How Does Shear Stress in Beams Relate to Compression and Tension?

[chetzread]

Homework Statement

In my notes , I was told that shear stress is maximum at the neutral axis . The normal stress will be maximum at one end , while the another end will be minimum...

Homework Equations

The Attempt at a Solution

Why the shear stress is maximum at the neutral axis ? When we 'tear ' an object , the boundary will move first , resulting the max shear stress occur at boundary , am i right ?

When we bend a beam , one part will undergo compression , while the another end will undergo tension ... So , the part which undergo compression will have the minimum normal stress? the another end will undergo tension will have max normal stress?

 

[SteamKing]

Homework Statement

In my notes , I was told that shear stress is maximum at the neutral axis . The normal stress will be maximum at one end , while the another end will be minimum...

Homework Equations

The Attempt at a Solution

Why the shear stress is maximum at the neutral axis ? When we 'tear ' an object , the boundary will move first , resulting the max shear stress occur at boundary , am i right ?

Shear stress depends on the orientation of the shearing force and the location of the neutral axis of the beam.

When we bend a beam , one part will undergo compression , while the another end will undergo tension ... So , the part which undergo compression will have the minimum normal stress? the another end will undergo tension will have max normal stress?

This all depends on the location of the neutral axis inside the cross section of the beam and the direction of the applied moment.

 

[chetzread]

Shear stress depends on the orientation of the shearing force and the location of the neutral axis of the beam.This all depends on the location of the neutral axis inside the cross section of the beam and the direction of the applied moment.

so, is the normal stress will be maximum at one end , while the another end will be minimum... ?

compression will have the minimum normal stress? the another end will undergo tension will have max normal stress?

is the statement that the shear stress is max at the neutral axis true?

 

[SteamKing]

so, is the normal stress will be maximum at one end , while the another end will be minimum... ?

compression will have the minimum normal stress? the another end will undergo tension will have max normal stress?

I'm having a hard time trying to understand what you are saying.

The normal stress is a maximum at "one end". "One end" of what?

The following diagram shows a typical bending stress distribution:

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is the statement that the shear stress is max at the neutral axis true?

Yes, the shear stress is a maximum at the neutral axis.

Shear stress τ is calculated by the following formula:

$\tau = \frac{V ⋅ Q}{I ⋅ t}$

where

V - is the shearing force
Q - is the first moment of area above the line where shear stress is calcuated
I - is the second moment of area
t - is the thickness of the section where the shear stress is calculated

Shear stress is typically distributed as follows:

​

 

[chetzread]

I'm having a hard time trying to understand what you are saying.

​

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from the diagra, the top part undergo compression, so thestress is minimum? the lower part is tension ,so stress is maximum?

 

[chetzread]

https://skyciv.com/tutorials/calculate-bending-stress-of-a-beam-section/

from the link, compression is negative stress, so the stress is minimum because of negative value?

 

[chetzread]

I'm having a hard time trying to understand what you are saying.

​

Yes, the shear stress is a maximum at the neutral axis.

Shear stress τ is calculated by the following formula:

$\tau = \frac{V ⋅ Q}{I ⋅ t}$

where

V - is the shearing force
Q - is the first moment of area above the line where shear stress is calcuated
I - is the second moment of area
t - is the thickness of the section where the shear stress is calculated

Shear stress is typically distributed as follows:

View attachment 102858
​

the thickness is measured from neutral axis? so at center , the thickness is minimum ,shear stress is max?