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## Q. 8.8

Draw the influence lines for the vertical reactions at supports $A$ and $C$ of the beam shown in Fig. $8.11 (\mathrm{a})$.

## Verified Solution

Influence Line for $\boldsymbol A_{y}$. To obtain the general shape of the influence line for $A_{y}$, the roller support at $A$ is removed from the given beam, and a small displacement, $\Delta$, is given at point $A$ of the released beam as shown in Fig. 8.11(b). The shape of the influence line is the same as the deflected shape of the released beam, as shown in the figure. By realizing that $A_{y}=1 \mathrm{kN}$ when the $1 \mathrm{kN}$ load is placed at $A$, we obtain the value of $1 \mathrm{kN} / \mathrm{kN}$ for the influence-line ordinate at $A$. The influence line thus obtained is shown in Fig. 8.11(b).

Influence Line for $\boldsymbol C_{y}$. The roller support at $C$ is removed from the given beam, and a small displacement, $\Delta$, is applied at $C$ to obtain the deflected shape shown in Fig. 8.11(c). Note that the deflected shape is consistent with the support conditions of the released beam. The shape of the influence line is the same as the deflected shape of the released beam, as shown in the figure. By recognizing that $C_{y}=1 \mathrm{kN}$ when the $1 \mathrm{kN}$ load is placed at $C$, we obtain the value of $1 \mathrm{kN} / \mathrm{kN}$ for the influence-line ordinate at $C$. The ordinates at $B$ and $E$ are then determined from the geometry of the influence line. The influence line for $C_{y}$ thus obtained is shown in Fig. 8.11(c). 