Torsion in a hollow beam cross-section

[beamsandthangs]

Homework Statement

The problem is regarding the question on the attached file called 'QUESTION3.png' This is urgent so please reply if you can.

Homework Equations

The attempt is in the file attached. Is my procedure correct? Am I missing something or is something wrong?

Also, how do I find the compressive axial force if N- = 20kN? What equation do I use?

The Attempt at a Solution

Attempt is attached.

Thanks.

 

[SteamKing]

1. Your section is closed. You are using τ = VQ/It to compute the shear stresses in the walls. This is incorrect. Have you studied how to analyze closed sections in shear?

2. The axial force is applied along the longitudinal axis of the beam. How do you calculate stress in axially loaded members? (Hint: it was probably the first stress formula you learned.)

 

[beamsandthangs]

1. Your section is closed. You are using τ = VQ/It to compute the shear stresses in the walls. This is incorrect. Have you studied how to analyze closed sections in shear?

I've done some research but couldn't find any clear information to learn from. I only have one example of the same question, which is from a friend and he uses the same equation : VQ/It (where t includes the wall thickness of both the left and right side. If you could give me a link explaining the equation for shear stress in hollow beams or just give me the equation that would be great. The information my lecturer gives me on the university website is very limited. This is a repeat exam and I'm currently outside the country my uni is in so I don't have any lecturers to explain this.

2. The axial force is applied along the longitudinal axis of the beam. How do you calculate stress in axially loaded members? (Hint: it was probably the first stress formula you learned.)

Oh. I assume it is the SigmaZ= N/A + Mx(Y)/Ix - My(X)/Iy equation.
If so, I have the values of N, A, Ix, Iy, but not Mx and My. How do I obtain the M values?
I assume after obtaining the Mx and My values, I replace the X and Y values for the top and bottom of the beam to find the normal force?

Reply is above in Bold

Edit:

In this example I found through google, the person uses VQ/It to find the shear at N.A :
http://faculty.ksu.edu.sa/modar/CE%20302%20Solved%20Problems/Solved%20Problems%20on%20Ch6.pdf

 

[SteamKing]

1. No mention is made of any bending in your problem, so Mx = My = 0.

2. In your example, there is no shear connection between the sides of the wooden box and the top and bottom plates except be the nails which connect them. This is not a good example to use on your problem, since you have a full shear connection at all four corners.

3. The attached example is for a beam which does have a thicker top plate than your problem.
http://www.engr.colostate.edu/~thompson/hPage/CourseMat/Tutorials/Solid_Mechanics/shear.pdf
On reading their description, it appears that if all plates are the same thickness, one can assume equal shear flow in the sides, and thus τ = VQ/It may be valid for your problem after all. I apologize for the earlier confusion. However, the attached method should also work for more general problems, as well as this one.

 

[PhanthomJay]

What happened to the Torsion and Bending part? The loads appear to be eccentrically applied?? Is this correct?