Cantilever Trianlge Truss Design

[caseyvoigt]

1. I am an architecture student and the assignment is to design a truss, set up the problem and solve it using graphic statics. I think I did it correctly using the graphical method but I am interested in solving it mathematically. Did I set the problem up correctly in my diagram and if so, where do I go from here? I know that if this was just a simple overhang, I would not need the members AD and BD but the top chord is supporting joists so I thought the chords AD and BD were necessary.




2. [tex]\sum[/tex]m=0
[tex]\sum[/tex]Fv=0
[tex]\sum[/tex]Fh=0
m=moments
v=vertical
h=horizontal


3. I Just used sum or forces in vertical and horizontal I removed chord AD because I realized it did not do anything. The new link Shows my work. I am concerned because I feel like the top chords (a,b and a,c) ahould not be equal for some reason but it does make sense that they are too. Did I do this problem correctly?


MY WORK

http://i1128.photobucket.com/albums/m490/caseyvoigt/TrussBwithwork.jpg"

 

[jbsteele]

Yes, you have set up the problem correctly in your diagram and you can solve it mathematically by using the equations of equilibrium. The equations are: \sumFv=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sumFh=0 \summ=0where Fv is the sum of vertical forces, Fh is the sum of horizontal forces, and m is the sum of moments. You can then use these equations to determine the forces in each member of the truss. For example, for the top chord (AB) you can use the equation of equilibrium to determine the force in AB by setting up two equations: FAB = FBC + FCA mAB = -FCA*hAB + FBC*hBC where hAB and hBC are the distances from the supports to the nodes A and B respectively. You can then solve for both FAB and FBC by solving these two equations simultaneously. Once you have determined all the forces in each member, you can then verify that the forces in the members are equal to the loads applied on the system. Yes, you did set up the problem correctly. The top chords (AB, BC, and AC) should all be equal because they are connected to the same joists and support the same loads.