# Stress And Strain In Strength Of Materials Pdf

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*Every component in a linear motion system experiences some form of loading due to applied forces or motion. Strain is the deformation or displacement of material that results from an applied stress. The most common way to analyze the relationship between stress and strain for a particular material is with a stress-strain diagram.*

- Book on Mechanics of Materials(Simple Stress and Strain)
- Stress and Strain Study Notes for Mechanical Engineering
- Strength of Materials

Stress is plotted on the Y-Axis and Strain is plotted on the X-axis. In material science and mechanical engineering, the stress-strain curve is widely used to understand the strength, deformation, and failure criteria of any material. In this article, we will explore details about the stress-strain curve.

## Book on Mechanics of Materials(Simple Stress and Strain)

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy. See our Privacy Policy and User Agreement for details. Published on Nov 27, This document gives the class notes of Unit Torsion of circular shafts and elastic stability of columns.

Subject: Mechanics of materials. SlideShare Explore Search You. Submit Search. Home Explore. Successfully reported this slideshow. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime. Unit 1- simple stress and strain. Upcoming SlideShare.

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Stress — strain relationships Bars with varying rectangular cross section Principle of Superposition. Due to cohesion between the molecules, the body resists deformation.

This resistance by which material of the body opposes the deformation is known as strength of material. Within a certain limit i.

Also within this limit the resistance is equal to the external force or applied load. But beyond the elastic stage, the resistance offered by the material is less than the applied load. In such a case, the deformation continues, until failure takes place.

Within elastic stage, the resisting force equals applied load. This resisting force per unit area is called stress or intensity of stress. Depending on the nature of the forces mentioned, the stress can be called the tensile stress or the compressive stress. The tensile stress is induced when the applied force has pulling effect on the body as shown in Table 1.

Generally, the tensile stress is considered positive. Generally, the compressive stress is considered negative. On the other hand, the shearing stress is induced when the applied load is parallel or tangent to the surface. Table 1. Elasticity 2. Plasticity 3. Brittleness 4.

Malleability 5. Ductility Many of these properties are contrasting in nature so that a given metal cannot exhibit simultaneously all these properties. For example, mild steel exhibits the property of elasticity, copper possesses the property of ductility, wrought iron is malleable, lead is plastic and cast iron is brittle.

Elastic Material II undergoes a deformation when subjected to an external loading such that the deformation disappears on the removal of the loading rubber. Plastic Material It undergoes a continuous deformation during the period of loading and the deformation is permanent. It does not regain its original dimensions on the removal o the loading aluminium. Rigid Material It does not undergo any deformation when subjected to an external loading glass and cast iron.

Malleability Materials ability to be hammered out into thin sheets, such as lead, is called malleability. There is little or no necking at fracture for brittle materials. Alternatively, the force per unit area or intensity of the forces distributed over a given section is called the stress on that section. The resistance of material or the internal force acting on a unit area may act in any direction. If area is expressed in centimeter square i. In the S. Normal stress is the stress which acts in a direction perpendicular to the area.

The normal stress is further divided into tensile stress and compressive stress. Tensile Stress: The stress induced in a body, when subjected to two equal and opposite pulls as shown in Fig. The ratio of increase in length to the original length is known as tensile strain.

The tensile stress acts normal to the area and it pulls on the area. Consider a section x-x, which divides the bar into two parts. This is shown in Fig. This resisting force per unit area is known as stress or intensity of stress. Compressive Stress: The stress induced in a body, when subjected to two equal and opposite pushes as shown in Fig.

And the ratio of decrease in length to the original length is known as compressive strain. The compressive stress acts normal to the area and it pushes on the area.

Let an axial push P is acting on a body in cross-sectional area A. Due to external push P, let the original length L of the body decreases by dL. The corresponding strain is known as shear strain. The shear stress is the stress which acts tangential to the area. The ratio of change of dimension of the body to the original dimension is known as strain. Strain is dimensionless. If there is some increase in length of a body due to external force, then the ratio of increase of length to the original length of the body is known as tensile strain.

But if there is some decrease in length of the body, then the ratio of decrease of the length of the body to the original length is known as compressive strain. The ratio of change of volume of the body to the original volume is known as volumetric strain. The strain produced by shear stress is known as shear strain. Linear Strain It is defined as Linear strain may be either tensile or compressive. If there is some increase in the length of a body due to external force, then the strain is known as tensile strain.

On the other hand, if there is some decrease in the length of the body due to external force, then the strain is known as compressive strain. Please note that both are linear strain only.

In the case of rod having uniform cross-section A. The shear strain is represented by the angle through which the other two faces have rotated as shown in Fig. If the external force is removed and the body comes back to its original shape and size which means the deformation disappears completely , the body is known as elastic body.

This property, by virtue of which certain materials return back to their original position after the removal of the external force, is called elasticity. The body will regain its previous shape and size only when the deformation caused by the external force, is within a certain limit. Thus there is a limiting value of force up to and within which, the deformation completely disappears on the removal of the force. The value of stress corresponding to this limiting force is known as the elastic limit of the material.

If the external force is so large that the stress exceeds the elastic limit, the material loses to some extent its property of elasticity.

## Stress and Strain Study Notes for Mechanical Engineering

The Tensile stress is like pulling the material on each side or might one side as figures shown below,. The Compressive stress is like pushing the material on each side or might one side as figures shown below,. The figure is shown below,. They have the tendency to hold the deformation that occurs in the plastic region. A material is brittle if, when subjected to stress, it breaks without significant plastic deformation. Brittle materials absorb relatively little energy prior to fracture, even those of high strength.

When a force is applied to a structural member, that member will develop both stress and strain as a result of the force. The applied force will cause the structural member to deform by some length, in proportion to its stiffness. Strain is the ratio of the deformation to the original length of the part:. There are different types of loading which result in different types of stress, as outlined in the table below:. In the equations for axial stress and transverse shear stress , F is the force and A is the cross-sectional area of the member. In the equation for bending stress , M is the bending moment, y is the distance between the centroidal axis and the outer surface, and I c is the centroidal moment of inertia of the cross section about the appropriate axis. In the equation for torsional stress, T is the torsion, r is the radius, and J is the polar moment of inertia of the cross section.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy. See our Privacy Policy and User Agreement for details. Published on Nov 27,

## Strength of Materials

Strength of Materials focuses on the strength of materials and structural components subjected to different types of force and thermal loadings, the limiting strength criteria of structures, and the theory of strength of structures. Consideration is given to actual operating conditions, problems of crack resistance and theories of failure, the theory of oscillations of real mechanical systems, and calculations of the stress-strain state of structural components. Strength of Materials is a translation of the peer-reviewed Ukrainian journal Problemy Prochnosti. Issue 5, September

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