Combined direct stress and bending moments

[andycampbell1]

Hi. I was assigned this coursework by my lecturer. The problem is I have only been taught how to analyse a solid beam section and not a hollow section as is shown in the problem. What I would like to know is how to calculate the area. Usually I would do this by calculating Length x Breadth. I am unsure what to do with the internal area which is missing.1. A Steel column has a doubly symmetrical hollow cross section, as shown in image. And is subjected to a vertical force of 200 kN at the corner A of its cross section.

a) To calculate the maximum compressive and tensile stresses in the column section respectively.

b) To determine the minimum vertical load that may have to be applied at the corner B in order that there is no resultant tensile stress caused by these two vertical loads
2. The equation I was using was

δ= P/A - (Pe_y]/I and

I=1/12bd³
3. My attempt at this was1/12 x 800 x 600³= 14400 x 10⁶ mm⁴

δ= P/A - (Pe_y]/I

δ= 200 x 10³/240 x 10³ - (200 x 10³x 300)x300/14400x10⁶

= 0.83333 - 1.25

I think it is the area that is throwing me off on this because I don't think the 14400x10⁶ is correct. What I did with the area was to calculate the total area and subtract the area missing in the middle.

 

[SteamKing]

First, why don't you take a stab at calculating the cross-sectional area? What have you tried?

 

[PhanthomJay]

Second, you should note that the vertical load causes bending about both axes.
Third, your calc for I is wrong...and you need to find it about both axes separately, not forgetting to subtract out the I of the hollow part.

 

[andycampbell1]

First, why don't you take a stab at calculating the cross-sectional area? What have you tried?

For my cross sectional area I multiplied the length x the breadth so that was 800 x 600 gave me 480 x 10³ I then did the same for the hollow section so that was 600 x 400 gave me 240 x 10 ³ I then subtracted 240 x 10 ³ from 480 x 10³ which left me with 240 x 10³.

 

[andycampbell1]

Second, you should note that the vertical load causes bending about both axes.
Third, your calc for I is wrong...and you need to find it about both axes separately, not forgetting to subtract out the I of the hollow part.

I knew it would cause bending about both axes, I have only covered with the lecturer in class loads at the centre of the beam and loads which are eccentrical from the centre of a solid beam. I was wondering how should I treat this load as it at the corner of the beam should it be taken as eccentrical from the centre or from a point on the actual beam?

So for I are you saying that I would need to work out for the actual beam 1/12 x 800 x 600³ and then the same for the hollow section 1/12 x 600 x 400³ then subtract from the first answer?

Thanks

 

[PhanthomJay]

I knew it would cause bending about both axes, I have only covered with the lecturer in class loads at the centre of the beam and loads which are eccentrical from the centre of a solid beam. I was wondering how should I treat this load as it at the corner of the beam should it be taken as eccentrical from the centre or from a point on the actual beam?

For a symmetrical beam in both directions, whether hollow, solid, I-shaped, etc., the ecentricity is measured from the centroid of the beam, that is, its center.

So for I are you saying that I would need to work out for the actual beam 1/12 x 800 x 600³ and then the same for the hollow section 1/12 x 600 x 400³ then subtract from the first answer?

Thanks

Yes, that is correct, about one axis. About the other axis, you have to do a similar calculation, where b is now h and h is now b, if you get my drift.