Moment Elevation Angle Beam Drawbridge

Overview

Engineering reference data for Moment Elevation Angle Beam Drawbridge in material science and properties.

Key Formulas

Stress

$\sigma = \frac{F}{A}$

Force per unit area.

Strain

$\varepsilon = \frac{\Delta L}{L_0}$

Change in length per original length.

Hooke's Law

$\sigma = E \varepsilon$

Stress proportional to strain in elastic region.

Thermal Expansion

$\Delta L = \alpha L_0 \Delta T$

Length change due to temperature.

Variables

Example Calculations

Horizontal Beam (α = 0°)

Given a 10-meter HE-B 340B steel beam with continuous mass $m = 134 \, \text{kg/m}$:

1. Resultant Force (Weight): $F = m \cdot g \cdot L = (134 \, \text{kg/m}) \cdot (9.81 \, \text{m/s}^2) \cdot (10 \, \text{m}) = 13,145 \, \text{N}$

2. Acting Distance (Center of Mass): $a = \frac{L}{2} = \frac{10 \, \text{m}}{2} = 5 \, \text{m}$

3. Moment at Support A: $M = F \cdot a = (13,145 \, \text{N}) \cdot (5 \, \text{m}) = 65,725 \, \text{Nm}$

Elevated Beam (α = 30°)

Using the same beam lifted at an angle $\alpha = 30°$:

1. Acting Distance (Projected): $a_\alpha = \cos(\alpha) \cdot \frac{L}{2} = \cos(30°) \cdot 5 \, \text{m} = 4.330 \, \text{m}$

2. Moment at Support A: $M_\alpha = F \cdot a_\alpha = (13,145 \, \text{N}) \cdot (4.330 \, \text{m}) = 56,920 \, \text{Nm}$

Elevation Angle Effects

The moment required to hold or control a drawbridge depends directly on the cosine of its lifting angle. This relationship has important practical implications:

• Maximum Moment at Horizontal: The critical, maximum moment occurs when the bridge is horizontal ($\alpha = 0°$, since $\cos(0°) = 1$).
• Reduced Moment with Elevation: As the bridge is raised, the effective lever arm $a$ decreases, reducing the required moment following $\cos(\alpha)$.
• Percentage Reduction: The moment at any angle $\alpha$ as a percentage of the maximum horizontal moment is: $\text{Moment \%} = \cos(\alpha) \times 100\%$ For example, at $60°$, the moment is $\cos(60°) = 0.5$, or 50% of the horizontal moment.

References

• Original Source