A1000mm long 15M rebar is placed on a frictionless surface s

A1000mm long 15M rebar is placed on a frictionless surface shortly after manufacturing. If there is no change in temperature, what is the stress in the rebar after 5 years, and what is the change in length? What would the stress in the rebar and the change in length if the temperature dropped by 40 degrees celcius?

Solution

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CONCEPT:

Stress is only developed when a body is facing some resistance.

It means whenever a body is in free state, there is no resistance to the body and as a result the stress acting in the body at that time is ZERO.

ANSWER:

Here, in first case, A1000mm long 15M rebar is placed on a frictionless surface shortly after manufacturing means that there is no resistance to the body. Also as there is no change in temperature so it can be said the stress in the rebar after 5 years will be ZERO.

As the stress is zero, the value of strain will be Zero and so the change in length will also be ZERO.

In second case, If the temperature is dropped by 40 degree centigrade , the change in length will be

= Length * expansion coefficient of steel * change in temperature

= 1000 * 13 x 10^-6 * ( - 40 )

= - 0.52 mm ( negative sign indicates decrease in length of bar)

Stress developed due to change in temperature = Strain * Modulus of Elasticity of steel

= ( 0.52 / 1000 ) * 2 * 10⁵

= 104 N/mm² ( tensile stress in rebar)