For all of the following, draw the requested influence lines and find the worst case for the corresponding response quantity for a uniform load w that can be placed anywhere on the beam. 1. Moment at C, reaction at B, and shear at C. Note that C is just an identifying point, not a hinge. A C

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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**Transcription for Educational Website**

For all of the following problems, you are required to draw the requested influence lines and determine the worst case scenario for the corresponding response quantity when a uniform load \( w \) is applied anywhere on the beam.

1. **Moment at C, Reaction at B, and Shear at C:**
    - Note: Point C is merely an identifying point and is not a hinge.
    - Diagram: 
      - A horizontal beam is shown with three spans marked: from A to C (10 ft), C to B (10 ft), and an extension past B (10 ft).
      - Point A is supported by a pin support, and point B by a roller. Vertical lines beneath indicate potential load applications.

2. **Reaction at A, Reaction at B, Shear Just Right of A, and Moment at C:**
    - Note: Point C is merely an identifying point and is not a hinge.
    - Diagram:
      - The beam is divided into equal sections (2 m each) marking points A, C, and B with supports at A and B.
      - Similar to the prior illustration, point A has a pin support while point B has a roller.

3. **Reaction at A, Shear Just Right of A, and (Negative) Moment at C:**
    - Diagram:
      - The beam is depicted with segments detailed by measurements in feet: 10 ft from the left edge to A, 10 ft from A to B, and 5 ft from B to C.
      - A is pinned, B has a roller, and C shows the beam extending without support indicated.

**Explanation:**
Each scenario requires constructing influence lines that depict how a specific force or moment varies along the beam in response to a moving load. In engineering terms, these diagrams help in analyzing how loads will influence reactions, shear, and moments at different points along a structural element like a beam.
Transcribed Image Text:**Transcription for Educational Website** For all of the following problems, you are required to draw the requested influence lines and determine the worst case scenario for the corresponding response quantity when a uniform load \( w \) is applied anywhere on the beam. 1. **Moment at C, Reaction at B, and Shear at C:** - Note: Point C is merely an identifying point and is not a hinge. - Diagram: - A horizontal beam is shown with three spans marked: from A to C (10 ft), C to B (10 ft), and an extension past B (10 ft). - Point A is supported by a pin support, and point B by a roller. Vertical lines beneath indicate potential load applications. 2. **Reaction at A, Reaction at B, Shear Just Right of A, and Moment at C:** - Note: Point C is merely an identifying point and is not a hinge. - Diagram: - The beam is divided into equal sections (2 m each) marking points A, C, and B with supports at A and B. - Similar to the prior illustration, point A has a pin support while point B has a roller. 3. **Reaction at A, Shear Just Right of A, and (Negative) Moment at C:** - Diagram: - The beam is depicted with segments detailed by measurements in feet: 10 ft from the left edge to A, 10 ft from A to B, and 5 ft from B to C. - A is pinned, B has a roller, and C shows the beam extending without support indicated. **Explanation:** Each scenario requires constructing influence lines that depict how a specific force or moment varies along the beam in response to a moving load. In engineering terms, these diagrams help in analyzing how loads will influence reactions, shear, and moments at different points along a structural element like a beam.
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