Girder Span Maximum Bending Moment Calculation

This question asks us to find the absolute maximum bending moment in a girder with a specific span when a single rolling load passes over it. Understanding how moving loads affect bending moments is crucial in structural engineering.

Understanding Rolling Loads on Beams

When a load moves across a simply supported beam, the bending moment at any point changes. The maximum bending moment occurs at different locations depending on the position of the load. For a single rolling load, the absolute maximum bending moment occurs when the load is positioned exactly at the center of the beam's span.

Formula for Maximum Bending Moment

The formula used to calculate the absolute maximum bending moment ($M_{max}$) for a single concentrated rolling load ($P$) on a simply supported beam of span ($L$) is:

$$M_{max} = \frac{P \times L}{4}$$

Step-by-Step Calculation

• Identify Given Values:
  • The magnitude of the rolling load, $P = 8 \text{ kN}$.
  • The span of the girder, $L = 15 \text{ m}$.
• Apply the Formula: Substitute the given values into the formula for the maximum bending moment.

  $$M_{max} = \frac{8 \text{ kN} \times 15 \text{ m}}{4}$$

• Perform the Calculation:
  • First, multiply the load by the span: $8 \text{ kN} \times 15 \text{ m} = 120 \text{ kN-m}$.
  • Then, divide the result by 4: $$M_{max} = \frac{120 \text{ kN-m}}{4}$$
• Determine the Result:

  $$M_{max} = 30 \text{ kN-m}$$

Therefore, the absolute maximum bending moment that will occur in the girder is 30 kN-m.