Calculate the stress/strain?

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In summary, the maximum proposed stress for the new design is 670MPa and the tensile strength of the steel has been measured using an appropriate standard. The load vs displacement graph is given and the steel sheet is 3mm thick with a width of 12.5mm and gauge length of 50mm. The stress strain graph can be plotted using the load and cross sectional area of 12.5x3mm.
  • #1
ipocoyo
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Homework Statement


The maximum proposed stress of their new design is 670MPa. You have measured the tensile strength of pieces of their steel, using an appropriate "standard" to guide you. (What does this even mean?) The load vs displacement graph is given. The steel sheet is 3mm thick. The width of the sample is 12.5mm and the gauge length sample is 50mm. Plot the stress strain graph.

Homework Equations


mm load, N
7.52E-03 1.32E+03
1.69E-02 3.30E+03
2.61E-02 4.85E+03
3.68E-02 6.53E+03
5.02E-02 8.48E+03
6.34E-02 1.05E+04
7.74E-02 1.25E+04
9.42E-02 1.44E+04
1.04E-01 1.63E+04
1.13E-01 1.81E+04
1.27E-01 1.98E+04
1.44E-01 2.14E+04
1.80E-01 2.27E+04
4.48E-01 2.34E+04
8.10E-01 2.40E+04
1.13E+00 2.47E+04
1.47E+00 2.52E+04
1.80E+00 2.57E+04
2.16E+00 2.62E+04
2.50E+00 2.65E+04
2.81E+00 2.69E+04
3.09E+00 2.75E+04
3.42E+00 2.80E+04
3.76E+00 2.83E+04
4.18E+00 2.80E+04
4.63E+00 2.74E+04
5.12E+00 2.72E+04
5.47E+00 2.67E+04
5.71E+00 2.59E+04
5.71E+00 2.49E+04
5.71E+00 2.37E+04
5.70E+00 2.21E+04
5.30E+00 2.03E+04

The Attempt at a Solution



How do I find the stress for each load? I know that it is F/A, but I thought this only applied to rods and not a metal sheet? Or am i allowed to use 12.5x5 as the cross sectional area?
 
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  • #2
ipocoyo said:

Homework Statement


The maximum proposed stress of their new design is 670MPa. You have measured the tensile strength of pieces of their steel, using an appropriate "standard" to guide you. (What does this even mean?) The load vs displacement graph is given. The steel sheet is 3mm thick. The width of the sample is 12.5mm and the gauge length sample is 50mm. Plot the stress strain graph.

Homework Equations


mm load, N
7.52E-03 1.32E+03
1.69E-02 3.30E+03
2.61E-02 4.85E+03
3.68E-02 6.53E+03
5.02E-02 8.48E+03
6.34E-02 1.05E+04
7.74E-02 1.25E+04
9.42E-02 1.44E+04
1.04E-01 1.63E+04
1.13E-01 1.81E+04
1.27E-01 1.98E+04
1.44E-01 2.14E+04
1.80E-01 2.27E+04
4.48E-01 2.34E+04
8.10E-01 2.40E+04
1.13E+00 2.47E+04
1.47E+00 2.52E+04
1.80E+00 2.57E+04
2.16E+00 2.62E+04
2.50E+00 2.65E+04
2.81E+00 2.69E+04
3.09E+00 2.75E+04
3.42E+00 2.80E+04
3.76E+00 2.83E+04
4.18E+00 2.80E+04
4.63E+00 2.74E+04
5.12E+00 2.72E+04
5.47E+00 2.67E+04
5.71E+00 2.59E+04
5.71E+00 2.49E+04
5.71E+00 2.37E+04
5.70E+00 2.21E+04
5.30E+00 2.03E+04

The Attempt at a Solution



How do I find the stress for each load? I know that it is F/A, but I thought this only applied to rods and not a metal sheet? Or am i allowed to use 12.5x5 as the cross sectional area?
Yes, you are, although it should be 12.5x3. What made you think that it only applies to a rod?

It certainly applies to a sheet if the thickness and width are small compared to the gauge length.

Chet
 
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  • #3
Chestermiller said:
Yes, you are, although it should be 12.5x3. What made you think that it only applies to a rod?

It certainly applies to a sheet if the thickness and width are small compared to the gauge length.

Chet
Thank you for clearing up the confusion!
 

What is stress/strain and why is it important?

Stress and strain are two important measurements in materials science and engineering. Stress is a measure of the internal forces acting on a material, while strain is a measure of the deformation or change in shape of the material in response to these forces. These measurements help us understand how materials behave under different conditions and are essential in designing safe and efficient structures.

What is the formula for calculating stress?

The formula for stress is stress = force/area. This means that stress is equal to the amount of force applied to a material divided by the cross-sectional area of the material. Stress is typically measured in units of force per unit area, such as pounds per square inch (psi) or pascals (Pa).

How do you calculate strain?

Strain is calculated by dividing the change in length of a material by its original length. This can be expressed as strain = change in length/original length. Strain is a dimensionless quantity, meaning it has no units of measurement.

What is the difference between stress and strain?

The main difference between stress and strain is that stress is a measure of the internal forces acting on a material, while strain is a measure of the resulting deformation or change in shape of the material. Stress and strain are related, as the amount of stress applied to a material will determine the amount of strain it experiences.

What factors can affect stress and strain calculations?

There are several factors that can affect stress and strain calculations, including the type of material being tested, the temperature and environment in which the material is tested, and the rate at which stress is applied. Additionally, the shape and size of the material can also impact stress and strain measurements.

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