# Built in Beams II

**Contents**

- Introduction
- Fixed At Both Ends. Uniform Load. Total Load W
- Fixed At Both Ends. Load At Centre.
- Fixed At Both Ends. Load At Any Point.
- Continuous Beam With Two Equal Spans. Uniform Load
- A Continuous Beam With Two Unequal Spans And Unequal Uniform Loads.
- A Continuous Beam With Two Unequal Spans With Two Unequal Loads At Any Point On Each
- Page Comments

## Introduction

*See Also*the section on "Built in Beams" . Revisiting the definition, a Beam is said to be Built-in or 'encastre' when both ends are rigidly fixed so that the slope at both ends can be assumed to be zero. In this section we present the solutions for the stress and deflection in a built in and continuous beam due to either uniform or point loads. With each solution the following definitions apply:

- is the bending at any point
- is the section module of the beam cross-section, equal to where is the distance from the beam centroid to the top or bottom edge of the beam.
- is the deflection at any point
- is the load on the beam
- is the modulus of elasticity
- is the moment of inertia for the cross section about the neutral axis

## Fixed At Both Ends. Uniform Load. Total Load W

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**Deflection**is a term that is used to describe the degree to which a structural element is displaced under a load.

## Fixed At Both Ends. Load At Centre.

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## Fixed At Both Ends. Load At Any Point.

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## Continuous Beam With Two Equal Spans. Uniform Load

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**beam**is a horizontal structural element that is capable of withstanding load primarily by resisting bending. The bending force induced into the material of the beam as a result of the external loads, own weight, span and external reactions to these loads is called a

**bending moment**.

## A Continuous Beam With Two Unequal Spans And Unequal Uniform Loads.

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Between and The Stress is given by: Stress at the Support is: The greatest Stress in the first span is at: And is The greatest Stress in the second Span is at: And is The Deflection between is given by: The Deflection between is given by: The above example is so complicated that convenient general expressions for the maximum deflections cannot be obtained

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## A Continuous Beam With Two Unequal Spans With Two Unequal Loads At Any Point On Each

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