# Engineering in the K-12 Classroom: Math and Science Education for the 21st-Century Workforce

## CONTENTS OF CURRICULUM UNIT 12.04.06

## The Road to Bridge Design

Your feedback is important to us!

After viewing our curriculum units, please take a few minutes to help us understand how the units, which were created by public school teachers, may be useful to others.

## Some Mathematics Behind the Bridge

For an example, the truss bridge is formed by the use of triangles. These bridges are used for the passage of trains over water. Each joint of the bridge must be in equilibrium which means that the two forces acting on it must be equal to zero. The directional forces are horizontal and vertical and their summations equal zero or ΣH=0 and ΣV=0. These expressions will yield two equations that can be solved for only two unknown forces. ΣH=0:
*
F
_{
1
}
*
cosθ

*- F*cosθ = 0 and ΣV=0: -

_{ 2 }*F*sinθ - F

_{ 1 }_{ 2 }sinθ = 0 where θ is the angle of inclination for example 45

^{ 0 }or 60

^{ 0 }. More complicated truss bridges may have more than two unknown forces and would need other analytical techniques such as matrices.

In addition to gravitational forces torque forces must also be balanced to zero or the bridge will rotate. Torque, is the cross product between the applied force relative to the position of an object's center of mass,
*
τ=F x d.
*

Commonly, mathematical applications in bridge design include differential calculus, integral calculus and Newton's Second Law: F=mg for which F is the force, m is the mass, and g is the gravitational acceleration.