Consider there is a rubber and I ask you to increase its length, what would you do? Obviously you will try to stretch it from both the ends. Because of this stress will be generated in the rubber and length of the rubber will increase. On the other hand if I ask you to reduce its length then you will compress the rubber from both ends. This application of force along the length of rubber and generating stress in it is nothing but normal stress. In this article we will be studying normal stress in detail.
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If a deforming force acts normal (perpendicular) to the surface of a body, then the internal restoring force set-up per unit area of the body is known as normal stress. Normal stress is also called longitudinal stress. So it is denoted by ().
Formula for longitudinal stress is given by,
Example: Bridges are constructed over the pillars. Pillars act as supporting elements and they lift the complete weight of the bridge. Because of the heavy weight, pillars undergo normal stress. If the quality of construction is poor and this stress exceeds its limiting value, the bridge collapses.
Depending on the direction of deforming force normal stress is of two types.
1. Tensile Stress
Tensile stress occurs due to the stretching force as shown in the figure below.
There is an increase in the length or extension of the body in the direction of force applied. So it causes elongation of the object. In this case the value of strain will be positive because of the increment in the length.
Example: When a solid cylinder is stretched by two equal forces applied normally to its cross sectional area. The restoring force per unit area in the body is tensile stress as shown in the figure below.
Here the length of the cylinder is increased from to because of the deforming force.
2. Compressive Stress
Compressive stress occurs due to the squeezing force as shown in the figure below.
There is a decrease in the length or compression of the body in the direction of force applied. So it causes reduction of the object length. In this case the value of strain will be negative because of the decrease in the length.
Example: When a solid cylinder is compressed by two equal forces applied normally to its cross sectional area as shown in the figure below. The restoring force per unit area in the body is compressive stress.
Here the length of the cylinder is decreased from to because of the deforming force.
Q 1. A rod has a radius of and a length of . A force is compressed along its length.Calculate the longitudinal stress developed in the rod?
Q 2. A massless rod of cross sectional area is suspended from a support. A mass of 15 Kg is attached to its end. Find the tensile stress in the rod?
Weight of the attached mass will act as tensile force so,
Q 3. A body is kept on horizontal ground along the x axis as shown in the figure. A force of 100 N is applied at an angle of 30 degrees to the horizontal. Find the longitudinal stress in the body assuming the top surface as its cross sectional area?
A. The vertical component of applied force will act as normal force. So
Q 4. Equal and opposite force F is applied on the bar as shown in the figure. The plane PQ makes an angle with a cross section of the bar. If the area of the cross section is A, find the normal stress on PQ?
A. The normal force acting on plane PQ is,
The affective area of PQ along which the force acts is
Q 1. What is the direction of deforming force in longitudinal stress?
Answer: Deforming force is perpendicular to the area of cross section in case of longitudinal stress.
Q 2. In which scenario the strain during normal stress will be negative?
Answer: If the normal stress is compressive in nature it will reduce the length of the object so in this case strain will become negative.
Q 3. What is the difference between compressive stress and tensile stress?
Answer: Length of the object gets reduced in compressive stress and length of the object gets increased in case of tensile stress.
Q 4. Where do we encounter normal stress in real life, give one example?
Answer: Pillars used in the construction of houses undergo normal stress as they support the weight of the building.