Stress, strain and deflections due to temperature change

In summary, the conversation discusses the problem of calculating the stress caused by excess deflection in a system with two different materials. The conversation explains the process of finding the force and strain of each material and how it relates to the total deflection. However, the speaker realizes that their stress calculations may be incorrect and needs to consider the expansion of each material in their calculation.
  • #1
Dell
590
0
in the following problem
Capture.JPG


i know that ΔT=120

now the maximum deflection is 0.5mm so i looked for the total deflection had there been no restrictions

ΔL(aluminium)=300*(23e-6*120)= 0.8280
ΔL(st steel)=250*(18e-6*120)= 0.5400

this is clearly more than the maximum deflection of 0.5- there are 0.868 "extra" which cause the stress.

now putting this all together is where i get stumped.


F=ε*E*A
and ΔL=ε*L

F(aluminium)=ε(al)*(70e9)*(2000)
F(steel)=ε(s)*(190e9)*(800)
ε(al)*300+ε(s)*250=0.5

now the force in the aluminium and in the steel must be equal so i have 3 equation system to solve, after solving i get

F= 1.3201e+011
ε(al)= 0.942928e-3
ε(s)=0.868486e-3

now simply using

σ=ε*E or σ=F/A

σ=ε*E
=0.942928e-3*70e9
=66004960

but the correct answer is -114.6MPa

i can see where this might be wrong, nowhere in my stress calculations do i take into account the amount that each material expands. but i have no idea how to fix it
 
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  • #2
think i got it,

F(aluminium)=ε(al)*(70e9)*(2000)
F(steel)=ε(s)*(190e9)*(800)
ε(al)*300+ε(s)*250=0.868
 
  • #3


I would like to first clarify that stress, strain, and deflection are all related but different concepts. Stress is the force per unit area that a material experiences, while strain is the deformation or change in shape of a material due to the applied stress. Deflection, on the other hand, is the displacement or movement of a material due to an external force or load.

In this problem, we are dealing with stress, strain, and deflection due to temperature change. When a material is subjected to a change in temperature, it expands or contracts, causing stress and strain. The amount of deflection that occurs depends on the material's properties, such as its coefficient of thermal expansion.

In order to solve this problem, we need to consider the thermal expansion of both materials, as well as the force and area of each material. We also need to consider the relationship between stress and strain, which is given by the material's modulus of elasticity (E).

To begin, we can calculate the total thermal expansion of each material using the given temperature change (ΔT=120) and the material's coefficient of thermal expansion. This will give us the total change in length (ΔL) for each material.

ΔL(aluminium) = 300 * (23e-6 * 120) = 0.828 mm
ΔL(stainless steel) = 250 * (18e-6 * 120) = 0.54 mm

Next, we need to calculate the strain for each material using the formula ΔL/L, where L is the original length of the material. This will give us the amount of deformation for each material.

ε(aluminium) = 0.828 mm / 300 mm = 2.76e-3
ε(stainless steel) = 0.54 mm / 250 mm = 2.16e-3

Now, we can use the relationship between stress and strain to calculate the stress in each material. Recall that stress is equal to E * strain, where E is the modulus of elasticity for the material.

σ(aluminium) = 2.76e-3 * 70e9 = 193.2 MPa
σ(stainless steel) = 2.16e-3 * 190e9 = 410.4 MPa

We can see that the stress in the aluminium is lower than the maximum allowable stress of 114.
 

Related to Stress, strain and deflections due to temperature change

What is stress and how does it relate to temperature change?

Stress is a measure of the force applied to a material per unit area. Temperature change can cause stress in a material because it can cause the material to expand or contract, leading to strains and deflections.

What is strain and how is it affected by temperature change?

Strain is a measure of the deformation of a material due to stress. Temperature change can affect strain by causing the material to expand or contract, leading to changes in its dimensions and shape.

What is the relationship between stress, strain, and deflection in materials due to temperature change?

When a material experiences a change in temperature, it can cause stress and strain within the material, which can lead to deflections or changes in its shape. The amount of deflection is directly related to the amount of stress and strain experienced by the material.

What are some common materials that are susceptible to stress, strain, and deflections due to temperature change?

Most materials are susceptible to stress, strain, and deflections due to temperature change, but some common examples include metals, plastics, and wood. These materials have different coefficients of thermal expansion, which can make them more or less affected by temperature changes.

How can engineers and scientists mitigate the effects of stress, strain, and deflections due to temperature change in materials?

Engineers and scientists can mitigate the effects of temperature change by carefully selecting materials with appropriate coefficients of thermal expansion, using materials that can withstand high temperatures, and designing structures with enough flexibility to accommodate changes in dimensions due to temperature. Additionally, using insulation or temperature control measures can help minimize the impact of temperature on materials.

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