1. Fundamentals for the Up-and-Coming Bridge Engineer
Forces on Beams and Material Properties

2. Outline Beam Strength and Deflection Moment of Inertia
Types of Forces Applied
Young’s Modulus (stress and strain)
Optimization
Outline

3. Every object acts as a spring – it will deflect when a force is applied
Extent of deflection depends on force applied, material properties and object shape
Beam Deflection

4. Moments of Inertia A measure of resistance to deflection
A larger moment of inertia means that the beam will be more resistant to deflection
I = Area Moments of Inertia (depends on object shape) b h
Instructor:
B=base
H=height
These values depend on the orientation of the object and the direction of the force that’s being applied. If the box on the left were rotated 90 degrees, the height would now be larger and the base would be smaller.
The example on the right shows a hollow box-shaped tube. This is beneficial because it has much less material than a solid shape, but preserves much of the moment of inertia of the larger box.
Moments of Inertia

5. To Increase the Moment of Inertia
Increase the size:
But as you increase the size, you increase the weight and cost
Change the cross-sectional shape:
A hollow cross-section is stronger for the amount of material used
To Increase the Moment of Inertia

6. Differences in Deflection
The beams have the same cross-sectional area, but the shapes and moments of inertia are different
With the same volume of material, the hollow beam is stronger (higher moment of inertia).
Differences in Deflection

7. Types of Forces on a Bending Beam
Top of beam – under tension
Bottom of beam – under compression
Types of Forces on a Bending Beam

8. Compression, Tension, and Torsion

9. Stress and Strain of Different Materials
Different materials have different strain responses to the same stress. Choose a material that suits your needs
Stress vs. Strain Curves:
Linear Portion (Hooke’s Law):
Young’s Modulus
(slope of curve or material stiffness)
Instructor:
Stress and Strain are linearly related to each other by Hooke’s law. Young’s Modulus is a stiffness constant that relates stress and strain, and is a property of the material. The curve shows stress versus strain for different types of materials. Each material has a linear region called the elastic region. The slope of those lines are determined by Young’s Modules. As stress increases, the material enters a plastic region, which means that the material will deform and no longer return to its original shape completely when stress is removed. The curves end abruptly when the material breaks. Note that the ceramic material breaks before entering the plastic region, and steel has a higher Young’s Modulus than aluminum.
Stress and Strain of Different Materials

10. Engineering is not about building the strongest possible bridge
Engineering is about building a bridge that is strong enough and balances cost, strength, time required to build, etc
Engineering is about trade-offs and meeting design specifications
Design Optimization

11. Beam strength depends on force applied, material properties and object shape
Important material properties include moment of inertia and Young’s Modulus (stress and strain)
Three types of forces are compression, tension, and torsion
These concepts will be helpful in the West Point Bridge Designer
Summary