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Determine the internal forces and bending moment at point C. Express these based on the sign convention following the given coordinate system. Two free body diagrams are required for this problem. Im 30° 2 m 3 m 15 N/m B

Determine the internal forces and bending moment at point C. Express these based on the sign convention following the given coordinate system. Two free body diagrams are required for this problem. Im 30° 2 m 3 m 15 N/m B

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter4: Numerical Analysis Of Heat Conduction
Section: Chapter Questions
Problem 4.28P
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**Analyzing Internal Forces and Bending Moment at Point C** **Problem Statement:** Determine the internal forces and bending moment at point C. Express these based on the sign convention following the given coordinate system. Two free body diagrams are required for this problem. **Diagram Explanation:** The diagram illustrates a structural member with the following characteristics: 1. **Support and Member Layout:** - Point **A** has a pinned support, which allows rotation but no displacement. - Point **B** has a roller support, which allows displacement in a single direction but prevents displacement in perpendicular directions. 2. **Member Geometry:** - The member is divided into two segments: A to C and C to B. - Segment AC forms an inclined plane with an angle of 30° to the horizontal and a length of 1 m. - Segment CB is a horizontal plane, 3 m long. 3. **Loading Conditions:** - There is a linearly varying distributed load on segment CB, starting at point C and increasing from 0 to 15 N/m at point B. 4. **Coordinates:** - The coordinate system has been defined with positive y-axis upwards and positive x-axis to the right. **Free Body Diagram Analysis:** Two free body diagrams should be drawn: 1. **For Segment AC:** - This segment is inclined at 30°, so the forces acting on it need to be resolved into components parallel and perpendicular to the segment. - The reactions at point A need to be determined: - Reaction Ay (vertical component) - Reaction Ax (horizontal component) - There is also an internal normal force, shear force, and bending moment to be determined at point C. 2. **For Segment CB:** - Identify the varying distributed load and calculate its resultant force and location. - Calculate the reaction at B considering the equilibrium equations. - Include internal forces at point C due to the effect of the external load and reactions. **Steps to Solve:** 1. Calculate reactions at the supports A and B using equilibrium equations. 2. Create free body diagrams for each segment. 3. Resolve the forces acting on segment AC and determine the internal forces (normal force, shear force) and bending moment at point C. 4. Use the internal load and moments acting on segment CB to finalize the values at point C. By using the proper sign convention and equilibrium principles for each diagram
Transcribed Image Text:**Analyzing Internal Forces and Bending Moment at Point C** **Problem Statement:** Determine the internal forces and bending moment at point C. Express these based on the sign convention following the given coordinate system. Two free body diagrams are required for this problem. **Diagram Explanation:** The diagram illustrates a structural member with the following characteristics: 1. **Support and Member Layout:** - Point **A** has a pinned support, which allows rotation but no displacement. - Point **B** has a roller support, which allows displacement in a single direction but prevents displacement in perpendicular directions. 2. **Member Geometry:** - The member is divided into two segments: A to C and C to B. - Segment AC forms an inclined plane with an angle of 30° to the horizontal and a length of 1 m. - Segment CB is a horizontal plane, 3 m long. 3. **Loading Conditions:** - There is a linearly varying distributed load on segment CB, starting at point C and increasing from 0 to 15 N/m at point B. 4. **Coordinates:** - The coordinate system has been defined with positive y-axis upwards and positive x-axis to the right. **Free Body Diagram Analysis:** Two free body diagrams should be drawn: 1. **For Segment AC:** - This segment is inclined at 30°, so the forces acting on it need to be resolved into components parallel and perpendicular to the segment. - The reactions at point A need to be determined: - Reaction Ay (vertical component) - Reaction Ax (horizontal component) - There is also an internal normal force, shear force, and bending moment to be determined at point C. 2. **For Segment CB:** - Identify the varying distributed load and calculate its resultant force and location. - Calculate the reaction at B considering the equilibrium equations. - Include internal forces at point C due to the effect of the external load and reactions. **Steps to Solve:** 1. Calculate reactions at the supports A and B using equilibrium equations. 2. Create free body diagrams for each segment. 3. Resolve the forces acting on segment AC and determine the internal forces (normal force, shear force) and bending moment at point C. 4. Use the internal load and moments acting on segment CB to finalize the values at point C. By using the proper sign convention and equilibrium principles for each diagram
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