Grade by Grade
D. Structures and Mechanisms · Form and Function

Loads, Force Diagrams and Strong Forms

D2 D2.3 A1.2 A1.5About 45 minutes
Learning goals
  • I can identify the dead loads and live loads on a structure.
  • I can draw a force diagram to scale, showing the magnitude, direction and point of application of each force.
  • I can explain how forms like triangles, arches and beams turned on edge handle the forces acting on and within them.

Words to know

external force
A force acting on a structure from outside, like gravity, wind or a person pushing.
internal force
A force inside the parts of a structure: compression, tension, torsion or shear.
dead load
The weight of the structure itself and anything permanently attached to it.
live load
A load that can come, go or change, like people, furniture, cars, snow or wind.
force diagram
A drawing that shows each force on an object as an arrow. The arrow starts at the point of application, points in the force's direction, and its length shows the magnitude.
truss
A frame made of triangles, used in bridges, roofs and towers.
arch
A curved structure that carries a load by squeezing its parts together and pushing outward at its feet.

Hook: why is a hydro tower full of triangles?

Look at a hydro tower, a crane or the roof trusses in a garage. They are full of triangles. Look at an old stone bridge. It has arches. These shapes are not just for looks. Each form is chosen because of how it handles the forces acting on it and inside it.

A tall steel hydro tower with many triangular braces, carrying power lines across a green farm field.
Look at how many triangles are in this hydro tower. Triangles keep their shape under load, so the tower stays stiff while using little steel. AI-generated image

Remember from Grades 3 and 5

In Grade 3 you learned about dead loads (the structure's own weight) and live loads (loads that come and go, like people, cars and snow). In Grade 5 you learned the four internal forces (compression, tension, torsion and shear) and sorted external forces into static and dynamic loads.

In Grade 7 you will show forces with force diagrams and explain how a structure's form handles them.

LoadDead or live?Static or dynamic?
the weight of a bridge's steel and concretedeadstatic
a car parked on the bridgelivestatic
trucks driving across the bridgelivedynamic
snow piled on a rooflivestatic (while it sits there)
a gust of wind on a towerlivedynamic
Two ways to sort the same loads

Drawing force diagrams

A force diagram shows forces as arrows:

  • The arrow starts at the point of application.
  • It points in the direction of the force.
  • Its length shows the magnitude, using a scale such as 1 cm = 10 N.
  • Label each arrow with its name and size.

If a shelf holds a 3 kg plant, the weight is about 3 × 9.8 = 29.4 N, so about 30 N. With a scale of 1 cm = 10 N, you draw a 3 cm arrow pointing down from the spot where the plant sits.

Strong forms and how they handle forces

  • Triangles: push on the corner of a square frame and it leans over into a slanted shape. A triangle can't change shape unless one of its sides changes length, so it stays rigid. That is why frames use trusses and diagonal braces.
  • Arches: a load on top of an arch is turned into compression that travels down the curve to the ground. Stone and concrete are very strong in compression, so arches suit them. But an arch also pushes outward at its feet, so it needs solid supports (called abutments) at each end.
  • Beams turned on edge: when a beam bends, the top is squeezed and the bottom is stretched. Putting more material at the top and bottom, like the tall shape of a floor joist on its edge or the I-shape of a steel I-beam, makes it much stiffer for the same amount of material.
  • Columns: short, thick columns resist compression well. Long, thin ones buckle sideways more easily.
square leanstriangle: rigidarch pushes out
Left: a push on the corner of a square frame makes it lean over (dashed shape). Middle: a triangle keeps its shape. Right: a load on an arch is carried down the curve, and the arch pushes outward at its feet.
Worked example

Let's draw a force diagram

A 20 kg child sits on the middle of a park bench. Draw a force diagram of the child's force on the bench, using a scale of 1 cm = 50 N.

  1. Magnitude: 20 × 9.8 = 196 N, about 200 N.
  2. Length of arrow: 200 N ÷ 50 N per cm = 4 cm.
  3. Direction: straight down.
  4. Point of application: the middle of the bench seat. Draw the arrow starting there, on the top surface (the plane of application).
  5. Label it: "child's weight, about 200 N".

A 4 cm arrow pointing down from the middle of the seat, labelled "about 200 N".

Worked example

Let's analyse a roof truss

A garage roof truss is a triangle: two slanted rafters meet at the top, and a horizontal bar (the bottom chord) joins their feet. Snow presses down on the rafters. Which parts are in compression and which in tension?

  1. The snow pushes down on the slanted rafters, so they are squeezed: compression.
  2. Squeezed rafters push their bottom ends outward, trying to spread the walls apart.
  3. The bottom chord holds the two feet together, so it is stretched: tension.
  4. Because the triangle can't change shape, the whole truss stays rigid under the snow load.

Rafters: compression. Bottom chord: tension. The triangle form keeps the truss rigid.

wallwallsnow loadrafter:compressionrafter:compressiontensionbottom chord is stretched as the rafters push their feet outward
In a roof truss under snow, the two rafters are squeezed (arrows pointing in) and the bottom chord is stretched (arrows pointing out). The triangle keeps the truss rigid.
Hands-on activity

Shape test: square vs triangle

You need: 9 straws (or rolled paper tubes): 4 for the square, 3 for the triangle and 2 to tape end to end for the longer diagonal, string or pipe cleaners, tape, scissors (with a grown-up's help), a ruler.

  1. Join 4 straws into a square by threading string through them or joining the corners with pipe cleaners. Join 3 straws into a triangle the same way.
  2. Lay each shape flat. Push gently on one corner, sideways. Which shape changes shape?
  3. Now add a diagonal across the square (tape two straws end to end and trim them to fit from corner to corner). Push again. What changed?
  4. Draw a force diagram of your push: estimate it as about 2 N (a gentle push), use a scale of 1 cm = 1 N, and draw a 2 cm arrow from the corner where you pushed.
  5. Explain in two sentences why bridges and towers use triangles.

What to look for: the square folds into a slanted shape (a parallelogram), the triangle stays rigid, and the diagonal brace turns the square into two triangles, so it becomes rigid too.

Just for fun

Why was the square frame so nervous on the playground?

One little push and it was bent out of shape. The triangle just stood there, totally rigid and calm.

Your turn

1

What is the difference between a dead load and a live load?

2

Is a bookcase's own weight a dead or live load?

3

In a force diagram, where does the arrow start?

4

Using 1 cm = 10 N, how long is the arrow for a 60 N force?

5

Why are triangles used in frames?

6

What force travels down the curve of an arch?

7

Why does an arch need strong supports at its ends?

More practice: warm-up

1

Is a truck crossing a bridge a dead or live load?

2

What does the length of an arrow show in a force diagram?

3

What shape is used in a truss?

4

Which internal force squeezes?

5

Which buckles more easily: a long, thin column or a short, thick one?

More practice: on your own

1

Using 1 cm = 20 N, draw (describe) the arrow for a 5 kg bag of flour on a counter.

2

A deck has a 2 × 8 board (a board about 4 cm thick and 18 cm wide) as a joist. Why is it installed on its narrow edge, not flat?

3

A garden gate made as a rectangle of boards sags at the corner over time. How could you fix it?

4

Name the dead load and two live loads on a hockey arena roof in winter.

5

Why are stone bridges usually built as arches instead of flat beams?

Challenge

1

A bridge has a dead load of 400 000 N. A bus with a mass of 15 000 kg drives onto it. What is the total load, approximately? (Use 9.8 N per kg.)

2

Explain why an I-beam can be lighter than a solid rectangular steel bar but still almost as stiff.

3

A student builds a straw tower that wobbles and leans to one side. Suggest two changes based on forms, and explain each.

Check your understanding

Quiz

1.

Which is a dead load?

2.

In a force diagram, the length of an arrow shows...

3.

Using 1 cm = 10 N, a 45 N force is drawn as an arrow...

4.

Why are triangles used in trusses?

5.

A load on an arch is carried down the curve mainly as...

6.

Why is a floor joist installed on its narrow edge?

For parents and teachers

Big idea (D2, D2.3): Students link structural forms to the forces acting on and within them, and draw force diagrams to scale. Dead/live loads (Grade 3) and internal forces and static/dynamic loads (Grade 5) are reviewed.

How to help: Look for triangles and arches on walks (bridges, roof trusses, playground equipment, hydro towers). Ask, "Which part is squeezed? Which is stretched?" Practise turning masses into newtons (× 9.8) and newtons into arrow lengths with a chosen scale.

Common difficulties:

  • Arrow drawn from the wrong place. It must start at the point of application.
  • Forgetting the scale. Always write it on the diagram (e.g., 1 cm = 10 N).
  • Safety: a grown-up should help with scissors when cutting straws.