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Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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### Beam Load and Rotation Analysis

When a force \( F = 1375 \, \text{N} \) and a uniformly distributed load \( q_o = 490 \, \text{N/m} \) are applied to the rigid beam ABC, it rotates clockwise through an angle \( \theta = 0.3^\circ \). The geometry of the setup is as follows: \( L = 2 \, \text{m} \) and \( h = 2.2 \, \text{m} \). The objective is to determine the tension and normal strain in cable DE under the applied loads. Assume the cable is made of steel and the beam is originally horizontal before any loads are applied.

#### Diagram Explanation

- **Beam ABC**: The beam is shown as a horizontal member supported at point A and connected to a cable at point C.
- **Forces Applied**:
  - The concentrated force \( F \) is applied upwards at point A.
  - There is a uniformly distributed load \( q_o \) acting downwards along the section of the beam between points A and B.
- **Dimensions**:
  - The length from A to B is \( L \), and B is connected to point C via a vertical cable.
  - The height \( h \) indicates the vertical distance from B to the point of connection of the cable at the ceiling.
- **Cable DE**:
  - The cable is connected to a point directly above B and extends vertically up to point C.

#### Calculation Variables

- **Tension in Cable BC (\( T_{BC} \))**: The calculated tension in the cable is 1898.2 N.
- **Normal Strain (\( \epsilon_{BC} \))**: The normal strain is expressed but requires calculation.

This setup serves to understand the interaction of forces and moments in a rigid body subject to a combination of point loads and distributed loads, analyzing the resulting tension in supporting cables and the rotational effects.
Transcribed Image Text:### Beam Load and Rotation Analysis When a force \( F = 1375 \, \text{N} \) and a uniformly distributed load \( q_o = 490 \, \text{N/m} \) are applied to the rigid beam ABC, it rotates clockwise through an angle \( \theta = 0.3^\circ \). The geometry of the setup is as follows: \( L = 2 \, \text{m} \) and \( h = 2.2 \, \text{m} \). The objective is to determine the tension and normal strain in cable DE under the applied loads. Assume the cable is made of steel and the beam is originally horizontal before any loads are applied. #### Diagram Explanation - **Beam ABC**: The beam is shown as a horizontal member supported at point A and connected to a cable at point C. - **Forces Applied**: - The concentrated force \( F \) is applied upwards at point A. - There is a uniformly distributed load \( q_o \) acting downwards along the section of the beam between points A and B. - **Dimensions**: - The length from A to B is \( L \), and B is connected to point C via a vertical cable. - The height \( h \) indicates the vertical distance from B to the point of connection of the cable at the ceiling. - **Cable DE**: - The cable is connected to a point directly above B and extends vertically up to point C. #### Calculation Variables - **Tension in Cable BC (\( T_{BC} \))**: The calculated tension in the cable is 1898.2 N. - **Normal Strain (\( \epsilon_{BC} \))**: The normal strain is expressed but requires calculation. This setup serves to understand the interaction of forces and moments in a rigid body subject to a combination of point loads and distributed loads, analyzing the resulting tension in supporting cables and the rotational effects.
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