Dean Hackett Structures Week 2

Dean Hackett In previous sessions… Brief review of previous learning: –Types of motion –Classes of lever –Turning moments

Dean Hackett Types of structure Mass Frame Shell

Dean Hackett Forces Compression Tension Torsion Shear Bending

Dean Hackett Applying forces Distributed (UDL) Concentrated (point) Static Dynamic

Dean Hackett 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

Dean Hackett Combining external forces Force A Force B What direction will the ball move in? Resultant force C

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

Dean Hackett Parallelogram of forces Force A 15N Force B 10N Resultant force C Draw forces accurately and to scale Complete the parallelogram (in this case a rectangle) Draw in the resultant Measure magnitude and angle

Dean Hackett Parallelogram of forces Force A 15N Force B 10N Resultant force C Draw forces accurately and to scale Complete the parallelogram (in this case a parallelogram) Draw in the resultant Measure magnitude and angle 60°

Dean Hackett Parallelogram of forces Force A 15N Force B 10N Resultant force C Draw forces accurately and to scale Complete the parallelogram Draw in the resultant Measure magnitude and angle 60°

Dean Hackett Parallelogram of forces Force A 37N Force B 25N Resultant force C Draw forces accurately and to scale Complete the parallelogram Draw in the resultant Measure magnitude and angle 45°

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

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

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

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

Dean Hackett 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

Dean Hackett 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

Dean Hackett Internal forces If we do not know what the internal forces are doing, we can still construct a triangle of forces: 150N 45° Label spaces as per Bow’s Notation AB C Draw the force that you do know, ab 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 b Assuming the structure is in equilibrium, there is only one way to complete the triangle using the force ca Measure the magnitude and note direction of the constructed vectors. c Transfer findings to original problem

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

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

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

Dean Hackett Stress Nominal Stress σ = Load Р/Original area А (N/m2) 2.4kN5kN 0.15m m 2 Which rod is under the most stress? Bar A 5000/0.15 = 33333N/m 2 = 33.3kN/m 2 Bar B 2400/0.08 = 30000N/m 2 = 30kN/m 2 AB

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

Dean Hackett Young’s Modulus Modulus of elasticity E = stress σ /strain ε (N/m2) Which rod is the most elastic? AB Bar A 33300/0.19 = 175kN/m 2 (175 kPa) Bar B 30000/0.2 = 150kN/m 2 (150 kPa) 33.3kN/m kN/m Note that a lower modulus of elasticity means more flexibility Pascals are a measure of load over an area or ‘pressure’.

Dean Hackett Young’s Modulus Complete the table on Excel to calculate Young’s modulus for your test pieces Mass (g)Load (N) Stress = load / area area = 1.57mm2 Length (mm) Extension (mm) Strain = Extension / original length Young’s modulus = stress / strain Plot a graph of stress/strain Compare elasticity of the springs with other groups

Dean Hackett 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.

Dean Hackett Common Beam Sections Closed SectionsOpen Sections Which of these sections is the most efficient? What problems might you expect to be associated with the different sections?

Dean Hackett 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.

Dean Hackett Weblinks Big resources for sustainable home designwww.greenhomebuilding.com Fantastic resources for sustainable designwww.sustainableabc.com Good set of eco linkswww.architect.org/links/sustainable_architecture.html Huge set of eco linkswww.ecosustainable.com.au Fantastic site, beautiful case studies Range of design programs to trywww.lanxun.com/pce/index.htm Nice but problematical site with good tutorialswww.architecturalresources.info