Fundamentals for the Up-and-Coming Bridge Engineer Forces on Beams and Material Properties OSU College of Engineering Summer Institute - Robotics

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

Beam Deflection 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

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

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

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).

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

Compression, Tension, and Torsion Reference:

Stress vs. Strain Curves: Young’s Modulus (slope of curve or material stiffness) Linear Portion (Hooke’s Law): Stress and Strain of Different Materials Different materials have different strain responses to the same stress. Choose a material that suits your needs

Design Optimization 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

Summary 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