1. Elasticity Tutorial 7 to answer just click on the button or image related to the answer

2. what is the Modulus of Elasticity, E? Question 1 a measure of the strength of a material b a measure of the stiffness of a material c a material’s tendency to be deformed elastically i.e. how a material responds to stress d the slope of the stress-strain curve a a and d e

3. what are the units for the Modulus of Elasticity, E? Question 2 MPa b MN c no units a

4. what is the stress in a rod? Question 3a 81.5 MPa b 163 MPa c 80 MPa a a footbridge carrying a load of 80 kN is supported by two 25 mm dia. aluminium rods 3 m long. Neglecting the self-weight of the rod and given that the Modulus of Elasticity of aluminium is 70,000 MPA 3m 80 kN

5. what is the strain in a rod? Question 3b 0.00116 (1.16 x 10 -3 ) b 0.02 (2 x 10 -2 ) c 3 mm a a footbridge carrying a load of 80 kN is supported by two 25 mm dia. aluminium rods 3 m long. Neglecting the self-weight of the rod and given that the Modulus of Elasticity of aluminium is 70,000 MPA 3m 80 kN

6. how much does the rod lengthen? Question 3c 4.5 mm b 3.5 mm c 35 mm a a footbridge carrying a load of 80 kN is supported by two 25 mm dia. aluminium rods 3 m long. Neglecting the self-weight of the rod and given that the Modulus of Elasticity of aluminium is 70,000 MPA 3m 80 kN

7. are the rods strong enough ? Question 3d yes a no b a footbridge carrying a load of 80 kN is supported by two 25 mm dia. aluminium rods 3 m long. Neglecting the self-weight of the rod and given that the Modulus of Elasticity of aluminium is 70,000 MPA 3m 80 kN given that the maximum allowable tensile stress for aluminium is 120 MPA

8. what does elastic behaviour mean ? Question 4 the material stretches under tension a the material responds to stress in a linear way b the strain is linearly proportional to the to stress c the deformations are irreversible d the deformations are reversible e b, c and d f b, c and e g

9. what does plastic behaviour mean ? Question 5 the material can be bent and reshaped a the material responds to stress in a linear way b the deformations are large c the deformations are irreversible / permanent d the deformations are reversible e a, c and d f a, c and e g

10. what does brittle behaviour mean ? Question 6 the material responds to stress in a linear way a the material fails suddenly soon after the yield stress b the material is strong in tension c the material is strong in compression and weak in tension d a, b and c e a, b and d f b and d g

11. is steel ? Question 7 plastic a brittle b elastic c both elastic and plastic d

12. draw the stress / strain curve for an elasto-plastic material Question 8 show me a next question b

13. draw the stress / strain curve for a brittle material Question 9 show me a next question b

14. what is the difference between the curves ? Question 10 none a the elasto-plastic one has an elastic range whereas the brittle one hasn’t b the brittle curve has almost no plastic range c

15. what are the advantages of elasto-plastic materials ? Question 11 none a they are stronger b large deformations after the yield stress is reached c give warning of danger d c and d e b, c and d f

16. which of these lists contains all brittle materials ? Question 12 concrete, timber, brick a masonry, cast iron, glass, cement, high-strength carbon steel b concrete, glass, brick, timber c steel, concrete, glass, brick d

17. why do we use brittle materials ? Question 13 because we like them a they are, in the main, cheap and good in compression b they are, in the main, cheap and good in tension c

18. how do we cure brittleness ? Question 14 by not using brittle materials a by introducing elastic material to take care of tensile stresses b you don’t c

19. what does having a high value of the Modulus of Elasticity, E, mean ? Question 15 the material is stronger a the material deforms less b a and b c

20. what dimensions should the column be (nearest 25mm) ? Question 16a 350 x 350 mm square or 375 mm dia a 275 x 275 mm square or 325 mm dia b 325 x 325 mm square or 350 mm dia c a ground-floor reinforced concrete column in a multi-storey building is 3m high and carries a load of 3.2 MN. Given that the max. allowable stress for concrete is 30MPa and the Modulus of Elasticity, E, of concrete is 25,000MPa

21. what is the actual stress in the column? Question 16b 2.6 MPa a 32.0 MPa b 26.1 MPa c a ground-floor reinforced concrete column in a multi-storey building is 3m high and carries a load of 3.2 MN. Given that the max. allowable stress for concrete is 30MPa and the Modulus of Elasticity, E, of concrete is 25,000MPa

22. what is the strain in the column? Question 16c 1.0 a 0.001 (10 -3 ) b 0.01 (10 -2 ) c a ground-floor reinforced concrete column in a multi-storey building is 3m high and carries a load of 3.2 MN. Given that the max. allowable stress for concrete is 30MPa and the Modulus of Elasticity, E, of concrete is 25,000MPa

23. by how much does the column shorten? Question 16d 3.0 mm a 1.0 mm b 30 mm c a ground-floor reinforced concrete column in a multi-storey building is 3m high and carries a load of 3.2 MN. Given that the max. allowable stress for concrete is 30MPa and the Modulus of Elasticity, E, of concrete is 25,000MPa

24. what are safety factors? Question 17a warning signs a margins of safety b the amount by which we over-design a structure c

25. why do we use safety factors? Question 17b to ensure that the structure doesn’t collapse a to provide a margin of safety so that failure is extremely unlikely b to prevent over-designing c

26. what value of safety factors do we use in buildings? Question 17c 1.0 – 3.0 a 1.0 - 2.5 b 1.5 – 2.5 c 2.0 – 3.0 d

27. which would require a lower safety factor ? Question 17d concrete a steel b timber c

28. next question enough ! the modulus of elasticity is a substance's tendency to be deformed elastically (i.e. non-permanently) when a force is applied to it. The elastic modulus of an object is defined as the slope of its stress-strain curve in the elastic deformation region:

29. let me try again let me out of here

30. let me try again let me out of here the modulus of elasticity has nothing to do with strength

31. let me try again let me out of here the modulus of elasticity indicates how stiff a material is, but that’s not what it is

32. next question enough ! E = stress / strain since strain has no units, E has the same units as stress i.e. MPa

33. let me try again enough ! E = stress / strain What are the units for stress? What are the units for strain? think again

34. next question enough ! f = F / A Force, F = 40 kN (per rod), A = πR 2 = 3.142 x 12.5 x 12.5 =491 mm 2

35. let me try again let me out of here not correct f = F / A What is the force? What is the area? (try keeping everything to Newtons and mms)

36. let me try again let me out of here not correct f = F / A What is the force? Don’t forget that 80 kN is carried by 2 rods What is the area? (try keeping everything to Newtons and mms)

37. next question enough ! E = f / e so, e = f/ E E = 81.5 / 70,000

38. let me try again let me out of here a rather large strain, don’t you think? What are the units of strain?

39. let me try again let me out of here check your calculations E = f / e So, e = f / E

40. next question enough ! e = ΔL / L so, ΔL = e x L change in length = strain x original length

41. let me try again let me out of here a rather large deformation, don’t you think?

42. let me try again let me out of here don’t guess ! check your calculations e = ΔL / L strain = change in length / original length so, ΔL = e x L

43. next question enough ! actual stress is 81.5 MPa maximum allowable stress is 120 MPa actual stress < maximum allowable stress

44. let me try again let me out of here what is the actual stress? what is the maximum allowable stress? is the actual stress greater or less than the max. allowable stress? so?

45. next question enough ! elastic behaviour means all of these. the material strains in a linear relationship to stress and the deformations are reversible. Also the deformations are very small

46. let me try again let me out of here all materials stretch under tension

47. let me try again let me out of here means other things too

48. let me try again let me out of here we’re talking about elastic behaviour think of a spring

49. next question enough ! plastic behaviour means all of these. The material can be bent and reshaped, the material has large deformations, the deformations are irreversible.

50. let me try again let me out of here means other things too

51. let me try again let me out of here we’re talking about plastic behaviour this is elastic behaviour

52. let me try again let me out of here we’re talking about plastic behaviour (e) is elastic behaviour

53. next question enough ! brittle behaviour means all of these. The material behaves elastically up to the yield point, Then snaps suddenly. Brittle materials are generally weak in tension.

54. let me try again let me out of here means other things too

55. let me try again let me out of here we’re talking about brittle behaviour brittle materials are not good in tension

56. next question enough ! steels are generally elasto-plastic. i.e. they are elastic up to their yield stress and then plastic High-strength-carbon steels can be brittle

57. let me try again let me out of here what else?

58. let me try again let me out of here generally not some high-strength carbon steels are brittle

59. next question enough ! strain plastic range elastic range stress ultimate failure yield stress yield point Elasto-Plastic Behaviour Graph At first, the material behaves elastically, up to the yield stress. After the yield stress is reached, large deformations occur for very little increase in stress. Note the large plastic range. The material still has strength after the yield point.

60. next question enough ! strain elastic range stress ultimate failure yield stress yield point Brittle Behaviour Graph At first, the material behaves elastically, up to the yield stress. After the yield stress is reached, the material snaps suddenly with no warning

61. next question enough ! brittle materials fail almost immediately the yield point is reached

62. let me try again let me out of here you’re not trying

63. let me try again let me out of here brittle materials DO have an elastic range

64. next question enough ! elasto-plastic materials because they undergo large, visible deformations give a good warning of impending failure. They are also strong in tension

65. let me try again let me out of here you’re not trying

66. let me try again let me out of here how many times must it be said elasticity has NOTHING to do with strength

67. let me try again let me out of here and …. ???

68. next question enough !

69. let me try again let me out of here timber is not brittle

70. let me try again let me out of here steel is not brittle some high-strength carbon steels are brittle but not generally.

71. next question enough ! for example, concrete is a relatively cheap material and it is a good sound and heat insulator and also fireproof

72. let me try again let me out of here what’s ‘like’ got to do with it?

73. let me try again let me out of here no!, no!, no! brittle materials are not strong in tension. Think of what happens if you pull on chalk. That’s why stone beams crack easily on the underside.

74. next question enough ! that’s why we have reinforced concrete

75. let me try again let me out of here we just said how good they are for many purposes

76. let me try again let me out of here c’mon – a little bit of effort

77. next question enough ! the Modulus of Elasticity has to do with stiffness and not strength. The higher the value of E, the more the material resists deformation

78. let me try again let me out of here strength has nothing to do with elasticity you should really know by now

79. next question enough ! f = F / A, A = F / f, A = 3.2 x 10 6 / 30 (keep everything to Newtons and mms) A = 106,667 mm 2 √106,667 = 326.7 πD 2 /4 = 106,667, D = 368.5 so, 327x327 mm needs to be upsized to 350x350mm and 368.5 mm to 375 mm

80. let me try again enough ! f = F / A, A = F / f, A = 3.2 x 10 6 / 30 (keep everything to Newtons and mms) A = 106,667 mm 2 √106,667 = ? πD 2 /4 = 106,667, D = ? check your calculations

81. let me try again enough ! f = F / A, A = F / f, A = 3.2 x 10 6 / 30 (keep everything to Newtons and mms) A = 106,667 mm 2 √106,667 = ? πD 2 /4 = 106,667, D = ? dimensions need to be upsized not downsized to nearest 25 mm check your calculations

82. next question enough ! f = F / A, f = 3.2 x 10 6 / (350 x 350) (keep everything to Newtons and mms) f = 26.1 N/mm 2 Remember 1 N/mm 2 = 1 MPa

83. let me try again enough ! check your calculations f = F / A, f = 3.2 x 10 6 / (350 x 350) (keep everything to Newtons and mms) Remember 1 N/mm 2 = 1 MPa

84. next question enough ! E = f / e, e = f / E, e = 26.1 / 25,000 e = 0.001 = 10 -3 strains are very small quantities

85. let me try again enough ! this is a very large value E = f / e, e = f / E strains are very small quantities

86. let me try again enough ! check your calculations E = f / e e = f / E strain = stress / Modulus of Elasticity So what is f? what is E?

87. next question enough ! e = ΔL / L, ΔL = e x L = 0.001 x 3000 ΔL = 3.0 mm elastic deformations are also very small

88. let me try again enough ! check your calculations e = ΔL / L, ΔL = e x L ΔL = strain x original length So what is e? what is L?

89. let me try again enough ! this is a very large value e = ΔL / L, ΔL = e x L ΔL = strain x original length So what is e? what is L?

90. next question enough ! safety factors are factors by which we over-design a structure to allow a margin of safety

91. let me try again enough ! safety factors are not warning signs. Think of the words

92. let me try again enough ! they provide margins of safety but that’s not what they are.

93. next question enough ! safety factors are factors by which we over-design a structure to allow a certain margin of safety. They ensure that failure is extremely unlikely without totally over-designing the structure They vary depending on the structure and the material

94. let me try again enough ! You can’t fully ensure that failure won’t occur under all circumstances

95. let me try again enough ! partly correct, but what do they do with regards to the safety of a structure?

96. next question enough ! depends on the building and on the material. The more serious the result of collapse or the more likely, The greater the factor of safety. Of course the more we over-design the greater the cost

97. let me try again enough ! what’s the use of a safety factor of 1?

98. let me try again enough !

99. finished ! you’ve graduated as an elasticity master since steel is fairly homogeneous and its properties are well known within small tolerances, it is much more predictable. Therefore one can use a lower safety factor

100. let me try again enough ! concrete varies a lot

101. let me try again enough ! timber varies a lot