Shear stress in a beam

In summary: Your name]In summary, to find the shearing stress at n-n, you can use the area under the shear diagram from point A to n-n. For the shearing stress at the point shown in the cross section, you would need to use the formula for shear stress and calculate the necessary values using the given information.
  • #1
a_hargy
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Homework Statement


A simply supported beam with its cross-section is shown in the attached figure 2.2. For the beam and loading shown, determine the largest shearing stress in the section n~n and shearing stress at point a shown in cross-section of the beam.


Homework Equations





The Attempt at a Solution


So to find the shearing stress at n-n I developed a shear diagram. Is it correct that the shear stress at n-n would be the area under this diagram from point A to n-n? That being 110kN x 0.3m which gives 33kPa?
I am stuck on how to calculate the shearing stress at the point shown in the cross section. Any help would be greatly appreciated.

Cheers,
Adam
 

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  • #2


Hello Adam,

Thank you for your question. It seems like you are on the right track with your approach to finding the shearing stress at n-n. The area under the shear diagram from point A to n-n would indeed give you the shearing stress at that point.

To calculate the shearing stress at the point shown in the cross section, you would need to use the formula for shear stress, which is:

τ = VQ/Ib

Where τ is the shear stress, V is the shear force, Q is the first moment of area of the cross section, I is the moment of inertia of the cross section and b is the width of the cross section.

In this case, the shear force at the point shown in the cross section can be found by taking the sum of the forces to the left of that point. Once you have the shear force, you can calculate the first moment of area and the moment of inertia of the cross section. Then, using the formula, you can find the shearing stress at that point.

I hope this helps. Let me know if you need any further clarification.


 

1. What is shear stress in a beam?

Shear stress in a beam is a type of stress that occurs when two forces act parallel to each other but in opposite directions, causing the beam to experience shear deformation.

2. How is shear stress calculated in a beam?

Shear stress in a beam can be calculated by dividing the shear force by the cross-sectional area of the beam.

3. What factors affect shear stress in a beam?

The factors that affect shear stress in a beam include the magnitude and direction of the applied forces, the cross-sectional area of the beam, and the length of the beam.

4. Why is shear stress important in beam design?

Shear stress is important in beam design because it can help determine the maximum load a beam can withstand before failure. It is also essential for ensuring the structural integrity and stability of a beam.

5. How can shear stress in a beam be reduced?

Shear stress in a beam can be reduced by increasing the beam's cross-sectional area, using stronger materials, or changing the direction of the applied forces. Proper beam design and reinforcement can also help to reduce shear stress.

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