Equivalent nodal loads?

[kvazipecaros]

Hello, I am trying to find equivalent nodal loads for the following scenario:

-column pinned on the bottom and fixed on the top, with horizontal uniform line load.

What would be the equivalent end moments and forces for this configuration?

I am making a spreadsheet to calculate simple frames and I would greatly appreciate some help.

 

[rb1957]

have you solved for the redundancy ? your problem is a propped cantilever.

 

[kvazipecaros]

That's what I figured, a propped cantilever. So I just used the reactions (but flipped their direction) as equivalent nodal loads.

Thanks!

 

[IDS]

I think the blog post here:

http://newtonexcelbach.wordpress.com/2009/01/31/frame-analysis-with-excel-1-single-beam/

answers your exact question. You need to calculate the end moments and reactions that would result from your loading if the beam was fully fixed at both ends.

The blog post has a download file with a spreadsheet to calculate the fixed end moments and reactions.

You might also like to have a look at the following posts, which progress from solving simple frames on the spreadsheet to complex frames with VBA routines (I haven't got round to linking to the compiled routines yet).

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[rb1957]

"You need to calculate the end moments and reactions that would result from your loading if the beam was fully fixed at both ends." ? that seems to be needlessly complicated ... a propped cantilever is easily solved (unit load method is my choice ... i'd reduce the beam to a cantilever, then figure out the force required to zero the displacement at the tip) ... or you can look it up Roark.

 

[IDS]

rb1957 - It isn't particularly complicated, and he asked about how to calculate equivalent nodal loads (for solving frame problems), not just how to solve a propped cantilever.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[corus]

IDS,Personally I'd concentrate on a general purpose spreadsheet for beams if I were you. I forget his name, but someone called Alex, I think, has posted a link on here for his 2D beam spreadsheet, which works very well and gives you all the nodal forces. The VBA code is all there if you want to tinker about with it. In general the code for 2D beams can be found in many books so the approach Alex has used is fairly standard.

Tara

http://tinyurl.com/4ydjg7m

 

[IDS]

Corus - was there something wrong with my response to the question in the OP then?

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[corus]

IDS, Nope, but as you generalised the problem to frames in general and referred to your site/blog on specific spreadsheets you are preparing I thought I'd suggest a more general aproach, which has already been made and could be enhanced. Trying to be helpful. Whatever.

Tara

http://tinyurl.com/4ydjg7m

 

[IDS]

IDS, Nope, but as you generalised the problem to frames in general and referred to your site/blog on specific spreadsheets you are preparing I thought I'd suggest a more general aproach, which has already been made and could be enhanced.

The spreadsheets I linked to have also already been made and are quite general.

I'm not suggesting there is anything wrong with the work of Alex Tomanovich (who I imagine you had in mind) by the way. He does a lot of good stuff, free and open source, as is mine.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[kvazipecaros]

Just to clarify, I am designing moment frames with pinned columns. So reactions include only forces, and no moments. That's why I was asking how to break down a line load (horizontal, representing wind) acting on one column that is pinned at the bottom and transfers moments to the beam on top. Should I treat it as a propped cantilever or as a fixed-fixed beam...that is, should one moment be wl^2/8 (and reactions 5wl/8 and 3wl/8) or wl^2/12 both top and bottom, and reactions wl/2 each?

That was my main question since I already worked out global and local matrices and the assembled reduced stiffness matrix. I just need the total load vector so I can find displacements and member forces...

Speaking of member forces, do I just multiply element global matrices with the deflection vector? Thanks again.

 

[rb1957]

sounds like the columns are propped cantilevers to me ... "that is pinned at the bottom and transfers moments to the beam on top."

 

[IDS]

kvazipecaros- you apply the fixed end moments and forces to each loaded member.

Yes, you mutliply the element global matrix by the deflection vector to get the nett force and moment at each node.

There is an example with a portal frame here:

http://newtonexcelbach.wordpress.co...alysis-with-excel-3-continuous-beam-or-frame/

Fixed end moments and forces are calculated by the function FEMact, and the matrices are set up and solved by the routine FormKG. The comments in the code should explain what is happening, but if anything isn't clear, please ask.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/