University of Florida/Eml4500/f08.qwiki/Lecture 4
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Trusses, matrix method
Truss with 2 Elastic (deformable) Bars
Note: Points 1 and 3 are fixed (constrained) to zero in both the x and y directions
Global FBD
Note: There are 4 unknown reactions and three equations of equilibrium making this truss statically indeterminant
Separate FBD's of the bar elements
Bar Element 1
Note: The superscript 1 in parenthesis on each force variable denotes that the force is applied to element 1
Bar Element 2
Note: The superscript 2 in parenthesis on each force variable denotes that the force is applied to element 2
Next Big Step:Force displacement relation (FD)
FD relation of 1-D spring element:
- 1 end fixed: f = kd (see above figure)
- 2 ends free:
Case 1: Observer sits on node 1
- f2 = k(d2-d1)
Case 2: Observer sits on node 2
- f1+f2=0 Therefore, f1 = k(d1-d2)