Elasticity

1. Tutorial 7 Elasticity to answer just click on the button or image related to the answer let's go !!

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

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

4. 81.5 MPa 163 MPa 80 kN 80 MPa 3m b a c Question 3a 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 what is the stress in a rod?

5. 0.00116 (1.16 x 10-3) 0.02 (2 x 10-2) 80 kN 3 mm 3m b a c Question 3b 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 what is the strain in a rod?

6. 4.5 mm 3.5 mm 80 kN 35 mm 3m b a c Question 3c 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 how much does the rod lengthen?

7. yes no 80 kN 3m a b Question 3d 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 given that the maximum allowable tensile stress for aluminium is 120 MPA are the rods strong enough ?

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

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

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

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

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

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

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

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

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

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

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

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

20. 350 x 350 mm square or 375 mm dia 275 x 275 mm square or 325 mm dia 325 x 325 mm square or 350 mm dia a b c Question 16a 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 what dimensions should the column be (nearest 25mm) ?

21. 2.6 MPa 32.0 MPa 26.1 MPa a b c Question 16b 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 what is the actual stress in the column?

22. 1.0 0.001 (10-3) 0.01 (10-2) a b c Question 16c 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 what is the strain in the column?

23. 3.0 mm 1.0 mm 30 mm a b c Question 16d 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 by how much does the column shorten?

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

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

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

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

28. enough ! Fantastic 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: next question

29. let me try again let me out of here Partly right !

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

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

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

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

34. enough ! that's grrr..eat !! f = F / A Force, F = 40 kN (per rod), A = πR2 = 3.142 x 12.5 x 12.5 =491 mm2 next question

35. let me try again let me out of here Sorry 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 Sorry 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. enough ! full marks ! E = f / e so, e = f/ E E = 81.5 / 70,000 next question

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

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

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

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

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

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

44. let me try again let me out of here Not happy !! 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. enough ! good one ! 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 next question

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

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

48. let me try again let me out of here No !, No!, No ! we’re talking about elastic behaviour think of a spring

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

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