Problem 7 The beam is subjected to a uniform live load of 2.5 kN/m, a dead load of 0.8 kN/m, and a single live load of 55 kN. Determine (a) the maximum positive moment created by these loads at E, and (b) the maximum positive shear at E. Assume A and C are roller, and B is a short link connection. AI 4 m B aja 4 m CI E 4m- ** 4 m

Structural Analysis
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Chapter2: Loads On Structures
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### Problem 7

**Description:**

The beam is subjected to a uniform live load of 2.5 kN/m, a dead load of 0.8 kN/m, and a single live load of 55 kN. The task is to determine (a) the maximum positive moment created by these loads at point E, and (b) the maximum positive shear at point E. The assumptions include that points A and C are roller supports, and point B is a short link connection.

**Diagram Explanation:**

The diagram provided depicts a beam with roller supports at points A and C, and a short link connection at point B. Here's a breakdown of the structural layout:

1. **Beam Layout:**
   - The entire length of the beam is divided into four equal segments, each 4 meters long.
   - Point A to B: 4 meters
   - Point B to C: 4 meters
   - Point C to E: 4 meters
   - Point E to D: 4 meters

2. **Loading Details:**
   - A uniform live load of 2.5 kN/m is applied along the length of the beam.
   - A uniform dead load of 0.8 kN/m is also applied along the length of the beam.
   - A single live load of 55 kN is applied at point D.

3. **Support Details:**
   - Supports at points A and C are roller supports, which can resist vertical forces but allow horizontal translations.
   - Support at point B is a short link connection, which typically restricts relative rotational movement and allows for the redistribution of moments and shears.

**Objectives:**

- **(a) Maximum Positive Moment at E:**
   Calculate the maximum positive moment at point E due to the combination of the specified loads.

- **(b) Maximum Positive Shear at E:**
   Calculate the maximum positive shear at point E as a result of the applied loads.

Understanding the forces and reactions at different points along the beam is essential for structural analysis and ensuring safety and stability in engineering designs. Use principles of statics, such as equilibrium equations, to solve for the moment and shear at point E.
Transcribed Image Text:### Problem 7 **Description:** The beam is subjected to a uniform live load of 2.5 kN/m, a dead load of 0.8 kN/m, and a single live load of 55 kN. The task is to determine (a) the maximum positive moment created by these loads at point E, and (b) the maximum positive shear at point E. The assumptions include that points A and C are roller supports, and point B is a short link connection. **Diagram Explanation:** The diagram provided depicts a beam with roller supports at points A and C, and a short link connection at point B. Here's a breakdown of the structural layout: 1. **Beam Layout:** - The entire length of the beam is divided into four equal segments, each 4 meters long. - Point A to B: 4 meters - Point B to C: 4 meters - Point C to E: 4 meters - Point E to D: 4 meters 2. **Loading Details:** - A uniform live load of 2.5 kN/m is applied along the length of the beam. - A uniform dead load of 0.8 kN/m is also applied along the length of the beam. - A single live load of 55 kN is applied at point D. 3. **Support Details:** - Supports at points A and C are roller supports, which can resist vertical forces but allow horizontal translations. - Support at point B is a short link connection, which typically restricts relative rotational movement and allows for the redistribution of moments and shears. **Objectives:** - **(a) Maximum Positive Moment at E:** Calculate the maximum positive moment at point E due to the combination of the specified loads. - **(b) Maximum Positive Shear at E:** Calculate the maximum positive shear at point E as a result of the applied loads. Understanding the forces and reactions at different points along the beam is essential for structural analysis and ensuring safety and stability in engineering designs. Use principles of statics, such as equilibrium equations, to solve for the moment and shear at point E.
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