Temperature Stress and Strain – Stress and Strain – Strength of Materials


Hello friends here in this video we are going to see the concept of temperature stress and strain let us get started it is temperature stresses and strains now what is the meaning of temperature stress and strain is first of all I will write down that when a material is heated it is free to expand similarly when a material is cooled it is free to contract that is if we are heating the material then it will expand there will be increase in its dimension and when we are cooling the material at that time there will be decrease in its dimension so now that results in free expansion I will write down hence free expansion and contraction is possible but what happens when we stop this free expansion or contraction then I can say that when the free expansion or contraction is partially or completely prevented then there will be stresses developed in the material so as I have written here that when the material is heated it is free to expand when it is cooled then it is free to contract hence we can say free expansion and free contraction is possible but when the free expansion or contraction is partially or completely prevented that is we do not allow the material to expand freely we stop its expansion or contraction then there will be stresses developed in the material and such stresses which are developed in the material because of temperature change are called as temperature stresses or we can say that they are thermal stresses so when the stresses developed in the material due to temperature change they will be called as temperature stresses or thermal stresses and I can say that corresponding strain developed in the material will be called as temperature strain or thermal strain so as we can see that when we are increasing or decreasing the temperature of any material then it is possible for the material to freely expand or contract but if we prevent this free expansion of attraction partially or completely then stresses are developed in the material and such kind of stresses are called as temperature stresses or thermal stresses and because of the stress the strain which is developed in the material will be called as temperature strain or thermal strain now after we have seen all the definitions now let me give the formula of temperature stress and strain so for that I will assume an example that if there is a rod made up of metal metal rod its length is capital L and now if we are heating this suppose I can give the example that here if we are heating this metal rod this is the heat which is provided so now at first this metal rod would have been at an initial temperature that would have been t1 now because of heating the temperature changes and suppose that temperature is t2 so there is change in temperature so that change in temperature is denoted by delta T which is equal to final temperature minus initial temperature and as the rod is made up of metal when heat is provided that fraud will expand and suppose this much is the free expansion of the rod this free expansion of the rod is there in this metal rod that is when we heat that it will freely expand but if anyhow we are stopping this free expansion suppose I have a wall here which is stopping this free expansion then there will be stress developed inside the metal rod and such kind of stress would be called as temperature stress and the change in dimension upon the original dimension which is the change in length upon original length that would be called as strain and here in this case we have temperature string so this free expansion it is denoted by Delta L so first I will write down that since free expansion of metal rod is given by the free expansion is given by deflection Delta L and that is equal to alpha into delta T multiplied by L this is the formula of free expansion so here I can see that where Delta L is equal to free expansion because you are I am considering heating if this would have been cooling then Delta L would have been free contraction so here I have three expansion of the rod unit will be mm Delta L is the free expansion of the rod alpha is called as coefficient of thermal expansion or contraction and it’s unit is per degree Celsius alpha indicates that how much the material will expand or contract if the alpha value is more that material will expand or contract due to temperature change if we have less alpha value that material will expand less or it will contract less now after getting alpha delta T is the temperature change which is denoted by final temperature minus initial temperature in per degree Celsius next I have n which is called as length of the rod which will again be in terms of mm that is the original length of the rod which is there before expansion now after understanding the free expansion the next thing is I will write down the formula first for temperature strain so since temperature strain is given by the formula of temperature strain is same as linear strain that is temperature strain is denoted by small E and that is equal to change in length divided by original length so therefore temperature stirring your change in length is Delta L original length is l and Delta L we have known that it is alpha into delta T multiplied by L upon L so from the numerator and denominator the original length gets cancelled out so here I have the formula of temperature strain which is alpha into delta T I will call this as equation number one so equation number one gives the formula for temperature strain next after hitting temperature strain now as I have derived this formula I will also calculate the formula for temperature stress so since temperature stress is given by here I will use the concept from Hookes law that is I will say that from Hookes law we know that stress is directly proportional to strain if I remove the proportionality sign there is constant capital e which is called as Young’s modulus so finally stress will become Young’s modulus into strain we have found out it was from equation 1 alpha into delta T so here I have the formula of capital e into alpha into delta T so I can even write this as alpha into delta T multiplied by Young’s modulus so here I will call this as second equation I can see that from equation number two temperature stress can be calculated so yon we have seen that in this video that what was meant by temperature stresses and strain I started the concept by explaining how the material will expand or contract when there is change in temperature then there would have been free expansion of Rican traction depending on the temperature change after that we have seen when the free expansion of contraction is partially or completely prevented then there will be stresses developed in the material and such kind of stresses are called as temperature or thermal stresses and the resulting strain are called as temperature strain or thermal strain and that I had explained with the help of a diagram of a metal rod which was heated and I the first formula we have got was the of the free expansion next we had seen the formula of temperature strain in equation number 1 that is alpha into delta T where alpha is the coefficient of thermal expansion of interaction Delta D is the change in temperature of the body similarly we have seen the formula of thermal stress that is alpha into delta T into young’s modulus where we can say that from this equation number 2 the thermal stress or temperature stress can be calculated so in this video we have seen temperature stresses and strain in detail

37 Replies to “Temperature Stress and Strain – Stress and Strain – Strength of Materials”

  1. Thankuu sir.. & apka video bahut acchey se samajh me aata.. Aur sir ek question hai sir simple stress and strain chapter. Me ek question hai.. Wo question ye hai.. Relationship between C, E and K. Plzz sir ye video samjhayiye ga

  2. i understand the formulea transposition, but i do not get why you incorperate the 'normal' equation for strain into the one for tempreature strain??? is it because the strain IS ONE THING and the tempreature IS ANOTHER if you understand me? πŸ™‚ but good vid tho as an HND engineering student, i like it

  3. Nice sir thanks for this video i can surely say now I'll not forget ever.
    Your method of deliver is very soft…
    Thanks again

  4. I think you have to buy a good microphone coz when i use a headphone only left side speaker works 😑😑😑 which irritates

  5. Hello Friends,

    Watch Complete Video Series of Subject Strength of Materials only on Ekeeda Application.

    Use Coupon Code "NEWUSER" and access any one Subject free for 3 days!

    Download Ekeeda Application and take advantage of this offer.

    Android:- https://play.google.com/store/apps/details?id=student.ekeeda.com.ekeeda_student&hl=en

    iOS:- https://itunes.apple.com/tt/app/ekeeda/id1442131224

Leave a Reply

Your email address will not be published. Required fields are marked *