what is the strain in a flat plate of 1m x 3m if it\'s subjected to a temperatur

Question

what is the strain in a flat plate of 1m x 3m if it's subjected to a temperature increase of 200. find the induced stress for both directions if the plate is constrained there. what is the strain in a flat plate of 1m x 3m if it's subjected to a temperature increase of 200. find the induced stress for both directions if the plate is constrained there. what is the strain in a flat plate of 1m x 3m if it's subjected to a temperature increase of 200. find the induced stress for both directions if the plate is constrained there.

Explanation / Answer

The question does not specify the material. We take it as steel.

We note the following properties for the steel :

= Coefficient of thermal expansion for steel 12 x 10-6 m/m/ok

E = Young’s modulus for steel = 200 GPa

= poison’s ratio = 0.3

Temperature raise : 200 oC

e = Strain in the material is defined as elongation/contraction per unit length = expansion due to temperature raise = 12 x 10-6 m/m/ok x 200 = 2.40 x10-3 m/m

This thermal expansion is same in both x and y directions.

When this thermal expansion is constrained, it will result in compressive stress corresponding to e.

Let x and y be the stresses in x and y directions. Then ex= (x- y)/E and ey= (y- x)/E

As we know the expansion is same in all directions we get same stresses induced in x and y directions.

Then we have x= y = eE/(1-) substituting the values we get x= y= 720 MPa

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.