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Structures

Structures. Week 2. In previous sessions…. Brief review of previous learning: Types of motion Classes of lever Turning moments. Types of structure. Mass Frame Shell. Forces. Compression Tension Torsion Shear Bending. Applying forces. Distributed (UDL) Concentrated (point)

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Structures

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  1. Structures Week 2

  2. In previous sessions… • Brief review of previous learning: • Types of motion • Classes of lever • Turning moments

  3. Types of structure • Mass • Frame • Shell

  4. Forces • Compression • Tension • Torsion • Shear • Bending

  5. Applying forces • Distributed (UDL) • Concentrated (point) • Static • Dynamic

  6. Reinforcing structures • Create the following shapes from the modelling materials supplied. Ensure free-moving pin joints. • Reinforce each shape internally using pin joints • Reinforce each shape internally using only string

  7. Combining external forces ForceA ForceB Resultant force C What direction will the ball move in?

  8. Using vectors Any value that has both magnitude and direction can be drawn as a vector Draw forces accurately and to scale Complete the parallelogram (in this case a square) ForceA 10N Resultant force C Draw in the resultant Measure magnitude and angle ForceB 10N

  9. Parallelogram of forces Draw forces accurately and to scale Complete the parallelogram (in this case a rectangle) Draw in the resultant Measure magnitude and angle Resultant force C ForceA 15N ForceB 10N

  10. Parallelogram of forces Draw forces accurately and to scale Complete the parallelogram (in this case a parallelogram) Resultant force C Draw in the resultant ForceA 15N Measure magnitude and angle 60° ForceB 10N

  11. Parallelogram of forces Draw forces accurately and to scale Complete the parallelogram Resultant force C Draw in the resultant ForceA 15N Measure magnitude and angle 60° ForceB 10N

  12. Parallelogram of forces Draw forces accurately and to scale Complete the parallelogram ForceB 25N Draw in the resultant Measure magnitude and angle 45° ForceA 37N Resultant force C

  13. Redraw forces accurately and to scale, with arrows nose to tail Triangle of forces Complete the triangle by drawing in the resultant Note that the resultant runs from start point ‘a’ to end point ‘c’ ForceA 260N a 60° The equilibrant completes the triangle with all arrows running nose to tail Equilibrant force E Resultant force D ForceB 180N This closed shape with all vectors running in sequence means the forces are in equilibrium b c

  14. Triangle of forces Calculate equilibrant for these forces using triangle of forces Redraw forces accurately and to scale, with arrows nose to tail ForceA 236N Draw in equilibrant, completing the triangle 20° Equilibrant ForceB 115N A B

  15. Polygon of forces Redraw forces accurately and to scale, with arrows nose to tail, C ForceA 27N Draw in equilibrant ensuring flow of arrows is continued D ForceD 6N B A 45° 50° Note that the order in which the forces are drawn does not matter, as long as the flow is consistent ForceC 20N 60° ForceB 18N B A D C

  16. Polygon of forces Redraw forces accurately and to scale, with arrows nose to tail, ForceA 150kN Draw in equilibrant ensuring flow of arrows is continued ForceB 70kN Equilibrant ForceD 160kN A 60° Note magnitude and direction. D 30° ForceC 180kN B C

  17. Internal forces If a compressive force is applied to the top of the column, what force must the column be applying back, in order to remain in equilibrium? What is happening at the base of the column? The red arrows indicate that the column is under compression and is, therefore, a strut

  18. Internal forces If a load is applied to the top of the structure, what do the internal forces look like? Are these struts or ties? The red arrows indicate that the members are under compression (they are pushing back) and are, therefore, struts

  19. Label spaces as per Bow’s Notation Internal forces Draw the force that you do know, ab If we do not know what the internal forces are doing, we can still construct a triangle of forces: We don’t know if bc is in compression or tension, so draw a line across the end of ab at the correct angle a Assuming the structure is in equilibrium, there is only one way to complete the triangle using the force ca 150N A B c 45° 45° Measure the magnitude and note direction of the constructed vectors. b C Transfer findings to original problem

  20. Internal forces Redo the calculations using a steeper angle 150N What do you notice about the forces in individual members? A B 60° 60° What are the problems in designing a structure in this way? C

  21. Internal forces Redo the calculations using a shallower angle 150N What do you notice about the forces in individual members? A B 30° 30° What are the problems in designing a structure in this way? C

  22. Hookes’ Law • Gradually load up and measure extension of a spring or other materials • Complete at least two full sequences, completing table as you go • Use Excel to plot graphs of load/extension

  23. Stress • Nominal Stress σ = Load Р/Original area А (N/m2) Which rod is under the most stress? 0.15m2 0.08m2 Bar A 5000/0.15 = 33333N/m2 = 33.3kN/m2 Bar B 2400/0.08 = 30000N/m2 = 30kN/m2 A B 5kN 2.4kN

  24. Strain • Strain ε= extension e/original length L (no units!) A B Which rod is under the most strain? 180mm 150mm Bar A 35/180 = 0.19 Bar B 30/150 = 0.2 180mm 215mm

  25. Young’s Modulus • Modulus of elasticity E = stress σ /strain ε(N/m2) Which rod is the most elastic? A B Bar A 33300/0.19 = 175kN/m2 (175 kPa) Bar B 30000/0.2 = 150kN/m2 (150 kPa) 0.19 0.2 33.3kN/m2 30.0kN/m2 Note that a lower modulus of elasticity means more flexibility Pascals are a measure of load over an area or ‘pressure’.

  26. Young’s Modulus Complete the table on Excel to calculate Young’s modulus for your test pieces Plot a graph of stress/strain Compare elasticity of the springs with other groups

  27. Young’s Modulus What does the graph show? The modulus of a material can be plotted against many other characteristics such as cost, thermal conductance, working temperature range, etc.

  28. Common Beam Sections Which of these sections is the most efficient? What problems might you expect to be associated with the different sections? Closed Sections Open Sections

  29. Task: Avoiding stress • Devise a method for testing the strongest practical way of producing a box corner in acrylic. • Create test pieces and test your ideas.

  30. Weblinks • www.greenhomebuilding.comBig resources for sustainable home design • www.sustainableabc.comFantastic resources for sustainable design • www.architect.org/links/sustainable_architecture.htmlGood set of eco links • www.ecosustainable.com.auHuge set of eco links • www.naturalspace.com Fantastic site, beautiful case studies • www.lanxun.com/pce/index.htmRange of design programs to try • www.architecturalresources.infoNice but problematical site with good tutorials

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