# Lesson: Investigating Torque

### Summary

Students learn about torsion as a force acting upon structures and have the opportunity to design something to withstand this force.

### Engineering Connection

Understanding how torsion affects objects helps engineers design products and structures (from bicycles to bridges) that are safe and sound. For civil and mechanical engineers, evaluation of the effect of torsional forces on objects, such as supporting beams in buildings or machine parts, is critical to making sure that structures and machines do not fail.

### Educational Standards

•   International Technology and Engineering Educators Association: Technology
•   Massachusetts: Science

### Learning Objectives

• Students learn the concept of a moment (torque) of a force and learn how to calculate moments.
• Students learn how moments ("turning forces") create bending and torsion loads on structures.
• Students understand the effects of bending and torsion loads.
• Students gain an appreciation of how engineers can design a structure to resist bending and torsion.

### Introduction/Motivation

Introduce students to all the keywords and recap the concepts from Fairly Fundamental Facts about Forces and Structures lesson.

### Lesson Background and Concepts for Teachers

Students should have a basic understanding of tension, compression, shear, bending, torsion and concept of a moment (torque). Review Lesson 1: Fairly Fundamental Facts about Forces and Structures, and complete the Introduction to Loads Acting on Structures lesson before beginning this lesson.
Moment and torque can be use interchangeably, physicists tend to use the word torque and engineers tend to use moment when referring to forces that cause rotation. The ability of any beam or structural member to resist bending and torsion, depends on the following factors (variables):
Material:: Every material has a different yield strength, tensile strength, and shear strength, which ultimately determine the load that a material can withstand and the amount of deformation (stretching, bending, twisting) that accompanies a given load.
Size: Engineers calculate the moment of inertia of a beam or column, which is a measure of the size and shape of its cross-sectional area, and how far away the area is from the center of the beam. The greater the moment of inertia, the greater the load that can be carried by the structural member. This means that increasing the cross-sectional area of a beam or taking a certain amount of area and spreading it out farther from the center, will increase the strength and stiffness of the beam (see Figure A).
It might be instructive for students to draw on graph paper different designs for beams, showing how the cross-sectional area, or the distribution of area can increase to make a stronger, stiffer beam. Have them try to draw two beam cross-sections that have the same areas, but different moments of inertia (meaning that the area of one beam is spread out farther away from the center, and the area of the other is more concentrated around the center).
Reinforcement / Composite Structure: Many structural members are composite materials, which means that they are made from two or more different materials bonded together. Foam board is an example of a composite material; it is a layer of foam sandwiched between two layers of paper. Reinforced concrete has steel rods (called rebars, short for reinforcing bars) that are placed inside the form before the concrete is poured. Concrete is a material that is very strong in compression, but very weak in tension; the steel rebars can take great tensile loads and thus they overcome the weakness of the concrete and make the composite material much stronger. Fiberglass, which is used to make canoes, is mostly a plastic epoxy resin; the epoxy resin by itself would not be that strong, however, it is reinforced by glass fibers inside that are very strong in tension.
Structural Bracing: Any structural members that help a structure to resist bending and/or torsion. Examples: wire cables (called guy wires) bracing a tower; truss bracing in bridges, towers and skyscrapers (a truss structure is a triangular formation of long, thin bars pinned together at the ends); brackets and braces such as those used to hold up book shelves and store signs, and strengthen table legs and dump truck bodies.

### Associated Activities

• Wimpy Radar Antenna - Students reinforce an antenna tower made from foam insulation so that it can withstand specified bending and twisting moments (torques) with minimal deflection. They discuss the problem, run initial tests and graph the results. Then they design, construct and test sturdier towers, and graph the results.

### Assessment

Assess students' understanding, individually or as a group, using the Investigating Questions provided in the associated activity.

### Contributors

Douglas Prime, Center for Engineering Educational Outreach, Tufts University