Structures Agenda: Forces & Architectural Form - review Material Properties - review

1. Structures Agenda: Forces & Architectural Form - review Material Properties - review Deflections - not on exam Allowable Stress Design (ASD) (member strength + stability)

2. Loading Moment Jurg Conzett – Traversina Bridge

4. Riccardo Morandi – Santa Barbara Power Station

6. Materials Review

7. Stress-Strain curve Fy = Modulus of Elasticity = E

8. Stress-Strain curve

9. Comparison of materials Yield Stress (Fy) Material Modulus of Elasticity (E) tension bending compression 36 ksi 29,000 ksi 36 ksi 36 ksi Steel 3100 ksi 0.5 ksi 3 ksi 0.3 ksi Concrete 1700 ksi 1.0 ksi 1.5 ksi 0.7 ksi Wood 10,000 ksi 24 ksi 145 ksi 24 ksi Glass

10. Comparison of materials Yield Stress (Fy) Material Modulus of Elasticity (E) compression bending tension 17 36 24 50 Steel 2 0.5 2 0.5 Concrete 1 1 1 1 Wood 6 24 97 34 Glass

11. Allowable Stress Design Make sure that materials do not reach their yield stress by providing a factor of safety (FOS).

12. Factor of Safety Steel: 0.6

13. Factor of Safety Steel: 0.6 Allowable flexural stress = factor of safety x yield stress Fb = 0.6 x Fy

14. Factor of Safety Steel: 0.6 Allowable flexural stress limit (Fb)= factor of safety x yield stress Fb = 0.6 x Fy Fb = 0.6 x 36 ksi Fb = 21.6 ksi

15. Moment = bending stress (fb) x SECTION MODULUS (S) What is section modulus?

16. Moment = bending stress x SECTION MODULUS (S) What is section modulus? Property of the cross sectional shape.

17. Moment = bending stress x SECTION MODULUS (S) What is section modulus? Property of the cross sectional shape. Where do you find it? Look it up in the tables OR calculate it

18. b h2 Section Modulus = S = 6 b b h h neutral axis

19. Deflection

20. Deflection • the measured amount a member moves depends upon: • Stiffness/Rigidity of the material (E) • Property of the cross sectional shape (I) • Length of beam (L) • Load on beam

21. Deflection • Rigidity or stiffness of the material • Modulus of Elasticity (E) • Property of the cross sectional shape • Moment of Inertia (I)

22. Moment of Inertia (I) • Property of the cross sectional shape • Where do you find it? • Look it up in tables OR calculate it

23. b h3 Moment of Inertia = I = 12 b b h h neutral axis

24. 14” 14” 14” Area = 14 in2 I = 1.2 in4 Area = 14 in2 I = 485 in4 Area = 14 in2 I = 229 in4

25. P L

26. P L P M Rx Ry L

27. P L P Deflection M Rx Ry L P L3 Deflection = 3 E I

28. w L w Deflection M Rx Ry L w L4 Deflection = 8 E I

29. w L w Rx Deflection Ry Ry L 5 w L4 Deflection = 384 E I

30. P L P Rx Deflection Ry Ry L P L3 Deflection = 48 E I

31. Moment of Inertia • Property of the cross sectional shape • Where do you find it? • Look it up in tables OR calculate it • Bigger Moment of Inertia, smaller deflection

32. STRUCTURAL ANALYSIS: Determining Strength Capacity

33. From Structural Analysis we have developed an understanding of all : Actions - Applied forces such as dead load, live load, wind load, seismic load. Reactions - Forces generated at the boundary conditions (rollers, pins, and fixed ends) that maintain equilibrium. Internal forces- axial, shear, and moment (P V M) forces inside each element

34. StructuralCapacity based upon element’sability to performwithout: Yielding - permanently deforming (tensile stretching or compression squashing of a squat (short & wide) compression element) Buckling– slender (tall & thin)compression element loses stability Deflecting Excessively– movement that may cause damage to attached materials/finishes – floor vibrations or bounce

35. TENSION and ALLOWABLE STRESS:

36. stress Plastic Range FY = yield stress Elastic Range deformation

37. A = AreaP = Forcefa = stress fa = P/A stress FY fa P1 Force on the spring generates stress and elastic deformation deformation

38. stress FY When force is removed, the spring returns to its original shape -- elastic behavior deformation

39. stress fa FY larger force (greater than Fy) generates axial stress causing plastic deformation deformation P2

40. stress fa FY When the larger force is removed, the plastic deformation remains (permanent offset) deformation

41. To be sure tension stress does not reach the yield stress, we set an: ALLOWABLE TENSILE STRESSLIMIT (FT) : FT = 0.60 FY (capital letter F for limit) stress FY FT deformation

42. Using Grade A36 Steel: FY = 36 ksi Allowable Tensile Stress (FT ): FT = 0.60 FY = 0.60 (36 ksi) = 21.6 ksi

43. fa stress A36 Steel : FY = 36 ksi Allowable Tensile Stress FT: FT = 0.60 FY = 0.60 (36 ksi) = 21.6 ksi P = 5,000 lb or 5 kips (get this from P diagram) fa = P/Area (actual axial stress fa = P/A) Aarea P force

44. FT stress A36 Steel : FY = 36 ksi Allowable Tensile Stress : FT = 0.60 FY = 0.60 (36 ksi) = 21.6 ksi P = 5,000 lb or 5 kips (get this from P diagram) fA = P/Area FT = Pmax/AreaRequired Areq Pmax

45. FT stress A36 Steel : FY = 36 ksi Allowable Tensile Stress : FT = 0.60 FY = 0.60 (36 ksi) = 21.6 ksi P = 5,000 lb or 5 kips (get this from P diagram) fA = P/Area FT = Pmax/AreaRequired AreaRequired= Pmax/FT Areq Pmax

46. 21.6 ksi A36 Steel : FY = 36 ksi Allowable Tensile Stress : FT = 0.60 FY = 0.60 (36 ksi) = 21.6 ksi P = 5,000 lb or 5 kips (get this from P diagram) fA = P/Area FT = Pmax/AreaRequired AreaRequired= Pmax/FT =5k / 21.6 ksi AreaRequired = .25 in2 Areq 5k

47. FLEXURAL and ALLOWABLE STRESS :

49. stress Plastic Range FY = yield stress Elastic Range deformation fb = M/S S = Section Modulus

50. P1 stress FY Load on the BEAM generates bending stress (tension and compression) and elastic deformation (fb = Mmax/S) fb deformation