# Bridges with Trigonometry Equals Engineering Achievement

By Gathing, Ahmed L. | Technology and Engineering Teacher, February 2011 | Go to article overview

# Bridges with Trigonometry Equals Engineering Achievement

Gathing, Ahmed L., Technology and Engineering Teacher

Introduction

Exemplary and fun technology education classes in high schools are always welcome. I introduce bridge building to my ninth graders and other students who comprise the Introduction to Engineering and Technology course within the first two months of the fall semester. In Georgia, Introduction to Engineering and Technology is the first of four technology education classes that students take in high school. Incoming students' knowledge will consist of at least basic algebra and science concepts. As students enter my class for the first time, they are excited to build while learning about different engineering concepts. Building bridges is a great beginning project that allows students to build upon their math skills using basic trigonometry formulas while learning how forces act upon a structure. They also get to enjoy building and testing their bridges. Integrating math into technology education activities is important to enhance their value as "engineering-oriented" activities. Math-related engineering projects have been a missing component in many technology education programs, but activities such as this bridge project will provide credibility to engineering programs. Since most technology education teachers are familiar with the balsa wood project, the implementation of math concepts will not be a difficult concept to conceive.

Background

Bridges

There are many different types of bridges. I introduce truss bridges to students at this level. Students are given the option to build from one of three types of truss bridges: Figure 1. Warren, Figure 2. Pratt, or Figure 3. Howe. These three types of bridges are symmetrical, so, mathematically, members on each side of the bridge should be equal. Another reason I chose these bridges is that students are able to build them within the necessary time period.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

Forces

Four forces are introduced during this lesson: compression, tension, shear, and torque. Compression and tension are the two primary forces acting on the bridge; therefore, I describe them in depth. Compression is a pushing force, and tension is a pulling force, and these can be calculated and described mathematically as will be shown in the explanation of the project that follows.

Project

Students choose a bridge and have to build the bridge using the following teacher-supplied constraints and criteria:

* Using 1/8" graph paper, each student individually must produce a rough drawing of a balsa wood frame bridge (3" wide x 3" high x 8" long).

* The bridge must be constructed with no more than 20' (240") of 1/8" x 1/8" square balsa wood stock, and no less than 16' (192") of 1/8" x 1/8" square balsa wood stock.

* The final drawing will only consist of the front view of the bridge, and the graph paper will also be used to do the math calculations for the amount of stock needed to produce the bridge.

After the students design their bridges and provide mathematical documentation that their bridges are within the constraints, they are given the amount of wood they calculated.

Math Portion

Students will use math equations to predict how the loads acting on the joints are going to affect each member of the bridge. While calculating the loads, students will also learn which members are in tension and which are in compression. If a member is in tension, the answer is positive; if the member is in compression, the answer is negative. I chose dimensions for the bridges that fit within the criteria, but any dimensions will work with your class as long as the equations are correct. The basic math equations needed for this exercise are shown in the next column.

Math equations needed

[summation][F.sub.y] = 0, [summation][F.sub.x] = 0

[A.sup.2] + [B.sup.2] =C2

Sin [theta] = opposite/hypothesis

Weight = mass*gravity

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