1. Basic structural theory

2. Statics Things dont 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 w = P/ l force-couple

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

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

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

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

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

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

25. Elastic modulus of materials Structural Steel = 200 GPa (29,023,300 lb/in 2 ) Titanium = 110 GPa (15,962,850 lb/in 2 ) Aluminum = 70 GPa (10,158,177 lb/in 2 ) Concrete = 21 GPa (3,047,453 lb/in 2 ) Douglas Fir = 13 GPa (1,886,518 lb/in 2 ) Why are titanium and aluminum used in aircraft?

26. 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 Density of materials Structural Steel = 489 lb/ft 3 Titanium = 282 lb/ft 3 Aluminum = 169 lb/ft 3 Concrete = 150 lb/ft 3 Douglas Fir = 32 lb/ft 3 1 lb/in 2 = 6891 Pa

27. Moment of Inertia of beam Dependent on cross-sectional geometry Not dependent on material properties Icc = Moment of inertia of a rectangle about the neutral axis – i.e. its centroid = width x height 3 /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)

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

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

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

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

33. Cantilever Moment connection

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

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

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

37. Cantilever Deflection - Resist bending with counterweight

38. Frame – Lateral load Racking

39. Frame – Lateral load Racking

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

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

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

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

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

45. Frame – Lateral load Pre-engineered shear panel

46. Frame – Lateral load Pre-engineered shear panel

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

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

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

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

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

52. Non-Funicular structures

53. Materials - Wood Tension & compression, no rigid connection

54. Materials - Wood Unpredictable failure mode (non-uniform material – organic)

55. Materials - Reinforced Concrete Wide range of possible forms

56. Materials - Reinforced Concrete Compression and some tension (steel), rigid connection through rebar

57. Materials - Reinforced Concrete Catastrophic failure mode

58. Materials - Reinforced Concrete Catastrophic failure mode

59. Materials - Reinforced Concrete Lab testing

60. Materials - Steel Tension & compression

61. Materials - Steel Rigid connection through welding

62. Materials - Steel Plastic failure mode