https://file.aiquickdraw.com/mathbot/file/1726245235019zcth1wqq.jpg

The problem involves a simply supported beam with an overhanging section subjected to two concentrated loads, and we need to solve it in three parts:

### Beam Setup:
- **Beam Length (AB)**: 6 meters (A and B are supports).
- **Overhanging Length (BD)**: 2 meters (D is the free end).
- **Loads**:
  - 6 kN acting at point B (midspan of the supported section).
  - 2 kN acting at point D (end of the overhanging section).

### Required:
1. **Evaluate the support reactions** at A and B.
2. **Compute the deflections** at the center of the supported span and at the free end of the overhang.
3. **Draw the bending moment diagram** for the beam.

#### a) Calculating Support Reactions
We can solve for the reactions at points A and B by using static equilibrium equations:

1. **Sum of Vertical Forces**: The total vertical forces must equal zero.
   \[
   R_A + R_B = 6 \, \text{kN} + 2 \, \text{kN} = 8 \, \text{kN}
   \]

2. **Sum of Moments about Point A**: Taking moments around point A to eliminate \(R_A\), we get:
   \[
   M_A = 6 \, \text{kN} \times 3 \, \text{m} + 2 \, \text{kN} \times 8 \, \text{m}
   \]
   This will give us \(R_B\).

Once we have \(R_B\), we can substitute it back into the first equation to

A car parking shed has its slab beam placed as a simply supported beam of span 6 m with an additional overhang span of 2m. The beam is subjected to concentrated loads of 6 kN and 2 kN at specified points. The tasks are to: a) Evaluate support reactions, b) Compute deflections, and c) Draw the bending moment diagram.

This problem involves a simply supported beam of span 6 m with a 2 m overhang, subjected to concentrated loads of 6 kN and 2 kN. The solution includes calculating the support reactions, deflections, and the bending moment diagram. Ideal for civil and structural engineering students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation