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EQUILIBRIUM

EQUILIBRIUM. As a whole. A system of elements. Structural Systems. The building must be stable as a whole There must be enough structural elements They must be in suitable places They must be strong and stiff enough, and suitably connected together. As a whole.

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EQUILIBRIUM

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  1. EQUILIBRIUM As a whole A system of elements

  2. Structural Systems • The building must be stable as a whole • There must be enough structural elements • They must be in suitable places • They must be strong and stiff enough, and suitably connected together As a whole A system of elements 1/26

  3. Stability • Structure may be in equilibrium but not stable • Arrangement of parts critical 2/26

  4. Qualitative and Quantitative Understanding • First we will try to understand the structural system qualitatively • If we don’t have the right kind of supports in the right kind of places, it won’t work • When we have a credible system, we can use precedent and simple rules to get credible sizes • We need to understand the quantitative basis of a final structural design 3/26

  5. Equilibrium of the Whole Building • The building supports its loads • All loads are finally resisted by the ground • Parts of the buildingintervene between loads and foundation • But first, let’s make sure the building as a whole is stable Loads Building ? Reactions from Foundation 4/26

  6. Loads Building ? Reactions from Foundation Overall Equilibrium What do we Need to Know? • all the possible loads • where the building can be supported • how big the reactions have to be for equilibrium 5/26

  7. Loads Bigger building Building Reactions from Foundation Overall Equilibrium What are the Problems? • downward loads just need big enough footings 6/26

  8. Loads Taller building Building Overall Equilibrium What are the Problems? (cont.) • horizontal loads might overturn a tall building • wider base and heavy building are more stable Reactions from Foundation 7/26

  9. Equilibrium of Forces • Newton’s Third law ‘to every force there is an equal and opposite reaction’ Reactions from Foundation 8/26

  10. Equilibrium (forces in line) • Every force is resisted by an equal and opposite one, exactly in line 9/26

  11. Maintains equilibrium Tries to overturn Tries to restrain Equilibrium (forces out of line) • Tendency to overturn • The turning effect is a moment • Can be resisted by other out-of-line forces 10/26

  12. doesn’t move Equilibrium • forces on whole structure and each part, just balance (sum equal zero) • not up-and-down, sideways or spin V = 0  H = 0  M = 0 12/26

  13. w w w w w w H F = 5kN  w = 6w  V = 0  H = 0  M = 0 F = 5kN EQUILIBRIUM (cont. 1) 13/26

  14. w w w w w w H H  w  V = 0  H = 0  M = 0 60kN 60kN EQUILIBRIUM (cont. 2) 14/26

  15. w w w w w w H H M M  w  V = 0  H = 0  M = 0 EQUILIBRIUM (cont. 3) 15/26

  16. 5 units beam 2.5 units 2.5 units Equilibrium of Elements • total downward load = total upward reaction • if the load is symmetrical, so are the reactions 16/26

  17. 5 units beam 2.5 units 2.5 units 2.5 units 2.5 units Equilibrium of Framework • Total downward load is carried down by columns We can follow the ‘Load Path’ 17/26

  18. 5 units beam 4L/5 L/5 1 unit 4 units Equilibrium of Framework (cont.) • If the load is off-centre, so are the reactions 18/26

  19. W (central) W R1 R2 R1 R2 Everything is symmetrical R1 = R2 = W/2 W is off centreR1, R2 must be calculated Work smarter, not harder • Most beams are symmetrical • If the reactions are equal, don’t make hard work of it 19/26

  20. W (known) W (known) R1 R2 R1 R2 Only W and R2 have a moment about the dot R1 and R2 have a moment about the dot Work smarter, not harder (cont.) • The M condition says the sum of moments about any point is zero • Pick a point that eliminates one of the unknowns, to make it easy 20/26

  21. Finding the Reactions ofa Cantilever • A cantilever has one V, one H, and one M reaction d1 M d2 W1 W2 • Vertically: R = W1 + W2 H=0 • Horizontally: H = 0 unless there is a horizontal load R d2 d1 • Moments: M = W1.d1 + W2.d2 22/26

  22. Free-bodies(Looking Inside the Elements) • can isolate any member or part of it to study it • must put back artificial forces to replace whatever supports were cut away 23/26

  23. 1kN 100kg 1kN 1kN 1kN 1kN 1kN 1kN Free-bodies can ‘cut’ the wire at any point 24/26

  24. 100kg 1kN 1kN 1kN 20kg 0.2kN 0.2kN 20kg 0.2kN 0.2kN 20kg 0.2kN 0.2kN 20kg 0.2kN 0.2kN 20kg 1kN 1kN 0.2kN 0.2kN 0.2kN 0.2kN 0.2kN 0.2kN 2kN 1.4kN 0.2kN 1.8kN 0.2kN 0.2kN 0.2kN 0.2kN 0.2kN 2kN 2kN Free-bodies (cont1.) 25/26

  25. Free-bodies (cont2.) 26/26

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