Compression in composite bars

[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.

 

[piercas]

I would approach this problem by first identifying the key equations and principles involved. In this case, we are dealing with the concepts of stress, strain, and modulus of elasticity. The stress-strain relationship can be expressed as σ = Eε, where σ is stress, E is the modulus of elasticity, and ε is strain.

To calculate the strain, we need to know the change in length of the column (ΔL) and its original length (L). The strain can then be calculated as ε = ΔL/L. However, in this problem, we are given the load applied (9Kn) instead of the change in length. To find the change in length, we can use Hooke's Law, which states that the change in length is directly proportional to the applied force and the modulus of elasticity. Mathematically, this can be expressed as ΔL = F*L/E.

To find the individual stresses of the concrete and steel, we need to first find the forces acting on each material. For the concrete, the force can be calculated as Fc = σc * Ac, where σc is the stress of concrete and Ac is the cross-sectional area of the concrete column. For the steel, the force can be calculated as Fs = σs * As, where σs is the stress of steel and As is the total cross-sectional area of the four steel rods.

To find the stress of each material, we can use the equation σ = F/A, where F is the force and A is the cross-sectional area. So, the stress of concrete can be calculated as σc = Fc/Ac and the stress of steel can be calculated as σs = Fs/As.

Now, we can substitute the values given in the problem to find the stresses of concrete and steel. For the concrete, we have Ac = 0.00785398 m^2 and σc = 20 GPa. Substituting these values into the equation, we get Fc = 0.157078 N. Similarly, for steel, we have As = 0.706856X10^-3 m^2 and σs = 200 GPa, which gives Fs = 0.141671 N.

Finally, we can use the equation for strain (ε = ΔL/L) to find the change in length of the column. Since we know the total force (9Kn) and the modulus of elasticity for