How Do You Calculate Reaction Forces in Complex Roof Trusses?

[hurcw]

Hi all,

I am having trouble with a work/course related issue.
As part of a project assignment I have decided to research the failure of some of the roof structure members at my place of work.
To do this I need to calculate the reactions forces in the roof supports, but some trusses have two supports and a large cantilever section in the middle, some have four supports & to make things more complicated the repaired roof has 6 supports. For the life of me I cannot figure out how to work out the reactions when there are more than two supports, I have gone through old coursework and trawled the net & books and cannot find any examples with more than two supports.
Can anyone please help.
See rough pic below.

 

[SteamKing]

Hi all,

I am having trouble with a work/course related issue.
As part of a project assignment I have decided to research the failure of some of the roof structure members at my place of work.
To do this I need to calculate the reactions forces in the roof supports, but some trusses have two supports and a large cantilever section in the middle, some have four supports & to make things more complicated the repaired roof has 6 supports. For the life of me I cannot figure out how to work out the reactions when there are more than two supports, I have gone through old coursework and trawled the net & books and cannot find any examples with more than two supports.
Can anyone please help.
See rough pic below.

It's not clear from what material or what kind of members this truss is fabricated, but because this truss is resting on more than two supports, it is not statically determinate, which is why applying the standard equations of equilibrium is insufficient to determine the support reactions.

The quickest way to analyze the original or the repaired truss would be create a model of the structure and apply the dead and live loads to it. The results of the analysis should give the internal forces in each member and the stresses as well.

 

[hurcw]

Hi SteamKing,

Thanks for the response much appreciated.
The structure is fabricated from 275 grade steel and is a combination of welded box section style members and bolted 'I' beam connections.
I know all the live loads and dead loads but would need to calculate the self-weight of the structure which may take some time as the truss is 60m wide.
The arched sections are made up of 4 bays each 5.94m wide and the centre flat roof section is two 5.94m bays each split into two smaller bays.
I was hoping to use the method of sections to determine my member forces, but I guess I could do it another way, but it has to be done analytically rather than by using software.
Would you suggest using the dead & live loads as a form of UDL/blanket force acting across the full structure.

 

[SteamKing]

Hi SteamKing,

Thanks for the response much appreciated.
The structure is fabricated from 275 grade steel and is a combination of welded box section style members and bolted 'I' beam connections.
I know all the live loads and dead loads but would need to calculate the self-weight of the structure which may take some time as the truss is 60m wide.

The dead loads often include the weight of the structure. If you have an itemized list of your dead loads for this truss, it should be easy to check if the weight of the structure is included or not.

The arched sections are made up of 4 bays each 5.94m wide and the centre flat roof section is two 5.94m bays each split into two smaller bays.
I was hoping to use the method of sections to determine my member forces, but I guess I could do it another way, but it has to be done analytically rather than by using software.

This sounds like HW rather than a work project. IMO, it's a poor choice of structure to use for any teaching purpose because of its complexity. Most of the techniques like the method of sections are illustrated using simple structures which are statically determinate. I think that the amount of calculation involved is going to increase the risk of making some kind of calculation error, so check your results carefully on completion.

If you must analyze this structure by hand, take advantage of its symmetry.

Would you suggest using the dead & live loads as a form of UDL/blanket force acting across the full structure.

No, I wouldn't. I'm not certain of the purpose of this exercise, and it's not totally clear to me for what purpose the results will be used.

The diagrams at the link below show how the reactions vary in different continuous beams under different types of loading:

http://www.yourspreadsheets.co.uk/continuous-beam-bending-tables.html

The beams used to calculate these reactions all have the same moment of inertia in each span. By inspection, the strength properties of your structure would vary quite a bit between each of the supports.

As far as using software to analyze trusses is concerned, there are free packages available on the web which can be downloaded and installed without much fuss. This is one such package which I have used:

http://www.grapesoftware.mb.ca/

Although this package can be registered for a fee, it is fully functional should you choose not to do so.

Good Luck!

 

[hurcw]

The dead loads often include the weight of the structure. If you have an itemized list of your dead loads for this truss, it should be easy to check if the weight of the structure is included or not.This sounds like HW rather than a work project. IMO, it's a poor choice of structure to use for any teaching purpose because of its complexity. Most of the techniques like the method of sections are illustrated using simple structures which are statically determinate. I think that the amount of calculation involved is going to increase the risk of making some kind of calculation error, so check your results carefully on completion.

If you must analyze this structure by hand, take advantage of its symmetry.No, I wouldn't. I'm not certain of the purpose of this exercise, and it's not totally clear to me for what purpose the results will be used.

The diagrams at the link below show how the reactions vary in different continuous beams under different types of loading:

http://www.yourspreadsheets.co.uk/continuous-beam-bending-tables.html

The beams used to calculate these reactions all have the same moment of inertia in each span. By inspection, the strength properties of your structure would vary quite a bit between each of the supports.

As far as using software to analyze trusses is concerned, there are free packages available on the web which can be downloaded and installed without much fuss. This is one such package which I have used:

http://www.grapesoftware.mb.ca/

Although this package can be registered for a fee, it is fully functional should you choose not to do so.

Good Luck!

Thanks again for responding.
The results of this analysis will not be used for anything, the idea of this exercise is to work through the original damage report and do some of my own analysis and see if anything can be added or any conclusions can be made.
How would you start.?

 

[SteamKing]

Thanks again for responding.
The results of this analysis will not be used for anything, the idea of this exercise is to work through the original damage report and do some of my own analysis and see if anything can be added or any conclusions can be made.
How would you start.?

I would forget about doing an analysis by hand for this structure. You will spend too much time and effort trying to do the calculations to obtain any real understanding of why this truss failed. Also, if you want to test different theories of why it failed, you have to start your calculations over from some point, introducing further risk that a mistake will occur.

1. Start with what you know about the truss and its construction. Making a structural model should not be too difficult, if you have good plans of its original design.
2. Figure out what kind of loads were supported by this structure and where they were applied. Structural programs can let you model different load configurations for a single structural model, so there may be several different load configurations which will have to be developed for your analysis.
3. It's not clear what kind of failure this truss suffered, nor how old it was at the time of failure. If there is the possibility that some members had lost strength over time, then you'll have to figure out how much strength remained in these members.
4. Since this truss is apparently part of a roof structure, you'll have to look at the entire roof and see how each truss shares the loads applied to the outer surface of the roof, i.e. whether each truss can be analyzed as if it were acting independently or if you must considered that multiple trusses act as if they are tied together structurally.
5. If there was a damage report prepared by a structural engineer who examined the damaged structure, read it and try to understand his conclusions. Such a report may include an explanation of where the failure originated and why it led to the damage to the truss (or trusses).
6. If there is no report, then you'll have to formulate your own theories of how the structure failed, which is why you don't want to get bogged down in trying to do a lot of hand calculations. Even with a structural model, there will be plenty of tedious work keeping you busy, everything from arranging the input data for the structure, to assembling the load cases, to analyzing the results obtained from the model and trying to make sense of what the analysis is telling you about how the structure behaves under load.

These are just some of the things off the top of my head, recognizing that I don't know much about your structure or the circumstances under which it failed. If you are not an engineer, this is an incredibly complex task to undertake single-handedly.