Structures

1. ClassAct SRS enabled. Structures This presentation will explore: • forces in 2D structures • space, free body and force diagrams • vectors • classification of 3D structures

2. Forces in 2D Structures There are different ways to show the forces acting on objects. We can draw: • space diagrams • free body diagrams • force diagrams We will now look at these three different techniques using a simple hanging clock structure. Let us suppose that the length PX=PQ=QX and that the clock weighs 20lbs. Next >

3. Question 1 What does the term 'equilateral' mean? A) All the sides are of equal length B) All the angles are 60 degrees C) All the angles add up to 180 degrees D) It can be represented by a triangle

4. Space Diagrams A space diagram for the clock would look like this: Since the three lengths are equal: PQ = PX = QX They form an equilateral triangle. Therefore the angle PXQ = 60° Next >

5. Free Body Diagrams In a free body diagram you have to imagine yourself at the point X and work out in which way all the forces are acting. In this case, all the forces are pulls so they are tension forces. Each arrow is drawn in the direction of the force. The angle between a string support and the center line is half the PXQ angle. Next >

6. Question 2 How many forces are there in the example of the hanging clock? Enter your answer and press Send.

7. Question 3 What is the angle between the vertical line of the clock and a support? A) 5 degrees B) 15 degrees C) 30 degrees D) 60 degrees

8. Question 4 In which direction does the weight of the clock act? A) Downwards B) At 60 degrees to the supports C) At 120 degrees to the supports D) At 30 degrees to the horizontal

9. Force Diagrams A force diagram will allow us to find the size of the force in the supports PX and QX. The length of an arrow represents the size of the force and the direction of the arrow represents the direction of the force. 1. Draw a vertical line 2 inches long to represent the weight of 20lbs (scale 1” represents 10lbs). 2. Draw XQ at 30° to this vertical line from the bottom point. 3. Now draw XP at 30° to the vertical line from the top point. The length is unknown at this stage. 4. Where the two lines cross is the third point of the triangle. We call this a triangle of forces. 5. Measure PX and QX. They each measure 1.15”. This is 11.5lbs on our scale. Next >

10. Vectors The three lines we have just drawn to represent the forces show the direction and magnitude (size) of each of the forces. Any quantity that can be represented in this way is called a vector quantity. Examples include weight, velocity and acceleration. Next >

11. Question 5 A falling object accelerates at 9.81 m/s² downwards. Is acceleration a vector or a scalar quantity? A) Vector B) Scalar

12. Simple Crane - Space Diagram This is the space diagram for the simple crane. This structure represents a simple crane. Next >

13. Simple Crane - Free Body Diagram This diagram is the free body diagram. Note that PX is in compression and QX in tension. This structure represents a simple crane. Next >

14. Simple Crane - Force Diagram The force diagram is shown below (1” = 100lbs). This structure represents a simple crane. • The length of QX is 2” (isosceles triangle) • The length of PX is 3½” (by measurement) • The tension in QX is therefore 200lbs and the compression in PX is 350lbs Next >

15. Question 6 In the simple crane you have just seen, was the shorter member in tension or compression? A) Tension B) Compression

16. 3D Structures - Roofs and Bridges Most structures are three dimensional. Many useful structures are in the form of roofs or bridges. You will now see some 3-D structures. Next >

17. Beam A Beam Bridge is supported at either end. The gap between the two supports is called the span. The strength of the bridge comes from the material it is made from. Typically beam bridges can only span small gaps. Next >

18. Suspension For a suspension bridge, support comes from huge cables, which are suspended from high pillars. The main cables appear to sag, but are further strengthened by lighter, vertical cables that are attached along the sides of the bridge. The cables are all under tension, and the pillars are under compression. Next >

19. Arches The load is transferred down the sides of the arch, ending where they are fixed firmly into the ground, pressing against the foundations. The weight is spread evenly around the arch. Next >

20. Cantilevers An example of a cantilevered structure is a football stadium roof. Cantilever beam is the name given to a beam that is fixed at one end. If the load on a cantilever beam becomes too heavy, it will break at the point where it is fixed. Next >

21. Trusses Warren truss Roof trusses Bollman truss Next >

22. Girder An example of a Box girder An example of an I-girder Next >

23. Question 7 A beam bridge constructed with a warren truss would have the top surface in tension and the bottom surface in compression. Is this true or false? Answer True or False.

24. Question 8 What is the distance between the two supports of a bridge called? A) The spin B) The gap C) The span D) The void

25. Question 9 Which type of bridge do you think will span the greatest distance? A) Beam bridge B) Cantilever bridge C) Suspension bridge D) Arch bridge

26. Question 10 Only one force is present within an arch bridge. What is it called? A) Torsion B) Compression C) Tension D) Friction

27. Summary In this presentation we have seen: • We need an understanding of forces, moments and balance. Forces are examples of vectors • Structures can be analyzed using space diagrams, free body diagrams and force diagrams • There are many different types of structures, each of which is suited best to different situations End >