To determine the correct influence line for the axial force in member G-I of the truss, we need to analyze how a unit moving load on the bottom chord affects this member.

Understanding Influence Lines for Truss Members

An influence line for a particular member in a truss shows how the axial force in that member varies as a unit load moves across the structure. The following steps outline the process:

1. Placing Unit Load: A unit load is placed at various points along the bottom chord of the truss.
2. Analyzing Each Position: At each position of the unit load, calculate the axial force in member G-I using methods such as the method of joints or the method of sections.
3. Qualitative Nature: For an interior diagonal member like G-I, typically, certain segments will be in tension and others in compression as the load moves.
4. Constructing the Influence Line: Based on the calculated axial forces, plot these on a graph where the x-axis represents the position of the load on the truss and the y-axis represents the axial force in G-I.

Analysis Conclusion and Correct Option

After analyzing, the correct influence line has to match the pattern that reflects alternating tension and compression based on the placement of the unit load:

• is the correct influence line for member G-I. This option correctly shows the changes between tension and compression as the load traverses across the truss.

Therefore, the correct influence line option is illustrated below: