How do I find the critical value of shear stress?

In summary, to find the critical value of shear stress at the junction and at the neutral axis, you will need to use the formula for shear flow rather than the formula for shear stress. This is because the formula for shear stress only applies to calculating bending stress and may not necessarily give the maximum stress. At points where there is a change in the distribution of material, such as the junction of the flanges with the web, the shear stress will also change drastically. Therefore, using the correct formula for shear flow will give you a more accurate analysis of this problem.
  • #1
w31ha-
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Homework Statement


Finding the critical value of shear stress at the junction and at the neutral axis

Homework Equations


stress max = (Bending moment x height from neutral axis)/Moment of inertia
Shear stress = Shear force/area

The Attempt at a Solution


I am able to do the first 2 parts but not the last one. I'm not really sure which of the 2 equations to use and what it meant by critical value.
 

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  • #2
w31ha- said:

Homework Statement


Finding the critical value of shear stress at the junction and at the neutral axis

Homework Equations


stress max = (Bending moment x height from neutral axis)/Moment of inertia
Shear stress = Shear force/area

The Attempt at a Solution


I am able to do the first 2 parts but not the last one. I'm not really sure which of the 2 equations to use and what it meant by critical value.

You are not going to be able to calculate any meaningful shear stresses with the formula:

Shear stress = Shear force/area

This formula:

stress max = (Bending moment x height from neutral axis)/Moment of inertia

is not for the maximum stress. It is the general formula for calculating only the bending stress, which may or may not necessarily be the maximum stress.

For this type of section, the shear stress is zero at the outer fibers of the flanges and a maximum at the N.A.

At points where there is a change in the distribution of material, at the junction of the flanges with the web, there is a drastic change in shear stress.

Find a better formula for shear stress and you'll have better success analyzing this problem.
 
  • #3
Do you know the shear flow formula?
 

1. What is shear stress?

Shear stress is the force per unit area that acts parallel to the surface of an object, causing it to deform or undergo a change in shape.

2. Why is it important to find the critical value of shear stress?

The critical value of shear stress is the maximum amount of shear stress that a material can withstand before it fails. This information is crucial in engineering and material design to ensure the safety and durability of structures under different loading conditions.

3. How do I calculate the critical value of shear stress?

The critical value of shear stress can be calculated using the formula: τc = σc/2, where τc is the critical shear stress, and σc is the critical tensile or compressive stress of the material. This formula assumes that the failure occurs at a 45-degree angle from the direction of the applied stress.

4. What factors can affect the critical value of shear stress?

The critical value of shear stress can be influenced by various factors such as temperature, material composition, and mechanical properties. For example, high temperatures can weaken the material, causing a decrease in the critical shear stress.

5. Can the critical value of shear stress be determined experimentally?

Yes, the critical value of shear stress can be determined through experimental testing, such as shear testing or tensile testing, where the material is subjected to different levels of stress until it fails. The maximum stress at which failure occurs is considered the critical value of shear stress.

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