# University of Florida/Eml4500/f08.qwiki/Lecture 4

**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

**Seperate 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)