Module 4: Moving Loads and Influence Lines - Examples

A simply supported beam has span $L=12\text{ m}$. A unit load is at $x=3\text{ m}$ from the left support. Find the influence ordinate for the left reaction $R_A$.

For the same $12\text{ m}$ beam, find the influence ordinate for the right reaction $R_B$ when the unit load is at $x=3\text{ m}$.

A $10\text{ m}$ simply supported beam carries two axles: $P_1=80\text{ kN}$ at $x_1=2\text{ m}$ and $P_2=120\text{ kN}$ at $x_2=7\text{ m}$. Find $R_A$ from the reaction influence line.

A simply supported beam has $L=10\text{ m}$. Find the influence ordinate for bending moment at midspan when a unit load is placed at $x=4\text{ m}$ from the left support.

Use the moment influence ordinate from Example 4. If the moving load magnitude is $P=50\text{ kN}$ at $x=4\text{ m}$, determine the moment at midspan.

A single downward load $P=90\text{ kN}$ can move anywhere on a simply supported $L=8\text{ m}$ beam. Determine its position for maximum positive midspan moment and the maximum value.

A reaction influence line is triangular from ordinate $1$ at the support to $0$ at the far end over $L=12\text{ m}$. A uniform load $w=5\text{ kN/m}$ covers the full span. Find the reaction contribution.

At a target section, the shear influence line is positive immediately to the left of the section and jumps downward by one unit to a negative ordinate immediately to the right. Where should a single downward point load be placed to maximize positive section shear?

Describe the qualitative influence line for the vertical reaction at the left simple support of a simply supported beam.

Two axle configurations produce target-section responses of $R_1=245\text{ kN}$ and $R_2=268\text{ kN}$ when evaluated from the same influence line. Which position governs the positive response?

A moving axle of $100\text{ kN}$ is still $0.5\text{ m}$ before entering a simply supported span. What is its contribution to any influence line defined only for response caused by loads on that span?