How do I determine the stresses on an I-Beam element?

[Ry122]

http://users.on.net/~rohanlal/MOHR.JPG

For this I-Beam which has a depth of 50mm I need to determine the Principal and maximum shear stresses acting on an element mid way between the Neutral Axis and the top of the flange (12.5mm from the top of the flange).

I don't know how to determine sigma_x and sigma_y and tau_xy.
I know Stress=Force/Area
so does this mean for an element of unit area 1mm^2 i use
Shear Stress = Shear Force/1 = 25/1=25 Pascals?
Is this on the right track or am i entirely using the wrong values and formula?

 

[Mapes]

But these forces don't act on just the element. For example, the axial load acts on the entire cross section of the beam.

Do you have a mechanics of materials book handy (e.g., Beer and Johnston)? They cover these types of problems in detail.

 

[Ry122]

I do have a mechanics textbook but I can't find any example problems similar to this one.

I'm only supposed to be determining the principal and max shear stresses at this one point 12.5mm from the top of the flange and 200mm across the beam (the beam is 450mm).
The shear force and axial force given do act act at this point don't they?

Can't I use them to determine sigma y and x and tau xy at this point so that I can use Mohr's Circle to determine the principal stresses and maximum shear stress?

 

[Mapes]

I do have a mechanics textbook but I can't find any example problems similar to this one.

I'm only supposed to be determining the principal and max shear stresses at this one point 12.5mm from the top of the flange and 200mm across the beam (the beam is 450mm).
The shear force and axial force given do act act at this point don't they?

Can't I use them to determine sigma y and x and tau xy at this point so that I can use Mohr's Circle to determine the principal stresses and maximum shear stress?

Yes and yes, but the stress from the axial load, for example, isn't just the load divided by the element area. The beam doesn't know the size and shape of your analysis element! That stress is the axial load divided by the cross-sectional area of the beam.

It's not clear from your diagram where the shear load acts, so it's harder for me to say how to treat this load.

 

[nvn]

Ry122: I agree with the above posts by Mapes. A mechanics of materials textbook will show you how to approach this problem, and it will give you relevant equations. As Mapes said, it is not clear from your diagram where the shear load acts.

By the way, there is a required template for homework questions. Is the template not appearing on your screen? Why are you always deleting the template?

You are required to list relevant equations yourself, and post a valid attempt.

The PF rules state, "You must make use of the homework template. You must show you have attempted to answer your question, in order to receive help."

 

[P0zzn]

Sorry but i think the normal stress on any element at any distance from NA is equal to axial load/cross section of beam, Provided that we are dealing with perfectly eccentric load.

But it's not true for shear stress.
For shear stress distribution in beam cross section, there's a relation
£=(VS)/(IB)
V is shear S first moment of area of strip about NA, I is moment of inertia of cross section about NA and B is width of beam at strip considered.

Solve the equation, to get shear stress at any distance from NA. And yes, area of strip isn't required and it's not 1 mm sq.

For your ease,
variation of shear stress in I beam is parabolic both in flange and web. And max shear is at NA.

It's your job to draw shear stress profile and do the Mohr's circle.

 

[Mapes]

Sorry but i think the normal stress on any element at any distance from NA is equal to axial load/cross section of beam, Provided that we are dealing with perfectly eccentric load.

Nobody is arguing against this (though I don't know what "perfectly eccentric" means). I'm arguing that you can't find the stress at an element by dividing the axial load by the element area. You approach is correct.

 

[P0zzn]

Oh I'm sorry i didn't meant to say that. Load SHOULD NOT BE ECCENTRIC, it should be perfectly centric. Else we'll have bending stress to deal with.
Thanks for correction