How Is Strain Calculated in a Composite Concrete and Steel Column Under Load?

[Batman1]

Homework Statement

A Concrete column 2M in height 100mm in diameter and containing four steel rods each at 15mm diameter calculate the stress and the amount the column is compressed due to the load of 9Kn. the modulus of elasticity for the concrete (in this case) is 20GPa and for the steel its 200GPa. I have worked out the total area of the steel bars to be 0.706856X10^-3 (meters squared) and the concrete to be 0.00785398 (meters squared).
But I don’t know how to work out the strain value (must be same for both materials) or the amount of force acting on the separate materials.

Homework Equations

Force = force of material 1 + force of material 2 (concrete and steel)
Stress of material A = total force/area of A X force acting on A


3. The Attempt at a Solution
I have tried several but they have all been incorrect because I can not find the individual stress for each material.

4. Thank you in advance for anyone who can help me to solve this problem
(see attachment for the Question.)

 

[PhanthomJay]

Homework Statement

A Concrete column 2M in height 100mm in diameter and containing four steel rods each at 15mm diameter calculate the stress and the amount the column is compressed due to the load of 9Kn. the modulus of elasticity for the concrete (in this case) is 20GPa and for the steel its 200GPa. I have worked out the total area of the steel bars to be 0.706856X10^-3 (meters squared) and the concrete to be 0.00785398 (meters squared).
But I don’t know how to work out the strain value (must be same for both materials) or the amount of force acting on the separate materials.

Homework Equations

Force = force of material 1 + force of material 2 (concrete and steel)
Stress of material A = total force/area of A X force acting on A


3. The Attempt at a Solution
I have tried several but they have all been incorrect because I can not find the individual stress for each material.

4. Thank you in advance for anyone who can help me to solve this problem
(see attachment for the Question.)

You must first calculate the load acting on the left column support (you don't specifically say if you have done this, but it is not 9kN). Then, yes, the strains (and deformations) would be equal in both materials, so you may write the stress-deformation equation as a function of E and A for each material, and set the deformations equal. Then you need to take note of the fact that the loads (not the stress) carried by each material must sum to the total column load. Then you can now calculate all the requested values.