Notes"14" Shear stress

Notes"14" Shear stress

For any symmetric form we can use the following formula to calculate the shear stress at any section.

The average shear stress on that face of the element could be obtained by the following formula.

τ : is the shear stress ;
S : is the shear force;
Q : is the first moment of area;
I : is the second moment of area;

b : is the width of the element at the cut .
 

Now we will discuss some problems to know how to use the latest relation.
if we have this cross section and we want to calculate the shear stress at distance y from the centroid .

previous formula could be used as shown :

 

As we use a symmetric section :
Q = (the area of cut area * the distance between the centroid of the cut area and the centroid of the section )
 

Let's learn more physics about the shear stress distrbution of this section.

 

  

 Lets calculate the shear stress at :

The latest results have a physical meaning .
What does it mean ?!

Now lets sail in the sea of the shear stress with the storms of the various cross sections .

Suppose We have the following  :

We want to calculate the shear stress
That acts on the nail but first we calculate the shear stress if we did not use the nails (if we used glue) to make this assembly.

lets study the cross section
the shear stress at distance h/2  from the centroid of the section
 

 

If we replaced the glue by the nails .

Note “d” is the distance between two nails .

Now what is your opinion about the last problem ..?

Another Example :

to get the shear stress at 1 we should cut the section as shown :

And simply use the relation :

To get the stress at 2 , We should cut as :

And simply use the relation :

Now , may we ask what are the constrains to cut
The main constrain is cut any where but keep the the section symmetric round the shear force .