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For Problems 3.8 through 3.10, solve för the support tions at A and B. 3.8 W=300/FT. 3.9 4 m W= 15 k/m A ↑ ↑ ↑ ↑ ↑ ↑ 3m

For Problems 3.8 through 3.10, solve för the support tions at A and B. 3.8 W=300/FT. 3.9 4 m W= 15 k/m A ↑ ↑ ↑ ↑ ↑ ↑ 3m

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Solve for the support reactions at A and B in figure 3.8 and 3.9.

### Support Reactions Problems #### Problem Statement: For Problems 3.8 through 3.10, solve for the support reactions at points A and B. --- #### Problem 3.8 **Diagram:** - A simply supported beam is depicted with: - A pin support at point A. - A roller support at point B, located 12 feet from point A (6 feet between A & a point denoted as 'O', and another 6 feet from 'O' to B). - Loads acting on the beam: - A concentrated load of 1000 pounds (lb) acting 6 feet from point A. - A uniformly distributed load \( w = 300 \frac{\text{lb}}{\text{ft}} \) spanning 6 feet from the point of the concentrated load to the right end of the beam. --- #### Problem 3.9 **Diagram:** - A simply supported beam is shown with: - A pin support at point A. - A roller support at point B, located 5 meters from point A (3 meters between A & B, and another 2 meters extending from B to point C at the far right end). - Loads acting on the beam: - A uniformly distributed load \( w = 15 \frac{\text{kN}}{\text{m}} \) over the 4 meters segment from A to B. --- ### Instructions for Solving: To solve for the support reactions at points A and B for both problems: 1. **Equilibrium Equations:** Utilize static equilibrium equations for each beam: - \(\sum F_y = 0\) (Sum of vertical forces must be zero) - \(\sum M_A = 0\) or \(\sum M_B = 0\) (Sum of moments about any point must be zero) 2. **Free Body Diagrams:** Draw the Free Body Diagram (FBD) of each beam isolating them from the supports. 3. **Resultant Forces:** Calculate the resultant forces of the distributed loads. 4. **Support Reactions:** Solve for the unknown support reactions at the pin and roller supports, usually resulting in a system of linear equations. By using these steps, one can determine the magnitude of the reactions at the supports A and B for the given load conditions on the beams.
Transcribed Image Text:### Support Reactions Problems #### Problem Statement: For Problems 3.8 through 3.10, solve for the support reactions at points A and B. --- #### Problem 3.8 **Diagram:** - A simply supported beam is depicted with: - A pin support at point A. - A roller support at point B, located 12 feet from point A (6 feet between A & a point denoted as 'O', and another 6 feet from 'O' to B). - Loads acting on the beam: - A concentrated load of 1000 pounds (lb) acting 6 feet from point A. - A uniformly distributed load \( w = 300 \frac{\text{lb}}{\text{ft}} \) spanning 6 feet from the point of the concentrated load to the right end of the beam. --- #### Problem 3.9 **Diagram:** - A simply supported beam is shown with: - A pin support at point A. - A roller support at point B, located 5 meters from point A (3 meters between A & B, and another 2 meters extending from B to point C at the far right end). - Loads acting on the beam: - A uniformly distributed load \( w = 15 \frac{\text{kN}}{\text{m}} \) over the 4 meters segment from A to B. --- ### Instructions for Solving: To solve for the support reactions at points A and B for both problems: 1. **Equilibrium Equations:** Utilize static equilibrium equations for each beam: - \(\sum F_y = 0\) (Sum of vertical forces must be zero) - \(\sum M_A = 0\) or \(\sum M_B = 0\) (Sum of moments about any point must be zero) 2. **Free Body Diagrams:** Draw the Free Body Diagram (FBD) of each beam isolating them from the supports. 3. **Resultant Forces:** Calculate the resultant forces of the distributed loads. 4. **Support Reactions:** Solve for the unknown support reactions at the pin and roller supports, usually resulting in a system of linear equations. By using these steps, one can determine the magnitude of the reactions at the supports A and B for the given load conditions on the beams.
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