$3$ni

Example $2-4$

nonprismatic column $DB.$ The beam has a pin support at $A,$ and the col$-$

pin connection. $F($see Fig. $2-20).$ Beam ABC and column

umn is pin suppo a cross$-$sectional area $A$; column segment $BF$

segment $DB$ have modulus of elasticity $E$ is the same for both

Sity has area $2A.$ The $2P$ is applied downward at $C,$ and load $P$ acts

$3$ members. Load $2P$ is apleweight of both members: The weight

at $D.$ Consider also the $($ Find expressions for the downward

$n^3$ density of the material column $DBF$ at $D({}_D)$ and also at $B({}_B).$ Plot

displacements of col and axial displacement $($ADD$)$ diagrams for

axial force $($AF

column $DBF.$

Solution:

Use a four$-$step problem$-$solving approach to find displacements

at joints $B$ and $D$ for this T$-$frame structure.

Conceptualize: Remove the pin at $B$ and split the frame

into two separate free$-$body diagrams: one for beam ABC

and the other for column $DBF($Fig$.2-21).$ Show reaction