Finding Tension and Compression
By Sara Lacy
It stands to reason that buildings fall down because forces act on them. Some forces are easy to see—the weight
of ten Mack trucks on a bridge. Others are not as easy to identify—the force of the ground pushing up on the
bottom of the house, equal and opposite to the weight of the house pushing down on the ground.
The forces acting on structures are either pushing or pulling its components. Forces pushing on components are
called compressive forces, and forces pulling on components are called tensile forces. A structure does not fall
down because it, and each of its members, are strong enough to resist the pushing and pulling on them.
If, however, the forces increase (e.g., Goldilocks sits on baby bear’s chair, or hurricane strength winds blow) or
the strength of a structure decreases (e.g., the material corrodes), the structure may not be strong enough to
resist the pushing and pulling. A structure fails when it is not sufficiently strong in tension or compression.
Engineers identify what’s in tension and what’s in compression in order to use structural components that have
sufficient strength. They use force vectors to identify the directions of
the forces acting on structures, and on the parts of a structure.
Force vectors
A force has a size and a direction. Mathematicians represent forces as vectors, the general mathematical term
for something that has a size and a direction. A vector can be represented by an arrow pointing in the direction
of the vector. A number on top of the vector can be used to represent its size.
For example, a vector of a force of 5 lbs pushing or pulling to the right would look like this:
A vector representation of a force of 5 lbs pushing or pulling to the left would look like this:
Sometimes the length of a vector is used to represent its size. For example, this might be 20
lbs to the right;
this might be 2 lbs to the right:
In this course, since we will be working mostly qualitatively, we will often use the length of vectors to indicate
their relative size.
Tension
When a component of a structure is pulled, it is in tension. For example, the chains on the swing set are pulled
—the weight of the child is a downward force on the chains.
Simultaneously, the bar at the top of the swing set pulls upward on the chain. The two forces act in opposite
directions, pulling on the chain.
The diagram shows a segment of the chain. The vectors represent the forces pulling in opposite directions and
pointing away from each other, indicating that the chain is in tension.
Note that when the child sits on the swing the net force—the sum of the downward force and the upward force
—is zero. The chain is said to be in equilibrium. The arrows are of equal length, in opposite directions.
A tensile force tends to stretch an element. If you pull on a rubber band, you can see it stretch.
When you pull on the chain of a swing set, the stretching may be so small that it is imperceptible.
Compression
When a component of a structure is pushed, it is in compression. For example, the stones in the stone arch
bridge are pushed—the weight of the bridge is a downward force on the arch.
Simultaneously, the ground at the bottom of the bridge pushes upwards. The two forces act in opposite
directions, pushing the stones of the arch together.
The diagram shows a segment of the arch. The vectors represent the forces pushing in opposite directions,
pointing towards each other and indicating that the stone is in compression.
Note that the arrows are of equal length, in opposite directions. The forces are equal and opposite. There is no
net force on the stone; it is in equilibrium.
A compressive force tends to make the thing it pushes on shorter. If you push on a sponge, you can see it
become shorter. When you push on a stone, the shortening is so small that it is imperceptible. Click on the
"compression" button below to see an animation of compression.
Bending
When a component of a structure bends, it develops both tension and compression. For example, when the wind
blows on a building, the distance between the roof and the ground on the windward side becomes longer; that
side of the building is in tension. On the leeward side, the distance between the roof and the ground becomes
shorter; that side is in compression.
What’s in tension? What’s in compression?
How do you decide if a structural component is in tension or compression? Try to identify the forces acting on
it. Decide if the component is being stretched or compressed. It may help to imagine you have inserted your
finger into the structure. Is it being pushed, becoming shorter, in fact being crushed? Or is it being pulled,
stretched out?
Look at the figures below. Where is there tension and where is there compression? On the diagrams below, use
vectors to show the forces on the highlighted portions.
Suspension bridge cables
The Verrazano Narrows Bridge © Metropolitan Transit Authority
The columns of the Parthenon
The Nashville Parthenon—Exterior view of the southeast side of the building at night. Photography by Gary
Layda, Photo courtesy of The Parthenon, Nashville, TN. © Metropolitan Government of Nashville
Engineering in your life
Look around your house and your place of work. Try to find examples of things in compression (e.g., an arch
bridge). Can you see things in tension (e.g., a stretched rubber band)?