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Chapter 8

Q. 8.10

Draw the influence lines for the shear in panel CD and the bending moment at D of the girder with floor system shown in Fig. 8.15 (\mathrm{a}).

Step-by-Step

Verified Solution

Influence Line for \boldsymbol S_{C D}. To determine the influence line for the shear in panel C D, we place a 1  \mathrm{kN} load successively at the panel points B, C, D, and F . For each position of the unit load, the appropriate support reaction is first determined by proportions, and the shear in panel C D is computed. Thus, when

\begin{array}{lll} 1  \mathrm{kN} \text { is at } B, & F_{y}=0 & S_{C D}=0 \\ 1  \mathrm{kN} \text { is at } C, & F_{y}=\frac{1}{4}  \mathrm{kN} & S_{C D}=-\frac{1}{4}  \mathrm{kN} \\ 1  \mathrm{kN} \text { is at } D, & B_{y}=\frac{2}{4}=\frac{1}{2}  \mathrm{kN} & S_{C D}=\frac{1}{2}  \mathrm{kN} \\ 1  \mathrm{kN} \text { is at } F, & B_{y}=0 & S_{C D}=0 \end{array}

The influence line for S_{C D} is constructed by plotting these ordinates and by connecting them with straight lines, as shown in Fig. 8.15(c). The ordinates at the ends A and H of the girder are then determined from the geometry of the influence line.

Influence Line for \boldsymbol M_{D}. To determine the influence line for the bending moment at panel point D, we place the 1  \mathrm{kN} load successively at the panel points B, D, and F. For each position of the unit load, the bending moment at D is determined as follows: When

\begin{array}{lll}1  \mathrm{kN} \text { is at } B, & F_{y}=0 & M_{D}=0 \\ 1  \mathrm{kN} \text { is at } D, & B_{y}=\frac{1}{2}  \mathrm{kN} & M_{D}=\left(\frac{1}{2}\right) 8=4  \mathrm{kN} \cdot \mathrm{m} \\ 1  \mathrm{kN} \text { is at } F, & B_{y}=0 & M_{D}=0\end{array}

The influence line for M_{D} thus obtained is shown in Fig. 8.15(\mathrm{~d}).