Finding the max shear stress at a point on a plate (with a hole)

In summary, to find the maximum shear stress at a point on a plate with a hole under tension, you can use experimental data to determine the principal strains at the point and then apply Mohr's Circle to find the maximum shear stress. This can also be calculated using the regular stress components. It is important to consider whether the problem is in plane stress and to follow the standard practice of numbering the highest principal stress as \sigma_1.
  • #1
bill nye scienceguy!
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i need to find max shear stress at a point on a plate (with a hole) under tension. i found using experimental data the principle strains at the point but i need to find the max shear stress using this data to compare it with a result found analytically.

any suggestions?
 
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  • #2
Are you considering this plane stress? If you are, you'll have two principal stresses. Think about Mohr's Circle for a second...The principal stresses lie in a plane with no shear stresses (they lie on the horizontal axis). So if you rotate around 90° in Mohr's circle, you'll get to the point of max shear (the highest point on the vertical axis). Geometrically speaking that is the same as saying

[tex]\tau_{max} = \frac{\sigma_1-\sigma_2}{2}[/tex]

This also assumes that you follow the standard practice of numbering the highest principal stress as [tex]\sigma_1[/tex].

You can double check it by running the calculation with the regular stress components:

[tex]\tau_{max}=\sqrt{\left[ \frac{\sigma_x-\sigma_y}{2}\right]^2 + \tau_{xy}^2}[/tex]
 
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  • #3


There are several ways to find the maximum shear stress at a point on a plate with a hole under tension. One approach is to use Mohr's circle, which is a graphical method for determining the principal stresses and maximum shear stress at a point. Another approach is to use the stress transformation equations, which relate the normal stresses and shear stresses at different angles to the principal stresses. Additionally, you could also use finite element analysis software to simulate the stress distribution at the point and determine the maximum shear stress. Whichever method you choose, it is important to ensure that your experimental data and analytical results are accurate and consistent. I would recommend verifying your experimental data through multiple trials and using a reliable analytical method to confirm your results.
 

1. What is shear stress and how does it affect a plate with a hole?

Shear stress is a type of stress that occurs when two forces act parallel to each other, causing a deformation in the material. In a plate with a hole, the presence of the hole causes the stress to be distributed unevenly, resulting in higher stress concentrations near the edges of the hole.

2. How do you calculate the maximum shear stress at a point on a plate with a hole?

The maximum shear stress at a point on a plate with a hole can be calculated using the Von Mises stress formula, which takes into account the tensile and compressive stresses as well as the shear stresses at the point. This formula can be derived from the Mohr's circle, which is a graphical representation of the stresses acting on a material.

3. What factors can affect the maximum shear stress at a point on a plate with a hole?

The maximum shear stress at a point on a plate with a hole can be affected by various factors such as the size and shape of the hole, the material properties of the plate, and the applied loads. Additionally, the orientation and location of the point on the plate can also impact the maximum shear stress.

4. How can the maximum shear stress at a point on a plate with a hole be reduced?

The maximum shear stress at a point on a plate with a hole can be reduced by increasing the thickness of the plate, using materials with higher strength and stiffness, or by changing the shape and size of the hole. Additionally, modifying the loading conditions or adding reinforcements can also help in reducing the maximum shear stress.

5. What are the limitations of using the Von Mises stress formula to calculate the maximum shear stress at a point on a plate with a hole?

The Von Mises stress formula assumes that the material being analyzed is isotropic and that the stress state is elastic. This means that it may not accurately predict the maximum shear stress in cases where the material is anisotropic or when the stress state is beyond the elastic limit. Additionally, the formula does not take into account the effect of stress concentration at the edges of the hole.

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