ENGR 1310 Introduction to Mechanical Engineering Fundamentals
Spring 2013Dr. Paul Griesemer
Case Study in Mechanical Engineering: Bridge Construction
• Why do bridges look the way they do? – Many different
shapes, sizes, construction techniques
What are the design issues in bridge construction?
• What are we trying to optimize with the “best” design– Strength– Safety– Cost
• Materials• Complexity• Longevity
• Suspension– Low cost over large
spans
• Arch– Strong, durable
• Truss– Simple, small members
over small spans
Types of Bridges• Pier & Beam (or just Beam)
– BP Pedestrian Bridge in Millennium Park, Chicago, Illinois
Types of Bridges• Suspension (or Cable-stayed)
– Akashi-Kaikyō Bridge (or Pearl Bridge) over the Akashi Strait in Japan
– World's longest spanning suspension bridge
Types of Bridges• Arch Bridge
– Si-o-se Pol bridge over Zayandeh River in Esfahan, Iran
Types of Bridges• Truss Bridge
– Kingston-Rhinecliff Bridge over Hudson River, New York, USA
Our goal will be to understand the basic design and analysis methods
• Our “design project” will be a truss structure– Predict the strength properties
Engineering Analysis of a Truss
• What is the maximum load a structure can support?
• How do you design a structure to meet load requirements?
• How do you determine the forces in each member of the truss?
• Answer: Mechanics
Mechanics
• Statics
– Nothing accelerating– Not time dependent
• Dynamics
– Forces lead to acceleration– Translation and rotation
maF 0F
Background: Forces and VectorsIn both Statics and Dynamics, forces must be treated as vectors.
• Scalars– Have only a magnitude– Examples:
• Volume• Time• Mass
• Vectors– Have magnitude and
direction– Examples
• Velocity• Position• Acceleration
𝜃
Addition of Vectors
• Vectors are added “tip to tail”– Vectors don’t have a designated location
F2
F1
F1 + F2
Components of a Vector
• Similarly, vectors can be broken into smaller vectors whose addition equals the original
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F
Fx
Fy
Fx = F cos(Θ) Fy = F sin(Θ)
Picture Frame Example:What is the best way to hang a 40 lb mirror on a wall? How much tension is in the hanger wire in each case?
Option 1: One Hanger in Wall Option 2: Two Hangers in Wall
48 in
12 in 12 in
12 in