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P9.12. Compute the reactions and draw the shear and moment diagrams for the beam in Figure P9.12. E is constant. A w = 4 kN/m 21 6 m B hinge -3 m P9.12 C 18 kN I |-—– 3 m -→-| 6 m D

P9.12. Compute the reactions and draw the shear and moment diagrams for the beam in Figure P9.12. E is constant. A w = 4 kN/m 21 6 m B hinge -3 m P9.12 C 18 kN I |-—– 3 m -→-| 6 m D

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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### Problem P9.12 **Objective:** Compute the reactions and draw the shear and moment diagrams for the beam in Figure P9.12. E is constant. #### Given Information: - The beam is subjected to a uniformly distributed load \( w = 4 \, \text{kN/m} \) from point A to point B. - There is a point load of \( 18 \, \text{kN} \) acting downward at 3 meters from point C. - Length from A to B \( = 6 \, \text{meters} \). - Length from B to the hinge \( = 3 \, \text{meters} \). - Length from the hinge to point D \( = 6 \, \text{meters} \). #### Explanation of the Diagram: The beam is supported as follows: - A fixed support at point A. - A hinge at point B which allows angular displacement but no vertical or horizontal translation. - A roller support at point D which allows horizontal translation but no vertical translation. The distributed load (w=4 kN/m) applies over the length from A to B. The total uniformly distributed load is therefore \( w \times 6 \, \text{meters} = 24 \, \text{kN} \). #### Steps: 1. **Determine Reactions at the Supports:** - Calculate the reactions at points A, B, and D through equilibrium equations. 2. **Shear Force Diagram (SFD):** - Plot the shear force at various points along the beam. - Key points include points A, B, hinge, and D using the equilibrium equations and load values. 3. **Bending Moment Diagram (BMD):** - Plot the bending moment at various points along the beam. - Using the computed shear forces, integrate across the beam to determine bending moments at key points, particularly points B and D. Using these computations, draft the corresponding shear force and moment diagrams to visualize the internal forces within the beam. **Figure P9.12:** - This figure represents a horizontal beam subjected to both distributed and point loads. - The left segment (point A to B) is under a uniformly distributed load of 4 kN/m. - The right segment (point C to D) has a point load of 18 kN at 3 meters from C. - Supports included are a fixed support at A, a hinge
Transcribed Image Text:### Problem P9.12 **Objective:** Compute the reactions and draw the shear and moment diagrams for the beam in Figure P9.12. E is constant. #### Given Information: - The beam is subjected to a uniformly distributed load \( w = 4 \, \text{kN/m} \) from point A to point B. - There is a point load of \( 18 \, \text{kN} \) acting downward at 3 meters from point C. - Length from A to B \( = 6 \, \text{meters} \). - Length from B to the hinge \( = 3 \, \text{meters} \). - Length from the hinge to point D \( = 6 \, \text{meters} \). #### Explanation of the Diagram: The beam is supported as follows: - A fixed support at point A. - A hinge at point B which allows angular displacement but no vertical or horizontal translation. - A roller support at point D which allows horizontal translation but no vertical translation. The distributed load (w=4 kN/m) applies over the length from A to B. The total uniformly distributed load is therefore \( w \times 6 \, \text{meters} = 24 \, \text{kN} \). #### Steps: 1. **Determine Reactions at the Supports:** - Calculate the reactions at points A, B, and D through equilibrium equations. 2. **Shear Force Diagram (SFD):** - Plot the shear force at various points along the beam. - Key points include points A, B, hinge, and D using the equilibrium equations and load values. 3. **Bending Moment Diagram (BMD):** - Plot the bending moment at various points along the beam. - Using the computed shear forces, integrate across the beam to determine bending moments at key points, particularly points B and D. Using these computations, draft the corresponding shear force and moment diagrams to visualize the internal forces within the beam. **Figure P9.12:** - This figure represents a horizontal beam subjected to both distributed and point loads. - The left segment (point A to B) is under a uniformly distributed load of 4 kN/m. - The right segment (point C to D) has a point load of 18 kN at 3 meters from C. - Supports included are a fixed support at A, a hinge
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