The gantry in following figure is made of steel (E=200 GPa).
The chord sections are:
1-2, 2-4 and 4-6: W250x73 and Ix= 113x106 mm^4
2-3 and 4-6: W310x97 and Ix = 222x106 mm^4
Analyze the gantry by hand, using the displacement matrix
method.
You can, if you wish, do a check with the Advanced Design
America software, but be aware that the software considers the
axial deformations of the chords and that the results will be
slightly different.
a) Build the global stiffness matrix of the frame considering only
the rotations due to bending.
b) Calculate the unknown rotations with the displacement matrix
method.
c) Calculate the moments at the ends of the five (5) chords as well
as the forces
associated edges.
d) Complete the calculation of the reactions from the equilibrium
of the global DCL.
e) Draw the shear and bending diagrams of the entire
frame.