The beam in the figure has constant \( E \) and \( I \) as shown for each of the two segments \( AB \) and \( BC \). Find the ratio of the displacement over the rotation (i.e., \( \frac{u_y}{\theta} \) ) at a distance 2.5 to the right of point \( A \).**Diagram Explanation:**- **Beam Structure**: The diagram shows a horizontal beam fixed at point \( A \) and extending through points \( B \) and \( C \).- **Segment Lengths**: - Segment \( AB \) is 6 meters in length, denoted as \( 2I \). - Segment \( BC \) is 3 meters in length, denoted as \( I \).- **Forces and Moments**: - A 120 kN force is applied downward at point \( B \). - A 300 kN·m clockwise moment is applied at point \( C \).The task is to calculate the specified ratio related to displacement and rotation at a particular point along the beam.

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The beam in the figure has constant E and I as shown for each of the two segments AB and BC. Find the ratio of the displacement over the rotation (i.e., Uy O at a distance 2.5 to the right of point A. 120 kN 300 kN · m A В 6 m 3 m 21 I

The beam in the figure has constant E and I as shown for each of the two segments AB and BC. Find the ratio of the displacement over the rotation (i.e., Uy O at a distance 2.5 to the right of point A. 120 kN 300 kN · m A В 6 m 3 m 21 I

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.

Question

The beam in the figure has constant \( E \) and \( I \) as shown for each of the two segments \( AB \) and \( BC \). Find the ratio of the displacement over the rotation (i.e., \( \frac{u_y}{\theta} \) ) at a distance 2.5 to the right of point \( A \).

**Diagram Explanation:**

- **Beam Structure**: The diagram shows a horizontal beam fixed at point \( A \) and extending through points \( B \) and \( C \).
- **Segment Lengths**:
- Segment \( AB \) is 6 meters in length, denoted as \( 2I \).
- Segment \( BC \) is 3 meters in length, denoted as \( I \).
- **Forces and Moments**:
- A 120 kN force is applied downward at point \( B \).
- A 300 kN·m clockwise moment is applied at point \( C \).

The task is to calculate the specified ratio related to displacement and rotation at a particular point along the beam.

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