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Basic structural theory

Basic structural theory. Statics Things don’t continue to move if forces are resisted – Static Equilibrium What resists the force? Equal and opposite Reaction Things deflect if forces are resisted Elastic and Plastic Deformation. Basic loads (forces) Vertical (y only) Lateral (x only)

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Basic structural theory

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  1. Basic structural theory

  2. Statics Things don’t continue to move if forces are resisted – Static Equilibrium What resists the force? Equal and opposite Reaction Things deflect if forces are resisted Elastic and Plastic Deformation

  3. Basic loads (forces) Vertical (y only) Lateral (x only) Rotational (moment) Concentrated loads Distributed loads force-couple w = P/l

  4. Basic components Linear – Column, Beam Planar – Wall, Floor

  5. Basic connections Simple (constrain y in direction of gravity, rotate freely)

  6. Basic connections Roller (constrain y, rotate freely)

  7. Basic connections Pin (constrain x & y, rotate freely)

  8. Basic connections Pin (constrain x & y, rotate freely)

  9. Basic connections Cable (Pin with tension only)

  10. Basic connections Cable (Pin with tension only)

  11. Basic connections Fixed/Rigid (constrain x, y, rotation)

  12. Basic connections Fixed/Rigid (constrain x, y, rotation)

  13. Basic connections Fixed/Rigid (constrain x, y, rotation)

  14. Basic connections Fixed/Rigid (constrain x, y, rotation)

  15. Basic connections Misleading pin connections

  16. Column – Vertical Load Axial load – Compression & Tension

  17. Column – Lateral Load Non-axial (lateral) load – Buckling in compression

  18. Beam – Vertical Load Non-axial load – Deflection

  19. w = P/l Basic loads (forces) Reactions are the same for Concentrated loads and Distributed loads Beam stresses are different

  20. Greater max. moment Greater deflection w = P/l

  21. C N T Beam – Stresses Compression, Tension, Neutral axis

  22. Greater max. moment Greater deflection Beam – Concentrated Vertical Load Resist bending with Moment connection

  23. Greater max. moment Greater deflection Beam – Distributed Vertical Load Resist bending with Moment connection

  24. Dmax =Pl 3/48EI Factors influencing deflection: P = load l= length between supports E = elastic modulus of material (elasticity) I = Moment of inertia (depth/weight of beam)

  25. Elastic modulus of materials Structural Steel = 200 GPa (29,023,300 lb/in2) Titanium = 110 GPa (15,962,850 lb/in2) Aluminum = 70 GPa (10,158,177 lb/in2) Concrete = 21 GPa (3,047,453 lb/in2) Douglas Fir = 13 GPa (1,886,518 lb/in2) Why are titanium and aluminum used in aircraft?

  26. 1 lb/in2 = 6891 Pa Density of materials Structural Steel = 489 lb/ft3 Titanium = 282 lb/ft3 Aluminum = 169 lb/ft3 Concrete = 150 lb/ft3 Douglas Fir = 32 lb/ft3 Yield Strength of materials Structural Steel=350-450 MPa Titanium (Alloy)=900-1400 MPa Aluminum=100-350 MPa Concrete=70 MPa (compressive) Douglas Fir= N/A

  27. Icc = Moment of inertia of a rectangle about the neutral axis – i.e. it’s centroid = width x height3 /12 Ixx = Moment of inertia of a rectangle about an axis parallel to the neutral axis = Icc + width x height x (distance between axes)2 Centroid = S (Area x distance to bending axis)/(Total area) Moment of Inertia of beam Dependent on cross-sectional geometry Not dependent on material properties

  28. Triangulated frame (Truss) – increase depth of beam Triangulated – all members axially loaded (truss) – no moments

  29. Triangulated frame (Truss) – increase depth of beam Triangulated – all members axially loaded (truss) – no moments

  30. Rigid Frame – Vertical load Reduce deflection: Rigid connection Columns resist force and deflect

  31. Thrust develops at base ofcolumns and must be resisted (beam / foundation / grade beam) Rigid Frame – Vertical load

  32. Cantilever Moment connection

  33. tension compression Cantilever Moment connection moment (force-couple)

  34. Greater max. moment Greater deflection Cantilevered Beam – Vertical load

  35. Lesser max. moment Lesser deflection Simple Frame – Vertical load Reduce deflection at mid-span: Cantilever

  36. Cantilever Deflection - Resist bending with counterweight

  37. Frame – Lateral load Racking

  38. Frame – Lateral load Racking

  39. Frame – Lateral load Triangulated – all members axially loaded (truss) – no moment connections

  40. Frame – Lateral load Triangulated – all members axially loaded (truss) – no moment connections

  41. Frame – Lateral load Rigid (moment-resisting) frame

  42. Frame – Lateral load Rigid (moment-resisting) frame

  43. Frame – Lateral load Shear-resisting (force in plane)

  44. Frame – Lateral load Pre-engineered shear panel

  45. Frame – Lateral load Pre-engineered shear panel

  46. Frame – Lateral load Shear-resisting (force in plane) Non-structural partitions

  47. Frame – Lateral load Shear-resisting (force in plane) Masonry must be grouted and steel-reinforced

  48. Funicular structures Tension (Cable) Compression (Arch)

  49. Funicular structures Tension (Cable) Compression (Arch)

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