The bar is snugly fit between points C and A before the loading is applied at Collar B. Assume E = 200 GPa for the steel. The circular bars in the assembly are solid. The bars are solid with a diameter of 15 mm. Assume a fixed rigid support at C and A. A C В 6 kN 3 m 2 m A) Show the FBD and compatibility equation for this problem. B) Determine the support reactions at A and C. (Horizontal forces only) Left side: Fc = Right side: FA =

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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### Educational Task: Analysis of a Loaded Steel Bar

The image presents a mechanical problem involving a steel bar assembly, snugly fit between two fixed rigid supports, labeled C and A, before the application of a load at Collar B. 

### Problem Details:
- **Material:** Steel  
- **Elastic Modulus (E):** 200 GPa  
- **Bar Characteristics:** Circular and solid with a diameter of 15 mm  
- **Positions and Distances:**
  - Length from C to B: 3 m
  - Length from B to A: 2 m
- **Load Applied at B:** 6 kN directed towards point A

### Tasks:
#### A) Show the Free Body Diagram (FBD) and Compatibility Equation:
- This involves drawing the FBD to illustrate forces acting on the bar, showing the load at B and reaction forces at A and C. 
- The compatibility equation should relate to deformations in the bar owing to elasticity and constraints by supports.

#### B) Determine the Support Reactions at A and C (Horizontal Forces Only):
- Calculate the reaction forces, \( F_A \) and \( F_C \), at supports A and C caused by the 6 kN applied load.
  
**Calculation Fields:**
- **Left side:**
  \[
  F_C = \underline{\qquad\qquad\qquad}
  \]
- **Right side:**
  \[
  F_A = \underline{\qquad\qquad\qquad}
  \]

By completing these tasks, the student will understand how to analyze forces and compatibility in a mechanical system with given constraints and material properties.
Transcribed Image Text:### Educational Task: Analysis of a Loaded Steel Bar The image presents a mechanical problem involving a steel bar assembly, snugly fit between two fixed rigid supports, labeled C and A, before the application of a load at Collar B. ### Problem Details: - **Material:** Steel - **Elastic Modulus (E):** 200 GPa - **Bar Characteristics:** Circular and solid with a diameter of 15 mm - **Positions and Distances:** - Length from C to B: 3 m - Length from B to A: 2 m - **Load Applied at B:** 6 kN directed towards point A ### Tasks: #### A) Show the Free Body Diagram (FBD) and Compatibility Equation: - This involves drawing the FBD to illustrate forces acting on the bar, showing the load at B and reaction forces at A and C. - The compatibility equation should relate to deformations in the bar owing to elasticity and constraints by supports. #### B) Determine the Support Reactions at A and C (Horizontal Forces Only): - Calculate the reaction forces, \( F_A \) and \( F_C \), at supports A and C caused by the 6 kN applied load. **Calculation Fields:** - **Left side:** \[ F_C = \underline{\qquad\qquad\qquad} \] - **Right side:** \[ F_A = \underline{\qquad\qquad\qquad} \] By completing these tasks, the student will understand how to analyze forces and compatibility in a mechanical system with given constraints and material properties.
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