Doing the Math: Analysis of Forces in a Truss Bridge
In this lesson, students learn the basics of the analysis of forces engineers perform at the truss joints to calculate the strength of a truss bridge. This method is known as the “method of joints.” Finding the tensions and compressions using this method will be necessary to solve systems of linear equations where the size depends on the number of elements and nodes in the truss.
The method of joints is the core of a graphic interface created by the author in Google Sheets that students can use to estimate the tensions-compressions on the truss elements under given loads, as well as the maximum load a wood truss structure may hold (depending on the specific wood the truss is made of) and the thickness of its elements.
A Southern Pacific Railroad bridge, now part of the Iron Horse Regional Trail crossing a channelized Walnut Creek at the Concord-Pleasant Hill boundary immediately south of Monument Boulevard, in Contra Costa County, California.Copyright 2006 Leonard G, Public Domain, Wikimedia Commons. https://en.wikipedia.org/wiki/File:RRTrussBridgeSideView.jpg
Determining the strength of structures is extremely important in civil and mechanical engineering. Engineers use sophisticated computer programs that solve all the equations resulting from a given problem solution. Engineers have to solve a wide variety of problems that requires finding the solution of one or many systems of linear equations. Because these systems may contain hundreds, if not thousands of equations, computers and software are used to solve them.
After this lesson, students should be able to:
- Identify the components of a truss bridge.
- Identify different type of trusses.
- Perform the analysis of forces at a truss’ nodes using free body diagrams.
- Use trigonometric ratios to find force magnitudes at a truss’ nodes.
- Use the method of joints to set up a system of linear equations to calculate the tensions and compressions on the truss elements.
- Use the substitution method to solve systems of linear equations larger than 3 x 3.