How do you calculate the force in a compression flange? 2

[Ozy001]

How do you calculate the force in a compression flange based on the moment?

Hi,

I am trying to calculate how much force is in the compression flange of a portal column based on its moment. I have to design a torsional restraint (capable of withstanding 2.5% of the force of the compression flange). The angle of the tie from the compression flange to the restraining member is very accute and as such I am a little worried about the steel angles which have been added. Was thinking it would go something like this:

Calculate the Z vale of the compression flange only.
Divide the moment by the Z value to get a stress.
Multiply the cross sectional area by the stress. That should give me a maximum applied force.
Find the resultant force based on the angle of the tie.
Check the angle against the maximum force in compression to see if it passes.

Any help would be really appreciated.

Thanks!!!

 

[ToadJones]

You could just be conservative and take the area of the compression flange and multiple by the yield stress.

 

[Ozy001]

Thanks TJ but I like the idea of working it out. Shows that I'm thinking about it. I'm pretty new to structural engineering so trying to be accurate.

Thanks again for the reply!

 

[ToadJones]

just take the max compressive bending stress at the location of the brace + the max axial compressive stress and multiply by the area of the flange.
The stress in the flange wont vary greatly across the thickness.

 

[rb1957]

or use the mid-thickness of the flange to calc the bending stress (rather than the extreme surface)

 

[Ozy001]

So would this be something like:

M=650kNm at brace
Area of compression flange= 4486mm^2
I=111444cm^4
Axial Force in Column=430kN

M/I=F
F*Area of compression flange=CF

CF*tan Angle=Compression Force the angle has to resist

I don’t quite understand why you would require the compressive force of the column.

One another note if I was to be conservative and multiply the cross section of the flange and multiply with by the tensile capacity of the steel (fy=355N/mm^2) I would end up with a force of 1682kN *2.5=42kN?

Thanks for your help as always.

 

[Ozy001]

*2,5%

 

[Ozy001]

Sorry I've put the I value of the cross section, this should be the I vale of the rectangular flange only.

 

[ToadJones]

Max compressive stress in the column at the brace:
P/A + Mc/I (or M/S)

Take this vale and multiply by the area of the flange.
This = the force in the flange.

Design your brace withstand 2.5% of this force.

 

[rb1957]

"CF" is the compression force in the flange due to bending, M.

the axial load is also compressing the flange (along with the rest of the section).

if you're designing the connection, ie what's the maximum load that could be in the flange, then using fty is conservative. if you're designing the flange, the allowable will be less than this, due to buckling.

 

[Ozy001]

Thanks a bunch TJ, its really appreciated.

 

[dik]

The stress is M/S where M is moment and S is section modulus.

Multiply that with the flange width x flange thickness...

Dik

 

[ToadJones]

if you want to take it a step further, use the force in the flange as calculated above as a horizontal force. Since your brace will be at an angle (presumably), do the statics and come up with the corresponding load in the brace ...it will be higher that the calculated force obviously.

 

[hokie66]

Just use .025M/d as the force. Close enough.

 

[tdstructural]

Hokie - that's what I would do. M/depth of the beam is a close and still conservative compression and tension force.

 

[asixth]

M*(distance of the flange centre to the neutral axis)/Ixx*0.025 if the member is pre yield. Area of flange*flange yield stress*0.025 if the section is post yield.

 

[hokie66]

asixth,
You left the area out of your first expression.

All,
So much ado about nothing. Why does everybody seem to object to simplification? Does anybody seriously see anything wrong with my approach? Of course, this has to be resolved into a bracing force as the OP knows.

 

[asixth]

Cheers hokie, stress*area gives a force. Nothing wrong with a simplification, but we can't carry too many simplifications into our calculations. Our clients are always concerned about cost so we need make designs efficient. Sometimes, like the calculations to justify to size of a fly brace can be typified. I would call up a 50*5EA at a 1H:1V angle with 1(no.)-12mm bolt for anything up to a 460UB and consider it a lateral restraint.

 

[Ozy001]

Thanks to all for contributing. Like I had mentioned I’m relatively new to structural engineering however I always believe we should work to the actual values rather than approximations (is this not what load factors are for?). Personally I need to calculate these values as I don’t have the bank of experience as most others do. As mentioned clients are keen to keep cost down, our duty as engineers should be to provide an economical design (both cost and environmental impact). I understand that the difference in calculating the compression forces exactly (see the second post by ToadJones) or using the cross section of the flange multiplied by the tensile strength (see the first post by ToadJones) won’t make a huge difference but its good practise to get into. I don’t think the most sensible thing to do is encourage graduate engineers to do approximate calcs, it should be on the button.

Thanks again to everyone who added to this thread.

 

[Lion06]

Just remember that our FIRST duty as engineers IS to provide a SAFE design. If I need to be conservative and redundant in order to make me sleep better at night, you can bet I'm going to. Just remember that real world engineering problems are often different than you encounter in school. In school, the majority if the problem is handed to you and you usually just work out the math. Now you are the one defining the paramaters of the problem, so a little conservatism goes a long way. Additionally, if I can get an answer that is within 3% - 5% in 5 minutes or spend 45 minutes getting the "exact" answer, my time is better spent approximating.