Four point loads 8 kN, 15 kN, 15 kN and 10 kN have centre-to-centre spacing of 2 m between consecutive loads and they traverse a girder of 30 m span from left to right with 10 kN load loading. The maximum shear force at 8 m from left support will be

Concept:

To determine the maximum positive shear force at a specific point on a girder, we analyze the effect of different point loads on the shear force at that point. The shear force is calculated by considering the contribution of each load based on its position relative to the point of interest.

Given Data:

• Point Loads: 10 kN, 15 kN, 15 kN, and 8 kN
• Center-to-center spacing between loads: 2 m
• Span of the girder: 30 m
• Point of interest for shear force: 8 m from left support

Calculation:

1. Shear Force with 8 kN Load:

\( \text{SF} = 10 \times \frac{8}{30} + 15 \times \frac{6}{30} + 15 \times \frac{4}{30} + 8 \times \frac{2}{30} \)

\( \text{SF} = 8.2 \, \text{kN} \)

2. Maximum Positive Shear Force Calculation:

\( \text{SF} = 10 \times \frac{16}{30} + 15 \times \frac{18}{30} + 15 \times \frac{20}{30} + 8 \times \frac{22}{30} \)

\( \text{SF} = 30.2 \, \text{kN} \)

3. Check for Another Load Position (15 kN Load on the Section):

\( \text{SF} = 10 \times \frac{18}{30} + 15 \times \frac{20}{30} + 15 \times \frac{22}{30} - 8 \times \frac{6}{30} \)

\( \text{SF} = 25.4 \, \text{kN} \)

The maximum positive shear force is 30.2 kN.