# Simple Supported Beams

**Contents**

- Introduction
- Simply Supported At Both Ends With A Uniform Load.
- Simply Supported At Both Ends . Load At Centre.
- Simply Supported At Both Ends. Load At Any Point.
- Simply Supported At Both Ends. Two Equal Loads Symmetrically Placed
- Simply Supported But With Both Ends Overhanging Symmetrically. Uniform Load.
- Simply Supported With Both Ends Overhanging, Supports Unsymmetrical, Uniform Load.
- Simply Unsymmetrically Supported With Both Ends Overhanging And A Load At Any Point.
- Simply Supported With Ends Overhanging. Single Overhanging Load.
- Page Comments

## Introduction

The stress and deflection for simply supported beams under a number of loading scenarios is illustrated within this page. The following symbols have been used throughout:- is the Stress at any point
- is the Section Modulus of beam cross section.
- is the deflection at any point.
- is the load on the Beam. Note for uniform loads where is the load per unit length
- is the Modulus of Elasticity ( Young's Modulus)
- is the Moment of Inertia of the cross-section about the neutral axis

## Simply Supported At Both Ends With A 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**.

An

**elastic modulus**, or

**modulus of elasticity**, is the mathematical description of an object or substance's tendency to be deformed elastically (i.e., non-permanently) when a force is applied to it. The elastic modulus of an object is defined as the slope of its stress-strain curve in the elastic deformation region

## Simply Supported At Both Ends . Load At Centre.

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## Simply Supported At Both Ends. Load At Any Point.

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## Simply Supported At Both Ends. Two Equal Loads Symmetrically Placed

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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.

## Simply Supported But With Both Ends Overhanging Symmetrically. Uniform Load.

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## Simply Supported With Both Ends Overhanging, Supports Unsymmetrical, Uniform Load.

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## Simply Unsymmetrically Supported With Both Ends Overhanging And A Load At Any Point.

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## Simply Supported With Ends Overhanging. Single Overhanging Load.

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