Learning Forum

[Hussam Khresat]

Hi all 

I have a cantilever beam length=48 in and square cross section 1x1 in. A vertically upwards force is applied at the free end = 50 lbs. The beam is massless.

I am trying to calculate shear stress XYat 20 in from the fixed support at the top of the CS in a static structural analysis. 

I am getting a non zero shear force which I think is wrong because Tau=VQ/Ib right?

Attached is a picture of my model. 

[peteroznewman]

A better way to look at the XY shear stress is on a surface that cuts through the center of the beam.

Below are the values for an element size of 0.5 inch which match the minimum value you found on the line, a value of 10 psi.

Below are the values for an element size of 0.25 inch, notice that the minimum values falls to 2 psi.

Below are the values for an element size of 0.1 inch, notice that the minimum values falls to 0.25 psi.

If you want to use equations from beam theory, use beam elements instead of solid elements.  Did you notice the "bow-tie" profile of shear stress along the Z axis?  The beam equation for Tau you showed above does not describe that effect either. The bow-tie profile is caused by a Poisson's Ratio of 0.3 and if that is set to 0.0, the bow-tie effect will go away as shown below.

[Hussam Khresat]

Thanks alot for your reply. I tried smaller mesh size= 0.05 in and actually now I get much better results.

But I then got shear stress at the free end top of the beam and bottom and I am getting 25 psi even with such small mesh size, shouldnt it also be close to 0?. (see attached)

Also the shear stress at the center of the CS at the free end is 50 psi which also doesnt match max shear stress value of 3/2 V/A = 75 psi. (see attached) 

Do you know what might be causing that?

 

Also another question, For all analysis that I refer to above I was using a massless beam. I added then a point mass at the free end center of CS as attached at the end = 440 lbm. When I reran the static structural analysis with the point mass the shear stress at the center of the CS at the free end now drops to 14 psi but top and bottom at free end remain 25 psi. Any reason for that? Given I didnt add gravity to my model which I think should make my model not cosider any forces from the mass.

Note: the point mass was added because I wanted to run a transient analysis afterwards.

[peteroznewman]

Look at the last image in my previous reply, it shows the maximum XY shear stress of 75.5 psi which is an error of only 0.7% from your equation that calculates the beam equation value of 75 psi.  Note that I changed the Material Properties and set the Poisson's Ratio to be 0.0 instead of 0.3 to get that result, along with a small element size of 0.1".

It is true that a point mass on the end of your beam will have no effect on the stress in the beam if there is no Gravity load.  Only the applied force will cause stress.

You don't seem to have learned the lesson I was trying to teach you in my previous reply about the importance of element size. Please try creating a plane to plot the XY Shear Stress as I described in my previous reply.