Statics or FEA required? Frame Drawing in Post
Statics or FEA required? Frame Drawing in Post
(OP)
I am trying to calculate the brace force of the attached frame. I can do it easily in RISA, but I want to incorporate it into a MathCAD calculation because it will be easier and faster to produce a calculation set for future projects. I've been racking my brain to figure it out because I know the stiffness of each element affects the load that the brace sees. So, I tried to simplify the properties of the members in the attached. The brace has the weakest moment of inertia and and cross-sectional area, I and A respectively. I then made the other members have arbitrary factors of I and A. The column is fixed to the foundation. The beam and braces have pinned ends. I showed the force outside the one column, but it is actually at the center of the beam (diaphragm load) so it loads each brace equally.
So am I stuck using RISA for each frame that comes up or can someone provide a (maybe not simple, but shortish) method of calculating by hand?

On a related note, if the base of the column is pinned, I did an "equivalent" analysis of the column as a beam with pinned supports at the beam and brace and a point load (equal to 1/2 the force) at the foundation which is assumed the free end. This works with the assumption that the translation at the brace and beam are equal. This is not exactly true, but because of the stiffness of the members and close proximity of the two points, ends up pretty close. The pinned base requires a stiffer column to keep the drift down, hence my attempt at the above.
So am I stuck using RISA for each frame that comes up or can someone provide a (maybe not simple, but shortish) method of calculating by hand?

On a related note, if the base of the column is pinned, I did an "equivalent" analysis of the column as a beam with pinned supports at the beam and brace and a point load (equal to 1/2 the force) at the foundation which is assumed the free end. This works with the assumption that the translation at the brace and beam are equal. This is not exactly true, but because of the stiffness of the members and close proximity of the two points, ends up pretty close. The pinned base requires a stiffer column to keep the drift down, hence my attempt at the above.
Juston Fluckey, SE, PE, AWS CWI
Engineering Consultant






RE: Statics or FEA required? Frame Drawing in Post
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RE: Statics or FEA required? Frame Drawing in Post
I think you can simplify the problem if the structure is symmetrical (which it looks to be).
As drawn it looks triply redundant (6 reactions, 3 equations) ... not impossible to solve by hand but a bit of a slog. I like the unit force method. Using symmetry reduces this to doubly redundant ... much easier.
Maybe solve the symmetrical case first, then generalise ?
another day in paradise, or is paradise one day closer ?
RE: Statics or FEA required? Frame Drawing in Post
Now draw in your knee brace. At the point where your knee brace intersects with your beam, the moment diagram can be modified to go from a peak at the knee brace intersection to zero at the end of the beam. Do the same thing on the column.
This implies certain vertical and horizontal forces in the brace. Back calculate the forces required to create the moment diagram.
You can obviously do this in numbers. I just think it's easier to visualize with the moment diagram.
This becomes less true to reality the further into your span the knee brace projects, because the stiffness assumptions in your frame analysis become questionable.
RE: Statics or FEA required? Frame Drawing in Post
^ My thought process was progressing as I was typing and I walked my self through to that conclusion. I never learned the unit force method. By education, I am an ME and we only used Singularity Functions which I attempted to incorporate into this problem. I also tried reducing the beam, brace, and column into spring constants but that was getting me deep into math I couldn't handle last night.
I know the shape of the moment diagram, but that doesn't help me determine my numbers unless I know the actual moment at the brace intersection, which I don't know unless I have that brace force I am trying to figure out.
Juston Fluckey, SE, PE, AWS CWI
Engineering Consultant
RE: Statics or FEA required? Frame Drawing in Post
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Statics or FEA required? Frame Drawing in Post
RE: Statics or FEA required? Frame Drawing in Post
but you also said you wanted to address the general solution "for future projects".
btw, isn't prying the moment reaction ? ("unless I super beef the plate to take the bending and eliminate (or calculate) the prying action") if the flange is flexible then no prying, if the flange is stiff then there is a moment reaction (evidenced by the prying).
sorry, but I have to add "who's prying now" ?
another day in paradise, or is paradise one day closer ?
RE: Statics or FEA required? Frame Drawing in Post
My approach will be to model the frame for a 1 kip lateral load and get the values from the RISA model and enter them into my calculation as a snapshot. I will make the beam extension as short as possible beyond the brace for the worst-case condition. Then I will just factor my model results by my actual lateral force divided by the 1 kip model value to get the values I need. I think this is easier than providing the RISA report at the end of my calculations. Example below which is my work in progress and I need to add snapshots for column shear, moment, and deflection diagram:
I have no question on the pinned base condition:
Juston Fluckey, SE, PE, AWS CWI
Engineering Consultant
RE: Statics or FEA required? Frame Drawing in Post
the FBD for the 1/2 frame is incomplete, as there is a moment in the horizontal on the CL.
The horizontal reaction is 1000 lbs; the vertical depends on the width (or 1/2 width of the frame).
I take it the knee brace reacts only axial load. The vertical component of the knee brace works with the load in the vertical (at the top) to create a couple reacting the mid-span moment, yes? So this component will be larger than the applied load, so the reactions at the LH end of the horizontal beam are both vertical and horizontal.
If you're trying for a general solution (in your Mathcad), avoid using fixed dimensions from the problem ... input all dimensions.
another day in paradise, or is paradise one day closer ?
RE: Statics or FEA required? Frame Drawing in Post
I am being conservative. Yes, the length of the frame matters, but the shortest length is worst-case. I put a vertical boundary at the right end of the beam (sorry, it wasn't shown). I don't need to put a moment boundary condition there because it is either a symmetric frame or the other end only has a pinned column with no knee brace. My only goal is to get the maximum axial load (yes, axial only member [the circles at the ends of the members indicate pinned condition]), which the model is doing. I will then check my beams and columns elsewhere in the calculation using the axial load in the brace (with my beloved singularity functions). Because my frame is actually longer than the model, I will always be conservative with the load I apply to the beams and columns.
Yes, I have both horizontal and vertical reaction at the left hand end of the beam, but that can be calculated from the axial load of the brace. I'm trying to reduce the information I need to pull from the model results. Really, all I need is the brace force and I can calculate everything else.
Juston Fluckey, SE, PE, AWS CWI
Engineering Consultant
RE: Statics or FEA required? Frame Drawing in Post
the knee brace load carries the equivalent moment (ie if you had a fixed connection between vertical and horizontal you wouldn't need a knee brace, in the absence of a fixed connection the moment is reacted as knee_brace_load * distance_to_frame_corner).
I think this is what your FBD should look like ...
another day in paradise, or is paradise one day closer ?
RE: Statics or FEA required? Frame Drawing in Post
RE: Statics or FEA required? Frame Drawing in Post
Input, deflected shape plot, and bending moments for 100 kN applied load are shown below.
Results should of course be checked with an independent calculation or software.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Statics or FEA required? Frame Drawing in Post
Sorry... just my two cents as a partner in a firm where I watch my partners waste countless hours doing things like this by hand to "avoid RISA" models that I could have done in 1/10th the time using RISA.
RE: Statics or FEA required? Frame Drawing in Post
Cheers
Greg Locock
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RE: Statics or FEA required? Frame Drawing in Post
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RE: Statics or FEA required? Frame Drawing in Post
If this were a one-off project, I wouldn't hesitate to model the whole thing in RISA. However, in the long run, this will save me a lot of time. This should be a repeat client and this method will make it faster to produce (10) sets of calculations rather than (10) sets of calculations and models. I don't like to waste time, but I do admit I can get sidetracked with math. But once that math is done, I can use it multiple times in the future. There is a trade-off though. I'm not going to spend the next 5 days trying to make the math work. I could never recover that time. I'm at a happy medium.
ARK: care to explain the handle? Are they initials or were you involved with the ARK project?
IDS,
Thanks for the spreadsheet, however it doesn't look like any analysis methods are visible to the user. I could accomplish the same thing using RISA, which I was trying to avoid.
Juston Fluckey, SE, PE, AWS CWI
Engineering Consultant
RE: Statics or FEA required? Frame Drawing in Post
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Statics or FEA required? Frame Drawing in Post
Seriously. I would have had the answer to that in my 25 year old 2-D frame program in less time it took to type the original post.
Time is money in this business.
RE: Statics or FEA required? Frame Drawing in Post
Juston Fluckey, SE, PE, AWS CWI
Engineering Consultant
RE: Statics or FEA required? Frame Drawing in Post
Now in your actual structure that moment must be provided by axial forces in the cross brace and the two main beams, and moments in the main beams where the cross brace joins. That looks like structures 101 to me.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Statics or FEA required? Frame Drawing in Post
Referring to your last comment - I greatly sympathize with your frustration of just wanting to stick to the problem at hand, rather than having to wade through a pointless sidebar conversation with those who try to explain how moot your post is. You are a PE and SE. There is little reason to treat you in that manner. It is a fair assumption to make that you do not need lessons in spending your work time wisely. 20 hours of my time a week is un-billed, which involves experimenting with projects similar to your post on real jobs I am working on. Sometimes the extra effort pays off, sometimes it doesn't. Frankly, I don't post much anymore because I am frequently concerned that I will be greeted with ad hominem attacks, or at a minimum, the vibe that others have been inconvenienced with task of reading, understanding, and answering the question(s).
-Mac
RE: Statics or FEA required? Frame Drawing in Post
I always thought that a nice feature in commercial software would be to be able to call it simply as a component from Excel. You know, feed it some nodes and loads table style and get some responses back in return. Stick FEM is pretty ancient tech. I feel as though we all just keep reinventing the same thing over and over again unnecessarily.
This is unacceptable. I've got too much invested in your development to not have regular access to you as a colleague. If this is not your preferred medium, please see if you can't get in touch with me by other means.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Statics or FEA required? Frame Drawing in Post
@KootK and P1Eng:
Give python a look we've been developing some tools over the last couple months that can tie in nicely to excel and even generate some DXF files. With the opensource libraries matplotlib, scipy, and numpy we've been able to create some decent modules the most advanced fully functioning one being a theory of three moment continuous beam tool that does all possible live load patterns and outputs enveloped ASD and LRFD results to excel csv file and to scale CAD file showing the enveloped shears, moments, deflections, and reactions.
Back on topic:
I would personally start with the pinned column base condition, especially with your two bolt base connections, and create a tool for that which like others have mentioned makes the problem simpler. I do like your approach with the 1 kip equivalent model in RISA.
RE: Statics or FEA required? Frame Drawing in Post
I think this allows you to appreciate though the different dimensions work in the solution, and to quickly say "this particular design is conservatively covered by this earlier design". Maybe you can see a general rule about sizing the members ... should they be the same section ?
Sure there are canned solutions, but I like someone figuring things out from first principles rather than just running RISA or a "25yo 2D frame program".
@IDS, can you run with pinned supports ?
another day in paradise, or is paradise one day closer ?
RE: Statics or FEA required? Frame Drawing in Post
P1ENG - I apologize for hijacking your post. To get back on track, wouldn't the classical portal method (attached) be the most simple to implement?
-Mac
RE: Statics or FEA required? Frame Drawing in Post
KootK/Mac,
Thanks for the attachments. I need to look at them yet, but I will! Mac, I think that is what I was looking for. I couldn't remember the name of the method. Like I said, I was limited to Singularity Functions in school for beam analysis, not portals. I need to understand this method. I think I looked at it shortly when I was studying for the SE exam, but I couldn't find a good tutorial.
Celt83,
Python/programming certainly appeals to me. I don't know if I would choose Engineering or CS if I had to go back to school. Matlab opened my eyes to the enjoyment of programming. Unfortunately, I'm not that great. I run Linux at home and I've written a few scripts, but actual, large programs would probably just go over my head.
rb1957,
I agree that is better to understand what is happening rather than just using a piece of software. The problem is that people like you and me aren't appreciated when we ask questions. I always felt like my senior thought I was just questioning his instructions, but I really just wanted to understand the "why".
Juston Fluckey, SE, PE, AWS CWI
Engineering Consultant