Transcript Material choices and beam bending

Fundamentals for the
Up-and-Coming Bridge Engineer
Forces on Beams and Material Properties
OSU College of Engineering
Summer Institute - Robotics
Outline
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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)
bi
h
b
I
1 3
bh
12
ho
hi
bo
I  Io  Ii
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):
  E
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