# Cantilivered beam deflection

1. Oct 1, 2014

### SteliosVas

1. The problem statement, all variables and given/known data

Okay this is the problem I have:

I have a Steel Channel beam which has an cross sectional height of 300mm. It is 150mm in depth. Its wall thickness is 20mm.

This beam is 6meters long as has a 10kN/m UDL applied. It is fixed at one side and unsupported at the tip.

I have worked out the Neutral Axis about the xx at 44.8214mm and the Moment of Inertia as 32.93x109mm4

I now need to determine maximum tensile bending stress and its exact location in the beam cross section.

2. Relevant equations

I know maximum bending stress is equal to (max stress = my/I)

3. The attempt at a solution

Now I know I, and I have YCenter at 150mm and xCenter at 44.8214mm now I don't know how to get Mmax and it's exact distance.

I think Mmax is (L2x10kn/m)/2 but I could be incorrect?

I have attached a picture of my working if that helps

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2. Oct 1, 2014

### SteamKing

Staff Emeritus
This is why you should get in the habit of constructing shear force and bending moment diagrams for these types of beam problems (not just cantilevers, however).

3. Oct 1, 2014

### SteliosVas

Okay I've got the reaction at the end (left hand side of beam to be) 60kN, and moment to be 180kn.

Where can I go from here?

4. Oct 1, 2014

### SteamKing

Staff Emeritus
I don't understand. Haven't you learned how to construct the shear force and bending moment diagram for a beam, given its loading? This procedure should have been taught and learned before you started tackling stress calculations.

5. Oct 2, 2014

### SteliosVas

Sorry I didn't convey my understanding properly.

I have found the maximum moment to be 180kn (60kn (UDL as point load) * length of cantilever)

Now I am just worried if my Moment of Inertia is correct or not. I have done it a few times and have different answers all the time.

I also know the y value in the equation given by (just 300mm (size of cross section) - 44.8214mm (where N.A is located) )

I obviously know maximum bending stress in a beam will occur at the fixed end, but as for where it appears in the cross section, will it occur at the top section since it is positive so (300mm-44.8124mm) =257.1786mm?

Last edited: Oct 2, 2014
6. Oct 2, 2014

### SteamKing

Staff Emeritus
The correct units for the bending moment are kN-m.

Why is that? This seems to be a rather simple cross section. The MOI can be calculated in at least a couple of different ways. Each method of calculation should agree with the other. I can't check you calculations because the image you attached is too small for me to read your handwriting.

It's not clear from your description if the beam is oriented with the 300 mm dimension in the vertical direction or the 150 mm dimension. In any event, only one of the neutral axis locations will give you the correct value of the bending stress in the beam, and it is not necessarily the one you have chosen.

For example, if the beam measures 300 mm deep in the vertical direction, then the y distance to the outer fiber must be based on this depth, and not the distance to the N.A. measured along the 150 mm dimension, which we could call the breadth of the beam, to distinguish it from the depth..

7. Oct 2, 2014

### SteamKing

Staff Emeritus
You might want to re-check your MOI calculation. The MOI of the channel cannot be greater than the MOI for a rectangular section which is 300 mm deep by 150 mm wide. Your MOI seems high, by at least two orders of magnitude. It's a simple calculation; you can type it into a reply message rather than posting an image.