# Variation of shear stress at the rectangle cross section

• fonseh
In summary, the shear stress in a beam varies parabolically along the vertical length and linearly across the width. This is true for most applications, but in cases where there are stress concentrations at corners or edges, the formula may not give accurate results. To fully understand this concept, one must have knowledge of partial differential equations and the Theory of Elasticity. However, it is not necessary to dwell on this topic unless studying at a graduate level. It is also important to note that the diagrams in 7-6 a and 7-6 b show a cross section of the beam, where the shear stress is maximum at the neutral axis and can be assumed constant across the width.
fonseh

## Homework Statement

In the notes , I don't understand why the shear stress is maximum at the edge ( circle part) .

## The Attempt at a Solution

I think it's wrong . Refer to another diagram attached , i found that the shear stress varies parabolically across the vertical length of the beam ... Or they are different case ? Can you explain the case in photo 1 ? [/B]

#### Attachments

• shear limitation.PNG
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• 5LkSu.png
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fonseh said:

## Homework Statement

In the notes , I don't understand why the shear stress is maximum at the edge ( circle part) .

## The Attempt at a Solution

I think it's wrong . Refer to another diagram attached , i found that the shear stress varies parabolically across the vertical length of the beam ... Or they are different case ? Can you explain the case in photo 1 ? [/B]
fonseh you are getting way too deep on this this is grad school level stuff. Stick to the basics. Vert shear stress distribution is parabolic along the height and horiz shear stress is linear across the flange. You may assume that it is constant across the thickness of the web or flange or rectangle,

PhanthomJay said:
fonseh you are getting way too deep on this this is grad school level stuff. Stick to the basics. Vert shear stress distribution is parabolic along the height and horiz shear stress is linear across the flange. You may assume that it is constant across the thickness of the web or flange or rectangle,
ok , that's the explanation for figure 2 in post # 1 , and I understand it . Can you explain based on figure 1? what is it about ? I don't really understand it

It's also stated at the bottom of the notes, the shear formula will not give accurate results when used to determine the shear stress at flange -web section, stress concentration here ... why the shear formula is not suitable to caluculate the stress at stress sudden change part ?

fonseh said:
It's also stated at the bottom of the notes, the shear formula will not give accurate results when used to determine the shear stress at flange -web section, stress concentration here ... why the shear formula is not suitable to caluculate the stress at stress sudden change part ?
The shear stress formula is an approximation which is good enough for most applications. If you want to learn grad school topics at this stage, , like stress concentrations at discontinuities or non constant shear stress across a width, then first learn about partial differential equations and then google on Theory of Elasticity and then I wish you luck.

PhanthomJay said:
The shear stress formula is an approximation which is good enough for most applications. If you want to learn grad school topics at this stage, , like stress concentrations at discontinuities or non constant shear stress across a width, then first learn about partial differential equations and then google on Theory of Elasticity and then I wish you luck.
do you mean the notes in photo 1 is another way we can find the shear stress which is at grad school stage ?

fonseh said:
do you mean the notes in photo 1 is another way we can find the shear stress which is at grad school stage ?
Yes, but it is quite complex to get an exact solution and you should not dwell on it. I was ready to quit engineering when I took elasticity theory in grad school land I've long forgotten it except to know that sttess concentrations occur at corners and edges and holes . Forget about it!

fonseh
PhanthomJay said:
Yes, but it is quite complex to get an exact solution and you should not dwell on it. I was ready to quit engineering when I took elasticity theory in grad school land I've long forgotten it except to know that sttess concentrations occur at corners and edges and holes . Forget about it!
just to be sure , the figure in 7-6 a and 7-6 b is the view of the blue plane, am i right ?

#### Attachments

• shear limitation.PNG
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fonseh said:
just to be sure , the figure in 7-6 a and 7-6 b is the view of the blue plane, am i right ?
Yes, that is the plane, but the plane is within the beam at a cut cross section. The vertical (and longitudinal) shear stress is maximum at the neutral axis and can be assumed constant across the width of the section, although in actuality is higher at the edges of the neutral axis.

fonseh
PhanthomJay said:
Yes, that is the plane, but the plane is within the beam at a cut cross section. The vertical (and longitudinal) shear stress is maximum at the neutral axis and can be assumed constant across the width of the section, although in actuality is higher at the edges of the neutral axis.
thanks , i am much clearer on this concept now !

PhanthomJay

## 1. What is shear stress at the rectangle cross section?

Shear stress at the rectangle cross section is the force per unit area that acts parallel to the cross-sectional area of a rectangular object. It is a measure of the internal forces that are resisting the deformation of the object.

## 2. How does shear stress vary at the rectangle cross section?

Shear stress varies at the rectangle cross section based on the distribution of forces acting on the object. The maximum shear stress occurs at the edges of the rectangle, while the minimum occurs at the center.

## 3. What factors affect the variation of shear stress at the rectangle cross section?

The variation of shear stress at the rectangle cross section is affected by the geometry of the object, the magnitude and direction of the applied forces, and the material properties of the object.

## 4. How can the variation of shear stress at the rectangle cross section be calculated?

The variation of shear stress at the rectangle cross section can be calculated using the formula τ = VQ/It, where τ is the shear stress, V is the applied shear force, Q is the first moment of area of the cross section, I is the moment of inertia of the cross section, and t is the thickness of the object.

## 5. Why is understanding the variation of shear stress at the rectangle cross section important?

Understanding the variation of shear stress at the rectangle cross section is important in designing and analyzing structures such as beams and columns. It helps engineers determine the maximum stress that a structure can withstand, and ensures that the structure is able to withstand the forces acting on it without failing.

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