ENGR 1310 Introduction to Mechanical Engineering Fundamentals Spring 2013 Dr. Paul Griesemer
Dec 26, 2015
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
𝜃
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