Gere & Goodno — Axially Loaded Members: Problem 2.3-29

2.3-29 A T-frame structure is composed of prismatic beam $ABC$ and nonprismatic column $DBF$ that are joined at $B$ by a frictionless pin connection. The beam has a sliding support at $A$ and the column is pin supported at $F$ (see figure). Beam $ABC$ and column segment $DB$ have cross-sectional area $A$; column segment $BF$ has area $2A$. The modulus of elasticity $E$ is the same for both members. Load $2P$ is applied downward at $C$, and load $P$ acts at $D$. Find expressions for the downward displacements of column $DBF$ at $D$ ($\delta_D$) and also at $B$ ($\delta_B$). Plot axial force (AFD) and axial displacement (ADD) diagrams for column $DBF$.