Consider the pin-jointed truss shown in the figure. Influence line is drawn for the axial force in the member G-I, when a unit load travels on the bottom chord of the truss. Identify the CORRECTinfluence line from the following options: Note: Positive value corresponds to tension and negative value corresponds to compression in the member.
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To find influence lines for truss members, use geometry-based influence line theory and remember that bottom chord members generally carry tension under downward unit loads.
We are to find the influence line for the axial force in member G–I when a unit load travels along the bottom chord of the truss.
From the geometry of the truss:
- Total span = \(6 \times 6 = 36\) m
- Height of truss \(h = 6\) m
- Panel point spacing = 6 m
- Distance from A to G = 2 panels = 12 m
- Distance from G to right support = 4 panels = 24 m
Now, to find the ordinate of the influence line for member G–I under G, we use the standard formula for diagonal or bottom chord members in simple trusses:
\[
\text{Ordinate} = \frac{a b}{l h}
\]
Where:
- \(a = 12\) m,
- \(b = 24\) m,
- \(l = 36\) m,
- \(h = 6\) m
Substitute into the formula:
\[
\frac{12 \times 24}{36 \times 6} = \frac{288}{216} = 1.33
\]
Hence, the influence line has an ordinate of \(+1.33\) under joint G, which corresponds to tension in member G–I. Therefore, the correct diagram is option (B).
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