Module 4: Moving Loads and Influence Lines - Examples

Drawing Influence Lines

Example 1: Influence Line for Reaction

Draw the influence line for the vertical reaction at AA (RAR_A) for a simply supported beam of length L=10 mL = 10 \text{ m}, supported at AA (x=0x=0) and BB (x=10x=10).

Step-by-Step Solution

0 of 3 Steps Completed
1

Example 2: Influence Line for Shear at Midspan

Draw the influence line for internal shear at point CC, located at midspan (x=5 mx = 5 \text{ m}) of the same 10 m10 \text{ m} simply supported beam.

Step-by-Step Solution

0 of 3 Steps Completed
1

Example 3: Influence Line for Moment at Midspan

Draw the influence line for internal bending moment at point CC (midspan, x=5 mx=5 \text{ m}) for the 10 m10 \text{ m} simply supported beam.

Step-by-Step Solution

0 of 3 Steps Completed
1

Maximum Response from Moving Loads

Example 1: Maximum Moment using Influence Line

A simply supported beam spans 10 m10 \text{ m}. A series of two wheel loads from a truck (P1=40 kNP_1 = 40 \text{ kN}, P2=80 kNP_2 = 80 \text{ kN}, spaced 3 m3 \text{ m} apart) moves across the beam. Find the maximum bending moment at midspan (CC).

Step-by-Step Solution

0 of 4 Steps Completed
1

Example 2: Absolute Maximum Bending Moment

For the same 10 m10 \text{ m} beam and moving truck (P1=40 kNP_1 = 40 \text{ kN}, P2=80 kNP_2 = 80 \text{ kN}, spacing 3 m3 \text{ m}), calculate the absolute maximum bending moment that can occur anywhere in the beam.

Step-by-Step Solution

0 of 4 Steps Completed
1

Example 3: Maximum Shear using Influence Line

Find the absolute maximum shear in the 10 m10 \text{ m} beam for the same moving truck.

Step-by-Step Solution

0 of 3 Steps Completed
1