Stresses and change in length in a compound bar

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The discussion focuses on calculating the stresses and changes in length of a compound bar under a compressive load of 40 kN, with mild steel and concrete as the materials involved. Initial calculations yield stress values of 1000 kN/m² for steel and 250 kN/m² for concrete, leading to strain values of 4.9 x 10^-6 for steel and 25 x 10^-6 for concrete. The corresponding free changes in length are calculated as 1.2 x 10^-6 m for steel and 6.25 x 10^-6 m for concrete. Participants suggest using the effective spring constant approach to determine the overall change in length of the joined bar, noting that both materials will compress the same distance under load. The conversation emphasizes understanding the relationship between stress, strain, and Young's modulus for accurate calculations.
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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.
 
Last edited by a moderator:
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Does the following help? I think you have figured out what I call k1 and k2.
 
Spinnor said:
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.
 
Can anybody else offer a solution?
 
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!
 
Last edited:
Spinnor said:
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.
 
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
 
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