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# Direct Stress and Strain

Intoduction to terms used in "Materials" and the concepts of Direct Stress and Strain

**Contents**

## Introduction

The following page introduces some of the terms associated with the study of "The Strength of Materials" and in particular those associated with Direct Stress.## Load

The simplest type of load is a direct pull or push, known technically as

**Tension**and**Compression**.**Acceleration**is the rate of change of velocity as a function of time,it is vector. Acceleration is the second derivative of position with respect to time or, alternately, the first derivative of the velocity with respect to time.

Examples of these

**types of load**are:- A rope hanging from hanging from a beam and carrying a load is in
**Tension**. The forces on the rope are the wight of the load acting downwards and the pull of the beam at the other. Since there is no movement these forces must be equal and opposite. - The piers of a bridge. The weight of the bridge presses down on the pier and the ground pushes up. As above, since there is no movement, the forces are equal and opposite.

**Pressure**is an effect which occurs when a force is applied on a surface. Pressure is the amount of force acting on a unit area. The symbol of pressure is .

**Load**is a Force and is measured in Pounds(lb.) Tons or Newtons.

## Stress

Across any section of a member, the Total Force carried must equal the Load . This is distributed amongst the internal Forces of cohesion, which we call**Stresses**. Imagine that the member is cut through at . Then each Portion must be in equilibrium under the action of the external load and the Stresses across .

Stress which are Normal to the plane on which they act are called

**Direct Stresses**and they are either tensile or compressive.The Load transmitted across any Section divided by the cross sectional area is called the

In some instances the Stress varies throughout the member and the Stress at any point is defined as the limiting ratio of for a small area enclosing the point.
**Stress**. Where the Load is uniformly distributed across the Section: = Load / Area =**Stress**is measured in Load per unit Area and is therefore lb./sq.in. tons/sq.in or Newtons/sq.mm.

## Principle Of St. Venant

**Principle of St. Venant**states that the actual distribution of the Load over the surface of its application will not affect the distribution of Stress or Strain on sections of the body which are at an appreciable distance (relative to the dimensions) away from the Load. Any statically equivalent loading may therefore be substituted for the actual Load distribution, provided that the Stress analysis in the region of the Load are not required.

- Centrally Concentrated.
- Distributed around the circumference of the rod.
- Distributed over the end cross-section

## Strain

**Strain**is the measure of the deformation produced in a member by the applied Load.

Direct Stress produces a change in length in the direction of the Stress. If a rod is in tension and the stretch or elongation produced is then the

Normally Tensile Strain is considered Positive and Compressive Strain (i.e. a reduction in length) negative.
Note that as Strain is a Ratio it is Dimensionless.**Direct Stress**is defined as the ratio: Elongation / Original Length. Or .## Hooke's Law. The Principle Of Superposition.

**Hooke'**

**s Law**states that Strain is Proportional to the Stress which Produced it.

**Elastic**if it obeys Hooke's Law.

Where a number of Loads are acting together on an Elastic Material, the

**Principle of Superposition**states that the resultant Strain will be the sum of the individual Strains caused by each Load separately.## Young's Modulus Or (modulus Of Elasticity)

**Stress**is a measure of the internal forces acting within a deformable body. It is a measure of the average force per unit area of a surface within the body on which internal forces act.

**Strain**is a normalized measure of deformation representing the displacement between particles in the body relative to a reference length.

**Young'**

**s modulus**is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. The slope of the stress-strain curve at any point is called the

**tangent modulus**. The tangent modulus of the initial, linear portion of a stress-strain curve is called

**Young'**

**s modulus**, also known as the

**Tensile modulus**. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. i.e. = Stress / Strain