8. Forces in a Roof Truss
Total weight of building (N) =
Wind Force On Roof (N) =
17,8000 N
3,4000N
8,9000 N 8,9000 N
34,000N
1) Will the building take off?
YES!
9. What about the forces in your design?
Will your design take off?
Wind (N)
Weight (N)
Wind (N)
Weight (N)
Wind (N)
Weight (N)
10. Forces in a Roof Truss
Total weight on trusses (N)
= 11,000 N
Wind Force On Roof (N)
=17,8000 N
8,9000N
8,9000 N
34,000N
2) What is the maximum possible load on 1 truss?
Total Force on Roof (N)
= 189000 N
Force on 1 Truss (N)
= 63,000 N
11. What about the forces in your design?
Start with the force on the pink members
12. What about the forces in your design?
What is the maximum possible load on the pink
structures?
Wind (N)
Wind (N)
Wind (N) Wind (N)
Weight (N)
Weight (N)
Weight (N)
Weight (N) Weight (N)
13. What about the forces in your design?
Work out the total downwards load for your
structure
Cart – You have 2 trusses. Work out the load on 1
truss
Umbrella – you have 3 supports. Work out the load
on 1 support.
14. Forces in a Roof Truss
Look at the overall forces on the object
63,000N
31500N 31500N
=
15. What about the forces in your design?
Draw your structure to scale on square paper
1square represents how many centimetres?
Draw your forces to scale onto your structure
1 square represents how many Newtons?
16. What about the forces in your design?
6.5cm = 13,000 N
6,500 N 6,500 N
8000 N
4000 N 4000 N
12,500 N 12,500 N
25,000 N10cm = 1m
6cm
= 0.6m
1 cm = 0.1 m
1 cm = 2000N
1 cm = 2000N
1 cm = 0.1 m
2 cm = 0.5 m
1 cm = 10,000N
1cm
6cm = 1.5m
17. How big are these forces?
Look at 1 joint (starting
at supports)
tension
compression
31500N
31500N
31500N 31500N
44,500N
63,000N
31500N 31500N
18. What about the forces in your
design?
Look at each joint in turn
What forces act on each joint?
Tension
Compression Compression
Tension
6,500 N
6,500 N
8000 N
12,500 N
8000 N
12,500 N
19. How big are these forces?
Look at 1 joint (starting
at supports)
tension
compression
31500N
31500N
31500N
31500N
44500N
63,000N
31500N 31500N
20. What about the forces in your design?
Tension Compression
Tension
Tension
Tension
6,500 N
6,500 N
Compression
4000 N 4000 N
4000 N
25,000 N
25,000 N
21. How big are these forces?
Look at 1 joint (starting
at supports)
63,000N
31500N 31500N
63,000N
44500N44500N
22. What about the forces in your design?
13,000 N
12,500 N
13,000 N
12,500 N
23. How big are these forces?
Look at the forces in the members of your
structure
Tension = 31500N
Compression =
44500N
Compression =
44500N
24. Challenge!
Use what you have just learnt to make this
bridge truss
Bridges are made out of straws
(compression), string (tension) and pins
Cheapest bridge wins!
5 rupees per
metre
5 rupees per
straw
1 rupee per
pin
12cm
25. What about the forces in your design?
What about the purple bits?
Wind (N) Weight (N)
Wind (N) Weight (N)
Wind (N) Weight (N)
Notes de l'éditeur
This lecture shows students how to work out the forces in the members that make up their design. This is useful because once you know the load a bar must take, you can work out how big it needs to be, without wasting material.
Ask the students why they think bar forces might be important. Explain that if you know the load each bar must be able to carry, you also know when it will break. You can also pick the right size of bar to carry the force.
Beams can be loaded somewhere in the middle, or at their ends. Which way is strongest? Beams are stronger when loaded from the ends, because they don’t bend. When loaded at the ends, beams can either be subject to pulling forces (tension) or pushing forces (compression)
Here are some examples of bending, tension and compression. Ask the students to see if they can identify where ther might be tension/compression/bending in each of the pictures. The first bridge is only small, because it is in bending. The second bridge is longer because the design ensures all supports are in tension or compression, not bending. Arches are strong because they work in compression. This bridge in Mumbai is a cable stayed bridge. The cables hold the bridge up, and are in tension, and the post supports both the weight of the cables and the bridge, so is in compression. On this picture you can see that the part of the bridge supported in tension by cables has a much larger span between supports. The parts of the bridge unsupported by cables (in bending) have a much shorter span between supports.
RCC works by tension and compression. When you bend a beam, the top surface is squeezed together and goes into compression. The lower surface is stretched, and goes into tension. Prove this to yourself by bending an eraser. Beams and columns often go into bending, so trying to make columns and beams out of concrete doesn’t work. Concrete is weak in tension, and easily cracks. This problem can be solved by including steel bars inside the concrete. Steel is strong in tension, and can carry the tensile forces preventing damage to the concrete.
Squares are weak shapes; they form mechanisms. Make a model out of pins and straws and show that squares collapse when a force is put on them. Demonstrate the same with triangles, to show triangles are strong shapes. Ask the students how the square could be improved to make it strong. The square can be strengthened by adding a bar to make it into 2 triangles.
Cylinders are strong against twisting forces. They are also good for containing liquids, which exert outwards pressure on the sides of the container holding the liquid. Circular shapes distribute this pressure force evenly; squares concentrate the pressure force at the corners, making the corners likely to fail. Domes work very much like circles, but in 3D. They can distribute load evenly, meaning there is no weak point where the load becomes abnormally high.
The force on one truss can be found by identifying the total load on the roof. There are 3 trusses, so one truss will carry 1 third of the total load on the roof.
Once the truss and forces have been drawn to scale, separately draw one joint, but with the forces enlarged. Looking at the diagram, you know that there is an upwards force of 31500N on the joint. You also know that the joint is not moving, so the forces must be balanced. Therefore you can say that there must be a 31500N force downwards on the joint. However, you also know that the forces in the bars can only act as a pushing force (compression) or a pulling force (tension). The downwards force is not in the same direction as either of these bars! This is where understanding angled forces is important. The downwards force must be one of the two smaller forces which make up a bigger angles force. You can find this angled force using the technique illustrated on the slide. You can also find the other small force which makes up the angled force. Now you know there is a force pulling ‘east’ on the joint, you can say there must be a force pulling ‘west’ to balance. Overall, the diagram shows a 44500N force in the direction of one bar, and a 31500N force in the direction of the other bar. Therefore you know the forces in the bars! If the arrow points into the bar, the bar is in tension. If the arrow points out of the bar, it is in compression. This is counterintuitive to what you know about tension and compression. The reason the arrows seem to be the wrong way round is because this diagram shows the forces on the joint, not the bars. The force on the bar will be the opposite to what it is on the joint.
