Calculate Sway for a moment-frame knowing the BM's 3

[As-Lag]

Dear Engineers.

I have calculated the bending-moments for a moment-resisting frame and now I want to calculate the sway. I have two 3m high columns with a 3m beam. Fixed base and a 2kN side thrust at beam level. Constant EI throughout. I have checked my calculations using SkyCiv frame-analysis software and my moments and reactions are correct.

I now want to calculate the sway. I have lots of examples of how to calculate the moments due to sway but not the other way round. Are there any examples of calulating the sway with known moments please. I have tried reorganising the slope-deflection equations for a beam with a sinking-foundation but keep getting stuck on the rotations.

Thanks. Daniel

 

[As-Lag]

Dear Engineers

I reworded my question and was directed to this thread: 'Estimate stiffness/drift in a steel moment frame'. In the thread 'gte447f (Structural)' (22 Feb 19) gave a solution that works.

Thanks gte447f (Structural).

 

[centondollar]

A simple method is the the unit load method. Apply a horizontal unit load at the frame location in which you want to evaluate the deflection.

Displacement_chosen_location = SUM[ integral(x=0, x=L) M*M1/(EI)]for all members, where M=moment due to loading, M1 = moment due to unit load. If you wish to account for axial and shear effects, you can add those terms to the equations; however, for steel, only bending will cause significant sway.

 

[271828]

Another vote for centondollar's suggestion. Sometimes this method goes by the name virtual work or principle of virtual forces.

 

[Obinna1992]

I believe that the calculation shown on the link below on the analysis of statically determinate and indeterminate determinate frames will be very helpful.

Deflection of statically determinate frames using virtual work method

Deflection of statically indeterminate frames

 

[MotorCity]

I am not familiar with the Skyciv software but I am surprised that a frame analysis software that is capable of calculating bending moments cannot also calculate the drift (frame deflection).

 

[phamENG]

MotorCity - I got the impression the OP was trying to do the analysis by hand. They used SkyCiv to check the strength calcs, but didn't know how to go about drift/sway calcs. I used SkyCiv a couple years ago - decent software and absolutely gives you displacements.

For hand calcs, I like the moment area method. Not perfect, but it's hard to beat for speed and 'close enough' when doing a hand calc. Took me about 15 minutes to program a spreadsheet with it. I do mostly wind design, so anything "more accurate" is something of a farce.

 

[As-Lag]

Dear all.

After many hours, i perfected my hand calculations for a moment frame which included P-delta effects. I used a combination of moment-area equations and some standard equations for P-delta. My results were the same as the SkyCiv results. Well pleased and thanks for all the help.

As a secondary issue with analysis software; the two I have used Staad Pro and SkyCiv are brilliant for steel and analysis, but when it came to timber, neither took into account Shear Deflection - which was naughty.

 

[Celt83]

...but when it came to timber, neither took into account Shear Deflection...

If you are in the US, be careful with software and the material properties entered. The NDS supplement values provide E[sub]apparent[/sub] which takes into account shear deformation, refer to NDS Appendix F for more info.

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