# Homework Help: Beam Analysis of C-section (C-channel)

1. May 10, 2013

### scottm212

Hi there,

I have a problem regarding a simply supported C-section steel beam that I can't seem to get my head around.

The beam is 6m long and supports a 15 Ton moving point load, the tensile yield strength of the steel is known and the structure must have a factor of safety of 3. The dimensions of the beam are W, H and T where H=2W and T=W/20. I have to use this information to find the dimensions of the C-section but after several attempts I can reach no conclusion. I think it must be something to do with the section modulus? But I can't seem to find any relationship between all the given data that can provide an answer for 'W'.

Any advice or information would be much appreciated, thanks.

2. May 10, 2013

### rock.freak667

How is the beam supported? Depending on that, you will need to figure out where the maximum bending moment will occur.

3. May 10, 2013

### PhanthomJay

Once you find the Max moment, can you calculate the section modulus in terms of W? Then solve for W using the allowable stress and bending stress calculation.

4. May 13, 2013

### scottm212

The beam is simply supported by a hinge pin at either end of the 6m length. The load is also variable point so max bending will occur at 3m. What is the equation that relates allowable stress, bending stress and 'w'? im not sure I have used any equations in the past that relate all 3. Thanks for the response!

5. May 13, 2013

### SteamKing

Staff Emeritus
If you find the section modulus of the beam using W, H, and T, you can develop an expression for the bending stress, to which you can apply the factor of safety. You have the proportions of H and T in terms of W, so W should be the only unknown.

6. May 13, 2013

### rock.freak667

Then your beam is fixed at both ends as the supports are resisting both horizontal and vertical loads.

Depending on how the beam is supported, (I may be wrong in calling it a fixed at both ends kind of beam), you will need to look up the bending moment formulas at the center and at the ends. The deflection can be maximum at the center but the bending moment may not be.

Your allowable stress will stress will depend on your yield stress and your safety factor. How does bending stress relate to the bending moment (M) and the section modulus (Z)?

7. May 13, 2013

### pongo38

Your responders so far have accepted your naiive approach considering bending alone has been considered. But, as this is a c-section there is likely to be torsion as well. The shear stresses due to shear and torsion do not add directly to the bending stresses, but would eat into the factor of safety. This issue might be beyond the scope of your question, but is a real issue in practice.