Lesson: Fairly Fundamental Facts about Forces and Structures

Contributed by: K-12 Outreach Office, Worcester Polytechnic Institute
 SummaryStudents are introduced to the five fundamental loads: compression, tension, shear, bending and torsion.
 Engineering Connection Relating science and/or math concept(s) to engineering Engineers take into consideration the impact of many types of forces when designing structures.

 Contents
 Grade Level: 7 (6-8) Lesson #: 1 of 3 Time Required: 45 minutes Lesson Dependency :None Keywords: bending, compression, design, force, load, moment, tension, torque, torsion, shear, structure My Rating: Avg Rating: Not Yet Rated.Teacher Experiences  |  Share your experience!

Related Curriculum

 subject areas activities

Educational Standards :

•   Common Core State Standards for Mathematics: Math
•   International Technology and Engineering Educators Association: Technology
•   Massachusetts: Science

After this lesson, students should be able to:
• Identify the five fundamental loads: compression, tension, shear, bending and torsion.
• Explain the concept of a moment, how to calculate one, and how moments create bending and torsion loads on structures

Everyone knows from experience that a force is a pushing or a pulling action that moves, or tries to move, an object. Engineers design structures, such as buildings, dams, planes and bicycle frames, to hold up weight and withstand forces that are placed on them. An engineer's job is to first determine the loads or external forces that are acting on a structure. Whenever external forces are applied to a structure, internal stresses (internal forces) develop inside the materials that resist the outside forces and fight to hold the structure together. Once engineers know what loads will be acting on a structure, they calculate the resulting internal stresses, and design each structural member (piece of the structure) so it is strong enough to carry the loads without breaking (or even coming close to breaking).

The five types of loads that can act on a structure are tension, compression, shear, bending and torsion.
1. Tension: Two pulling forces, directly opposing each other, that stretch out an object and try to pull it apart (for example, pulling on a rope, a car towing another car with a chain – the rope and the chain are in tension or are "being subjected to a tensile load").
 Figure 1. Tension
1. Compression: Two pushing forces, directly opposing each other, that squeeze an object and try to squash it (for example, standing on a soda can, squeezing a piece of wood in a vise – both the can and the wood are in compression or are "being subjected to a compressive load").
 Figure 2. Compression
1. Shear: Two pushing or pulling forces, acting close together but not directly opposing each other – a shearing load cuts or rips an object by sliding its molecules apart sideways (for example, pruning shears cutting through a branch, paper-cutter cutting paper - the branch and paper are "subjected to a shear loading").
 Figure 3. Shear
(For example, pulling on two pieces of wood that have been glued together - the glue joint is "being subjected to a shear loading").
 Figure 4. Shear forces on glued wood.

A Moment of a Force

Before you can understand the last two types of loads, you need to understand the idea of a moment of a force. A moment is a "turning force" caused by a force acting on an object at some distance from a fixed point. Consider the diving board sketch in Figure 5. The heavier the person, and the farther s/he walks out on the board, the greater the "turning force," which acts on the concrete foundation.
 Figure 5. Moment of a force.
The force (F) produces a moment or "turning force" (M) that tries to rotate the diving board around a fixed point (A). In this case, the moment bends the diving board.
The stronger the force, and the greater the distance at which it acts, the larger the moment or "turning force" it will produce.
A moment or "turning force" (M) is calculated by multiplying a force (F) by its moment arm (d). The moment arm is the distance at which the force is applied, taken from the fixed point:
 Figure 6: Equation for a moment of a force.
(As long as the force acting on the object is perpendicular to the object)
If you have a force measured in Newtons multiplied by a distance in meters, then your units for the moment are N-m, read "Newton-meters." If your force is measured in pounds and you multiply it by a distance given in inches, then your units will be lb-in., read "pound-inches." The units for moments can be any force unit multiplied by any distance unit.
1. Bending: Created when a moment or "turning force" is applied to a structural member (or piece of material) making it deflect or sag (bend), moving it sideways away from its original position. A moment that causes bending is called a bending moment. Bending actually produces tension and compression inside a beam or a pole, causing it to "smile." The molecules on the top of the smile get squeezed together, while the molecules on the bottom of the smile get stretched out. A beam or pole in bending will fail in tension (break on the side that is being pulled apart) (for example, a shelf in a book case, and the earlier diving board example).
 Figure 7. Bookcase example of bending.
1. Torsion (Twisting): Created when a moment or "turning force" is applied to a structural member (or piece of material) making it deflect at an angle (twist). A moment that causes twisting is called a twisting or torsional moment. Torsion actually produces shear stresses inside the material. A beam in torsion will fail in shear; the twisting action causes the molecules to be slid apart sideways (for example, a pole with a sign hanging off one side).
 Figure 8. Torsion

Questions: Evaluate students' understanding of the material, individually or as a group, using the Investigating Questions provided in the associated activity.
Problem 1: Calculate the moment resulting when a person weighing 150 lbf stands at the end of a 120 in. diving board (use the moment equation: M = F x d) (Answer: 18,000 lbf-in.)
Problem 2: If 1 N = 0.2248 lbf and 1m = 3.28 ft, convert the units in the previous problem to obtain a solution in Nm (Answr: 18,000 lbf-in. x 1 N / 0.2248 lbf x 1 ft / 12 in. x 1 m / 3.28 ft = . 203 Nm)

Contributors

Douglas Prime, Tufts University, Center for Engineering Educational Outreach