Fundamentals for theUp-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)

ih oh

ob

ib

3

12

1bhI

io III 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: http://www.diydoctor.org.uk

Stress vs. Strain Curves:

E

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