How to solve for the centroid of the composite body using the principle of moments and treat each part as a finite element of the whole figure (show a step by step solution) **Problem 6.8** - Determine the reactions at supports A and B.**Diagram Explanation:**The diagram shows a simply supported beam with supports at points A and B. The beam is subject to a varying distributed load across its length, which has a sinusoidal shape. The load intensity varies as:\[ w = w_0 \sin\left(\frac{\pi x}{L}\right) \]where:- \( w_0 \) is the maximum load intensity occurring at the midpoint of the beam.- \( L \) is the length of the beam.- \( x \) is the distance from the leftmost support (A).Key points:- The distributed load starts at zero at both supports (A and B) and reaches a maximum at the center.- The beam length is denoted as \( L \), spanning from support A to support B.- Arrows indicate the direction of the distributed load acting downward on the beam.The task is to solve for the reaction forces at supports A and B due to the applied load.

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Engineering

Civil Engineering

- Determine the reactions at supports A and B.

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

Equilibrium and Support Reactions

Civil engineers deal with structures that are composed of several members connected or with individual members such as beams and columns. To analyze such structures, the condition of statics must be applied. Under the static condition, the members are considered to be in equilibrium under the action of forces, that is, the members are assumed to be having negligible velocity.

Question

How to solve for the centroid of the composite body using the principle of moments and treat each part as a finite element of the whole figure (show a step by step solution)

**Problem 6.8** - Determine the reactions at supports A and B.

**Diagram Explanation:**

The diagram shows a simply supported beam with supports at points A and B. The beam is subject to a varying distributed load across its length, which has a sinusoidal shape. The load intensity varies as:

\[ w = w_0 \sin\left(\frac{\pi x}{L}\right) \]

where:
- \( w_0 \) is the maximum load intensity occurring at the midpoint of the beam.
- \( L \) is the length of the beam.
- \( x \) is the distance from the leftmost support (A).

Key points:
- The distributed load starts at zero at both supports (A and B) and reaches a maximum at the center.
- The beam length is denoted as \( L \), spanning from support A to support B.
- Arrows indicate the direction of the distributed load acting downward on the beam.

The task is to solve for the reaction forces at supports A and B due to the applied load.

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