Fundamentals for the UpandComing Bridge Engineer Forces on

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) h b

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 Top of beam – under tension Bottom of beam – under compression

Compression, Tension, and Torsion Reference: http: //www. diydoctor. org. uk

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)

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