shown below. Discuss the constraints (proper, improper, partial, redundant) and determine whether it is statically determinate. Explain your answers, considering stability as well. --- **a. Beam Fixed to Wall and Resting on Roller** *Diagram Description:* - The beam is fixed to the wall at point A and rests on a roller at point B. - A moment of 10 kN·m is applied at point A. - A vertical force of 5 kN is applied downward near point B. - The fixed support at A can resist vertical, horizontal forces, and moments. - The roller support at B allows horizontal movement but resists vertical forces. *Analysis:* - **Constraints:** Proper; the fixed support and roller provide the necessary reactions for equilibrium. - **Static Determinacy:** Statically determinate; there are three equations of equilibrium and three unknowns (vertical reaction at B, and vertical and moment reaction at A). --- **b. Beam Supported by Pin and Roller** *Diagram Description:* - The beam is supported by a pin at point A and a roller at point B. - A vertical force of 10 N is applied downward in the middle of the beam. - The pin support at A can resist both vertical and horizontal forces, but not moments. - The roller support at B allows horizontal movement but resists vertical forces. *Analysis:* - **Constraints:** Proper; the pin allows rotation and prevents translation, while the roller allows horizontal movement and prevents vertical movement. - **Static Determinacy:** Statically determinate; three equilibrium equations and three unknown reactions (vertical and horizontal at A, vertical at B). --- Both configurations are crucial for understanding the basic principles of statics and structural analysis, focusing on determining reactions and ensuring stability.
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