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Fundamental Concepts

Fundamental Concepts. units in the SI system. mass and weight. force and pressure. vectors . moments . equilibrium . 1/23. deci centi milli micro nano pico. 10 -1 10 -2 10 -3 10 -6 10 -9 10 -12. c m m. deca hecto kilo mega giga tera. 10 10 2

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Fundamental Concepts

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  1. Fundamental Concepts • units in the SI system • mass and weight • force and pressure • vectors • moments • equilibrium 1/23

  2. deci centi milli micro nano pico 10-1 10-2 10-3 10-6 10-9 10-12 c m m deca hecto kilo mega giga tera 10 102 103 106 109 1012 k M The SI System • length - mm, cm, m, km • mass - mg, gm, kg Notation 2/23

  3. “The bill comes to $54.72. Now, among the seven of us, that comes to $7.817142857 each” Precision of Numbers • don’t necessarily use all the numbers • on your calculator • a bricklayer can’t measure to micrometres 3/23

  4. Think !!! • common sense • how many bricks in 1 sq m? • what is the weight of something? • how much does something deflect? 4/23

  5. Mass and Weight • common vs scientific usage • mass is amount of ‘stuff’ - doesn’t change • weight is a force - depends on gravity I weigh 70 kg (common usage) My mass is 70 kg (correct - pompous) I weigh 700 Newtons (correct - uncommon) 5/23

  6. 1kN is about the weight of a large footballer Weight and Force • weight is a force - given in newtons, N • 1kg produces a force of 9.81 N on earth - call it 10 N • 1000N = 1kN, kiloNewton • a load is a force • in buildings use kiloNewtons, kN 6/23

  7. “My weight is 700 Newtons on earth, 5000 N at blastoff and 120 N on the Moon” (an astronaut) Weight and Force (cont.) • weight is a property of a mass in a force field 7/23

  8. F = m x a Force • something which tends to change the state • of something else • acts to cause a change in motion or shape • ‘push’ or ‘pull’ • most forces in a building caused by gravity 8/23

  9. Newton’s Laws • ‘a body at rest tends to remain at rest’ • ‘Force = mass x acceleration’, F= m x a • ‘to every action there is an equal and opposite reaction’ 9/23

  10. F F F F 4xF F F Action & Reaction • equal and opposite reaction 10/23

  11. action reaction External & Internal Forces • forces acting on building - external forces • resisted by internal forces & ground 11/23

  12. P = F/ A Pressure • force acting over an area • measured in Pascals, Pa 1 N/m2 = 1 Pa 1 kN/m2 = 1 kPa 1 N/mm2 = 1 MPa 1 MN/ m2 = 1 MPa 12/23

  13. P = F/ A 4kN 4kN 4kN 4kN 4kN 1m 1m 1m 1m 1m 1m 1m 1m Pressure • force acting over an area • same force over smaller area - greater pressure e.g. stiletto heels, knife P = 4 / 4 = 1kN/m2 = 1 kPa P = 16 / 4 = 4kN/m2 = 4 kPa 13/23

  14. magnitude & direction X Dig 500m NE from the tree Vectors ‘go 500m Northeast’ 14/23

  15. N 1km S 1km N 1km E Vectors (cont.) • 1km South not same as 1km North • “if I go 1km S then 1km E then 1 km N and I end up where I started from, what is the colour of the bear I see?” 15/23

  16. a force is a vector 2kN 2kN 3kN 2kN 2kN 3kN Vectors (cont.) • magnitude in force units • acts in a particular direction 2kN 16/23

  17. M = F x D Force Distance The wrench exerts a moment on the nut (it also exerts a force) Moments • a moment is aturning effect caused by a force • moment = force multiplied by a distance 17/23

  18. “Give me a place to stand and I will move the Earth” 500N 300N 800N Moments (cont. 1) • levers • balance analogy 18/23

  19. F” F D P F’ M = F x D moment arm line of action of force + - Moments (cont. 2) • about a point,P • units - Nm, kNm • sign convention 19/23

  20. Fv = Fsinq F q Fh = Fcosq Forces in Many DirectionsResolution of Forces • find components of a force • usually vertical and horizontal • numerically - can use trigonometry or graphically 20/23

  21. use moments to work out resultant magnitude & direction Parallel Forces • can replace number of parallel forces with • one resultant 21/23

  22. 3kN 5kN 3kN 5kN 8kN A A 2m 3m 2m 3m D = Parallel Forces (cont1.) • for given point, A 3.875 31 = 8 x D MA = (3 x 2) + (5 x 5) D = 3.875 m = 31 kNm 22/23

  23. 18kN 2kN 6m 3m 3m Parallel Forces (cont2.) 23/23

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