Truss Analysis with Fixed Supports (Welded) 3

[Audronic]

Good Morning All,

Could someone please shine some light on how I would go about analysing the truss as per the image below? In reality, the truss members are SHS's where every point specified on the diagram is a weld.

In order to analyse the problem, I was going to assume the following:

-Members EG and FH are zero force members and so can be neglected from the analysis
-The reaction forces and moments acing at supports G and H can be neglected assuming that members EG and EH are zero force members
-The force applied to member BD will cause a compressive for in member CD
-Supports A and B can be changed to a pin and roller support respectively in order to simplify the analysis

Furthermore, once all the forces have been calculated in the truss, am I able to treat all the various members as beams in order to calculate SFD and BMD?

Any help or advice on these matters would be greatly appreciated.

 

[jayrod12]

If everything is fully welded, therefore 6 degrees of freedom at each node, then you cannot assume EG and FH are zero force members. You would need to stiffness matrix this to solve it, it is indeterminate.

 

[KootK]

I like the assumptions that you've suggested so long as members AB and CD are not very stiff flexurally. And yes, you will be able to treat the members as beams for the purpose of working out the shear and moment diagrams.

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.

 

[jayrod12]

I guess I should clarify, for a worst case scenario of the members not including EG and FH, then your assumptions would be ok. However EG and FH are going to attract load the biggest question is how much.

 

[Audronic]

Many thanks to you both for your comments.

KootK Is there a numerical range that differentiates a flexurally stiff member from a not very stiff member?

Just to clarify that if I was to go ahead with my assumptions, would I be taking a more conservative approach than if I was to apply a stiffness matrix where each node has 3 degrees of freedom (Fx,Fy and Mz)?

 

[KootK]

KootK Is there a numerical range that differentiates a flexurally stiff member from a not very stiff member?

Darn it! I had a hunch that you would ask this. And I'm not sure that there's a great, non-judgement way to quantify this that's really any easier than just running the full analysis. Anyhow, here's what I can think of:

1) Run the truss using your assumptions and get the displacement at point C.

2) Use the results of #1 to estimate the displacement at points E & F perpendicular to members AC and BC. Ratios and such. No need for great precision.

3) Treating the displacement in #2 as imposed, back calculate transverse member forces at E & F that would produce such displacement.

4) Use the force from #3 to estimate moments on members AC and BC. If those moments are less than 5% of the moment capacities or yield moments of the sections used, the effect of members EG and FH are inconsequential.

For kicks, why don't you tell us the sections and materials used for members AB and BC as well as the lengths of those members? Dollars to doughnuts, I'll bet that Jayrod and I will be in complete agreement when it comes down to judging the real thing.

Just to clarify that if I was to go ahead with my assumptions, would I be taking a more conservative approach than if I was to apply a stiffness matrix where each node has 3 degrees of freedom (Fx,Fy and Mz)?

You would be conservative in some respects but unconservative in others. For example, your calculation of nodal deflections would be conservative because you'd have ignored some sources of stiffness/restraint but your design of members AB and BC may be unconservative because you'd have neglected the transverse bending and shear resulting from the restraint provided to those members at points E & F. You'd also have neglected any moments induced at the member ends due to joint rigidity coming about from the connection welds.

I didn't agree with your proposed assumptions because they were universally conservative. I agreed with them because I suspect that the inaccuracies involved will be of little consequence and the the model that you've proposed will capture the fundamental aspects of the truss behavior. You never capture everything in a structural model. Designer judgment is required to estimate how granular a level of detail is granular enough.

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.

 

[jayrod12]

Oh Koot you know me so well. Let's be honest here, I'm already in full agreement with your answers as they come from the reasonable design world and mine are the true mathematical design world in this case.

If I were designing it I would do my hand calcs with the same assumptions, but then modelling it to double check that the true behavior is not too far from the assumptions.

 

[KootK]

We'll see. Sometimes questions from mechanical folks thwart my intuition. I'm thinking 6' truss chord and this will end up representing a 2" cam or something...

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.

 

[Audronic]

Sorry in advance for the units guys.

I'll give the full analysis ago and then try and validate against some frame analysis software that I have been using.

 

[KootK]

Sorry in advance for the units guys.

Not to worry: jayrod and I are both Canadian and therefore metri-philes. Or at least metri-tolerators.

With your proportions (L/d~17), I'm inclined to stand by my original recommendations. I'd say that you're starting to get close to where those E/G restraints would matter though.

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.

 

[jayrod12]

I'd tend to agree with the above assessment (both the metri-toleration and the assumptions). Although I would really be considering throwing it into a model just to see. I actually expect you may have some issues with your bottom chord given the applied loading and the proportions.