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