# State of stress, strain and hookes law

• Dell
In summary, the conversation is about finding the state of stress based on the given state of strain. The speaker used Hooke's law and the given values for E, v, and strain components to calculate the stress components. However, the resulting values do not match with the expected answers from the question. The speaker also mentions difficulties in finding the value for the shear stress component, \tauxy. They question whether they have made a mistake or if there could be errors in the expected answers.
Dell
in the following question i am asked to find the state of stress given the state of strain.
http://lh6.ggpht.com/_H4Iz7SmBrbk/SwBtHnG3qkI/AAAAAAAAB9M/rFS_orHMbGo/Capture.JPG
i went about solving this using hookes law

$$\sigma$$xx=E[(1-v)$$\epsilon$$xx + v($$\epsilon$$yy+$$\epsilon$$zz)]/[(1+v)1-2v)]

using the given
E=30*106
v=0.3
$$\epsilon$$x=0.001
$$\epsilon$$xy=-1.25*10-3
$$\epsilon$$y=-0.005

i get
$$\sigma$$xx=-4.6154*104
$$\sigma$$yy=-1.8462*105
$$\sigma$$zz=-6.9231*104

but as you can see these are not the correct answers according to the question.
can anyone see where i have gone wrong ?

also how do i find $$\tau$$xy?

Last edited by a moderator:
$$\tau$$xy=G*$$\gamma$$xy=-0.0025*(30*106/2(1.3)=-0.0025*11.53846*106=-2.8846*104

from this i already see that the answers are not going to be the same as the answers in the book, and there is nowhere i have gone wrong with the math here,

am i doing something fundamentally wrong or could they be wrong with their answers,??

Your calculation for the state of stress appears to be correct, based on the given values and using Hooke's law. However, it is possible that there is a mistake in the given values or the question itself. It would be helpful to double check the values and make sure they are accurate.

To find the shear stress, \tauxy, you can use the formula:

\tauxy = G * \gammaxy

where G is the shear modulus and \gammaxy is the shear strain. The shear modulus can be calculated using Hooke's law as:

G = E / (2 * (1 + v))

Substituting the given values, we get:

G = (30 * 10^6) / (2 * (1 + 0.3)) = 15 * 10^6

Now, we can calculate the shear strain, \gammaxy, using the given value for \epsilonxy:

\gammaxy = \epsilonxy = -1.25 * 10^-3

Finally, substituting these values into the formula for shear stress, we get:

\tauxy = (15 * 10^6) * (-1.25 * 10^-3) = -18.75 * 10^3

Therefore, the shear stress is -18.75 * 10^3, which is the correct answer according to the given values.

## 1. How is stress defined?

Stress is defined as the force acting on a material per unit area. It is a measure of the internal forces within a material that resist external forces.

## 2. What is the difference between tensile and compressive stress?

Tensile stress occurs when a material is being pulled or stretched, causing it to elongate. Compressive stress, on the other hand, occurs when a material is being pushed or compressed, causing it to shorten.

## 3. How is strain related to stress?

Strain is a measure of the deformation or change in shape of a material due to stress. It is directly proportional to stress, meaning that as stress increases, strain also increases.

## 4. What is Hooke's law and how is it used?

Hooke's law states that the stress and strain in a material are directly proportional within the elastic limit. This means that if a material is subjected to a small amount of stress, it will deform by a small amount and return to its original shape when the stress is removed. Hooke's law is used to calculate the amount of deformation in a material under a given amount of stress.

## 5. What is the difference between elastic and plastic deformation?

Elastic deformation occurs when a material is subjected to stress within its elastic limit, meaning it can return to its original shape once the stress is removed. Plastic deformation, on the other hand, occurs when a material is subjected to stress beyond its elastic limit, causing permanent deformation.

• Engineering and Comp Sci Homework Help
Replies
1
Views
2K
• Classical Physics
Replies
3
Views
2K
• Mechanical Engineering
Replies
2
Views
2K
• Mechanical Engineering
Replies
7
Views
2K