I know that frequency depends on material properties, geometry, support conditions and in plane loading. I have played around with these figures except that I maintained the same material steel because, I want it to be practical and cost effective.
However, the natural frequencies still fall within the critical range of a bridge 1(.5hz-4.5hz). I have struggled with this for weeks. Please any ideas or suggestions that could help me please.
What are the lower and upper limits for the cross-sectional area of the truss members?
Did you consider a static load case? What are the nodal forces P?
Did you consider displacement constraints?
~Hi Nils. the cross sectional area was not varied. By this, I mean that each member has a fixed cross sectional area selected from the blue book. The reason I plotted the mode shapes was to observe the each member behaviour in term of tension and compression and then modify the stiffness, but I wasn't successful. The nodal forces are 100KN each
Hello Rita Akonobi ,
What did you model as connection between the elements in the truss?
Did you make a static study of your truss? With the picture you sent it appears that there is an error in the definition of the elements seeing the deformations that you get.
Damien Decret if I understand correctly you are asking if, they are connected by bolts or welded. If so, I didn't consider this in my studies. What I did eventually was to eliminate the irrelevant members by looking at the deformed shape. This significantly reduced the total weight of the structure and increased the frequency as well, for example the member bounded by the two fixed supports was removed. Please if I didn't get your question right, kindly correct me. Thanks
Rita Akonobi ,
Actually, what I do not understand is your optimized structure. How do you get it? You do not keep the original shape? Because with the shape you seem to keep (and for me it is not realistic since it is not a truss anymore), I think depending on how you link your elements at the nodes your stiffness tensor may vary.
Can you describe better what are the original data for your work and what you can modify in order to find a solution?
Damien Decret The optimized structure was obtained using the default 'ga' function in MATLAB. The design parameters were created in a datafile (Set by the designer/user), so the the algorithm performs optimization based on the data it reads. The essence of this optimization is to obtain an optimal structure that weighs less and retains structural integrity. The con of this type of optimization is some times the optimized shape is not conventional (which is why it might no longer look like a truss after optimization). There are other optimization methods like shape optimization and so on but this is outside the scope of my current research. I hope this helps, I can still try to explain further if required
Damien Decret the original data includes the cross- sectional area for each member and corresponding second moment of area chosen from the construction institute, the other parameters are dependent on the material and in this case the material I chose is steel with density 7850kg/m3
Rita Akonobi
OK, I get it. So in a mathematics way, your optimization is correct. However, in an engineering way, it may be different. For me, such a shape is not something that we may encounter in a construction. Maybe I am wrong but I do not have somthing like that in mind. Moreover, depending on the implemention on site, it may be impossible that it fits in the construction. What kind of bridge is it? Where the truss is supposed to be in the bridge?
Damien Decret I agree with you but optimization is not limited to bridges. This structure is particular is a cantilever. Also studies are still on going in this field.
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