## STRENGTH OF MATERIAL

## STRESS

## FORCE PER UNIT AREA OR INTENSITY OF THE FORCE DISTRIBUTED OVER A GIVEN SECTION IS CALLED THE STRESS ON THAT SECTION AND IS DENOTED BY SIGMA.THE STRESS IN A MEMBER OF CROSS SECTIONAL AREA "A" SUBJECTED TO THE AXIAL LOAD"P" IS OBTAINED BY DIVIDING THE MAGNITUDE "P" OF THE LOAD BY THE AREA "A".THE UNIT OF STRESS IS PASCAL OR N/mm^2.

### The figure above shows the force "P" on the section having cross section area "A". The body will set internal resistance to oppose this force to avoid deformation. The formula for stress is given by Stress=Force/Area.

### In general we come across some different types of stress based on nature of application of force that are discussed below:-

__COMPRESSIVE STRESS (a)__

Opposite of tensile stress is compressive stress. In this force is applied in direction of specimen. Under compressive stress the material's length decreases and its diameter or thickness increases. The compressive stress can be calculated in the similar way as tensile stress is calculated.

Compressive stress=Force/Area.

__TENSILE STRESS (b)__

### The nature of force in tensile stress is away from the body. As in the figure a specimen is subjected to force F across the area A. At any instant the stress induced in the body. Due to tensile stress body suffers elongation in length and subsequently decreases in the diameter.

__SHEAR STRESS (c)__

It is surface phenomenon. When stress is applied along the surface of body (say in tangential direction along the line of action) the body is said to have shear stress. The figure shows the tangential stress or shear stress along the upper surface.

When a body is given force from all the directions such that the forces are acting perpendicular to the surface in equal magnitude then the body is said to be under volumetric stress.

Consider a cube as shown in figure, compressive force from all direction is applied and in equal magnitude. This type of stress results in change in volume of body and at the same time retaining the shape of body.

__STRAIN IN MECHANICS__

When a body is stressed or force is applied on it then the shape of body changes due to stress. The strain in simple words can be explained as changes in shape of body from original shape. The ratio of changed shape to the original shape is called strain. It is unit less quantity. The type of strain depends on the mode of application of force on the body and noticeably deformation or change occurring in the body.

The three types of strains that we study in mechanics are:-

1) Longitudinal strain occurring due to change in length

2) Volumetric strain occurring due to change in overall volume of body.

3) Shear strain which occurs due to deformation of surface.

__LONGITUDINAL STRAIN:-__

When the body is subjected to change in length by application of external force then it is said to develop longitudinal strain. Let L be the original length and ΔL be the increase in the length by small amount Δ. Then final length developed in the body is L+ΔL on application of force. When there is elongation in the length of specimen after application of force it is called tensile strain. Similarly when the length of specimen decreases it is called compressive strain.

LONGITUDINAL STRAIN= Change in length/Original length = L+ΔL/ L

__VOLUMETRIC STRAIN:__

__-__

When a body is deformed from all direction or in other words when the volume of body changes with respect to its original volume then the body is said to be subjected to volumetric strain. Let the initial volume of body be V and let ΔV be change in the volume of body then volumetric strain can be estimated by dividing change in volume to original volume.

VOLUMETRIC STRAIN=Change in volume/original volume= V+ΔV/ΔV.

__SHEAR STRAIN:-__

When force acting on the surface of the body then shear strain develops. The shear strain tries to move the upper surface of the body along the direction of force. The magnitude of applied force is responsible for the deformation caused.

1) Consider P be the load and A be the area, stress is expressed as

1) A/P

2) A*P

3) P/A

4) P-A

2) Who discovered that stress is directly proportional to strain within elastic limit?

1) Robert hook

2) Mech huge

3) Alferd Nobel

4) None

3) The point at whole weight of body is assumed to act is called?

1) Moment of inertia

2) Center of buoyancy

3) Center of gravity

4) Center of velocity

4) The ratio of change of volume to original volume is called ?

1) Tensile strain

2) Shear strain

3) Volumetric strain

4) Shear strain

__Objective questions:-__1) Consider P be the load and A be the area, stress is expressed as

1) A/P

2) A*P

3) P/A

4) P-A

2) Who discovered that stress is directly proportional to strain within elastic limit?

1) Robert hook

2) Mech huge

3) Alferd Nobel

4) None

3) The point at whole weight of body is assumed to act is called?

1) Moment of inertia

2) Center of buoyancy

3) Center of gravity

4) Center of velocity

4) The ratio of change of volume to original volume is called ?

1) Tensile strain

2) Shear strain

3) Volumetric strain

4) Shear strain

5) Ratio of shear stress to shear strain is called?

1) Poisson's ratio

2) Young modulus

3) Modulus of rigidity

4) None

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