#1LEARNING ACTIVITYExperiment Forces in structures

How does a Structure Carry Load ?

One of the most important learning objectives of this project is to understand how a truss bridge carries load. But what exactly is a “load,” and what does it mean for a structure to “carry a load?” To answer these questions, we will need to introduce (or perhaps review) some basic concepts from physics.

ForcesMuch of structural engineering deals, in some way, with the concept of force. A force is simply a push or a

pull applied to an object. A force always has both magnitude and direction. When a truck crosses a bridge, it exerts a force on the bridge. The magnitude of the force is the weight of the truck, and the direction of the force is downward. Mathematically, we represent a force as a vector. By definition, a vector is a quantity that

as both magnitude and direction. To show a force on a picture or diagram, we normally represent it as an arrow (which shows the direction) and a magnitude (in units of force, such as pounds or newtons),like this:

In structural engineering, it is useful to distinguish between three different kinds of forces—loads, reac- tions, and internal member forces.

LoadsTo illustrate what loads, reactions, and internal member forces are, let’s do a simple experiment. Find a

nutcracker like the one shown below, and tie the ends of the handles together with a piece of string. Ensure that the string is taut. You have just built a simple truss composed of three members—the two handles and the string. Now put the ends of the nutcracker on a smooth, flat surface, and press down on the center hinge. You are applying a load to the nutcracker truss. A load is simply a force applied to a structure.

A simple 3-member truss made from a nutcracker.

Actual structures are subjected to many anydifferent kinds of loads, including the following:

n Weight of the items intended to be supported by structure

n Weight of structure

n Weight of the add-on’s to the structure

n Environmental factors (wind, water) pushing on the structure

n Weight of snow, ice, or rainwater

n Forces caused by earthquakes

In designing a roll cages, the structural designer must consider the effects of all these loads, including cases where two or more different kinds of loads might occur at the same time.

ReactionsNewton’s First Law—one of the basic principles of physics—states that an object at rest will remain at

rest, provided it is not subjected to an unbalanced force. In other words, if an object is not moving, then the total force acting on it must be zero. When you apply a downward force to your nutcracker truss, it does not move; thus, according to Newton’s First Law, the total force on the truss must be zero. But how can that be? Suppose you push down on the nutcracker with a force of 10 newtons. The nutcracker does not move, because the table pushes back upward with a force of 10 newtons. In this particular example, because the structure touches the table at two points, the table actually pushes upward with two forces, each with a magnitude of 5 newtons, as shown below. The structure is said to be inequilibrium, because the total upward force equals the total downward force. A structure that is not moving must be in equilibrium. Mathematically, the vector sum of all forces acting on the structure is zero. If we assume that the upward direction is positive, then

+ 5 + 5 – 10 = 0

In our example, the two upward forces are called reactions. Reactions are forces devel- oped at the supports of a structure, to keep the structure in equilibrium. Supports are the points where the structure is physically in contact with its surroundings. On our nut- cracker truss, the supports are located at the ends of the handles, where the nutcracker touches the table. On an actual bridge, thesupports are located at the abutments or piers. (See Section 1 above.)

Geotechnical engineers are particularly interested in the reactions of a structure,

The two 5-newton reactions keep the nutcracker truss in equilibrium with the 10-newton load.

because the foundations must be designed to carry these forces safely and efficiently.

Internal Member ForcesWhen you apply external loads to a structure, external reactions occur at the supports. But internal

forces are also developed within each structural member. In a truss, these internal member forces will always be either tension or compression. A member in tension is being stretched, like the rubber band in the picture below. Tension force tends to make a member longer.

Tension is an internal force that tends to make a member longer.

#1LEARNING ACTIVITY

A member in compression is being squashed, like the block of foam in the picture below. Compression force makes a member shorter.

Compression is an internal force that tends to make a member shorter.

Tension and compression are among the most important concepts in structural engineering. A renowned engineer and author named Mario Salvadori once wrote,

In our nutcracker truss example, the two handles are in compression, while the string is in tension, as shown here. If you push down hard enough on the nutcracker, you can actually see the string stretching in tension. Unfortunately, you can’t see the nutcracker handles shortening in compression—steel is so stiff that the shortening of the handles is too small to be seen with the naked eye. But the handles actually do get shorter!

Like loads and reactions, internal member forces must obey the laws of physics. Internal forces must be in equilibrium with each other and with the loads and reactions. By applying the concept of equilibrium and some relatively simple math, we can actually calculate the internal force in every member of a truss. We’ll see how to do this Learning Activity #3.

StrengthLet’s return once again to our nutcracker truss

example. As we have already seen, if you press down on the hinge at the top of the structure, a tension

force is developed in the string. If you press down harder (that is, if you increase the load), the tension force in the string increases. If you are very strong, or if the string is very weak, you should be able to apply a

downward force that is large enough to break the string.

Tension and compression in the nutcracker truss.

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What causes the string to break? The string breaks when its internal member force becomes larger than its strength. This observation leads us to two closely related definitions:

(1) The strength of a structural component is the largest internal force the component can experience before it fails.

(2) Failure occurs when the internal force in a structural component becomes larger than its strength.

If you have ever bought fishing line, you might have noticed the words “100 pound test” or something similar on the label. “100 pound test” means that the line is guaranteed not to fail, as long as the internal force in the line is less than 100 pounds. To put this in structural engineering terms, the strength of the line is100 pounds. 4

How Does a Structure Carry Load?Having discussed loads, reactions, internal member forces, and strength, we can now answer the

important question posed at the beginning of thissection: what does it mean for a structure

to carry load?

In this learning activity, you will build and load-test a model bridge. If you build the bridge well, it will carry the load successfully, and you will have an

opportunity to observe how the structure works.

When you apply a load to a structure, internal forces—tension and compression—occur in each member. If the strength is greater than the internal force for every member in the structure, then the structure will carry the load successfully.

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1.The Project Team: Key Players and Contributions

Building a model bridge is a great way to start learning about the process used to design and construct actual structures. But before we can fully understand this process, we need to meet the key players in the design-construction process and learn about how they contribute to its ultimate product—a completed struc- ture or facility. This section applies equally well to any civil engineering project, not just to a bridge project.

The Project TeamMajor construction projects are always performed by a project team, composed of many different special-

ists. Each member of the team contributes unique capabilities or resources to the project, and all must work together to make the project successful. The team has four key players—the Owner, the Design Professional, the Constructor, and the Project Manager—organized as shown in the diagram on the following page.

4 Actually, the true strength of the line is probably somewhat higher than 100 pounds. In order to guar- antee a strength of 100 pounds, the manufacturer would normally design the line to be somewhat stronger than that–say 150 pounds. Small variations in the dimensions or material characteristics of the line will always occur during manufacturing.