Stresses and change in length in a compound bar

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Homework Statement

Determine the stresses and the change in length of the compound bar.

compressive load F = 40kN
Length L = 0.25m
material (a) mild steel E = 205 GPa
material (a) area = 0.04m^2
material (b) concrete E = 10 GPa
material (b) area = 0.16m^2

For a similar example see example 2 of this PDF:
http://fetweb.ju.edu.jo/staff/che/ymubarak/Strength-lectures/chapter2.pdf

My calculations so far are:
(a) σ = 40/0.04 = 1000kNm^2
(b) σ = 40/0.16 = 250kNm^2

E=σ/ε → ε=σ/E

(a) ε = 1000*10^3/205*10^9
= 4.9*10^-6

(b) ε = 250*10^3/10*10^9
= 25*10^-6

Free change in length = ΔL = ε*L

(a) ΔL = 4.9*10^-6*0.25
= 1.2*10^-6m

(b) ΔL = 25*10^-680.25
= 6.25*10^-6m

After those calculations I am unsure what to do next to find the change in length in a joined compound bar.

Homework Equations

See PDF

The Attempt at a Solution

See above

Thanks a lot for any help in improving my understanding of this.

 

[Spinnor]

Does the following help? I think you have figured out what I call k1 and k2.

 

[Spinnor]

Does the following help? I think you have figured out what I call k1 and k2.

I forgot the following,

 

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It may be related but I can't deduce anything from it.

 

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Can anybody else offer a solution?

 

[Spinnor]

Young's modulus, Y = Stress/Strain = (F/A)/(ΔL/L)

So F = (Y*A*ΔL)/L = kΔL which is the relationship between the applied force on a "spring" and the distance it compresses. In your problem both the steel and concrete are compressed the same distance, they each have an effective spring constant for the problem as stated. So in your case you know k_steel and k_concrete as given above so,

ΔL = F/(k_steel + k_concrete)

Good luck!

 

[Spinnor]

Young's modulus, Y = Stress/Strain = (F/A)/(ΔL/L)

So F = (Y*A*ΔL)/L = kΔL which is the relationship between the applied force on a "spring" and the distance it compresses. In your problem both the steel and concrete are compressed the same distance, they each have an effective spring constant for the problem as stated. So in your case you know k_steel and k_concrete as given above so,

ΔL = F/(k_steel + k_concrete)

Good luck!

After another reading of your link it probably makes sense that the concrete is under compression and the steel is under tension which is a common configuration of those materials, so in that case,

F = k_steel*ΔL_steel = - k_concrete*ΔL_concrete

the concrete gets shorter and the steel gets longer.

 

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Thanks a lot for the replies spinnor, what is it that you are referring to with k btw? is it the Young's Modulus of the materials? concrete E = 10 GPa and mild steel E = 205 GPa

Thanks a lot again