WORKSHEET 2 FAILURE, STRESS AND STRAIN

1. WORKSHEET 2FAILURE, STRESS AND STRAIN

2. a) b) tension? compression? Q1 What happens to an element under: material tends to be pulled apart element stretches - becomes longer and thinner finally breaks particles pushed against each other element shortens - becomes squatter finally breaks slender elements may buckle first

3. d) c) bending? shear? Q1 What happens to an element under: particles slide relative to each other material tears side closest to load shortens and comes under compression side furthest from load lengthens and comes under tension neutral axis remains same length

4. Q2 When does buckling occur when a slender element is put under compression

5. b) a) the member is more slender? the member is longer? Q3 Can a compression member carry more or less load before it buckles (i.e. is the buckling load greater or smaller if: carries less load - buckling load is smaller carries less load - buckling load is smaller buckling load is a function of the slenderness ratio (the slenderness ratio is the ratio between the effective length and the width of the member)

6. d) c) one of its ends is free? it is rigidly restrained at its ends? Q3 Can a compression member carry more or less load before it buckles (i.e. is the buckling load greater or smaller if: carries more load - buckling load is greater reduces the effective length by 1/2 carries less load - buckling load is smaller increases the effective length by 2

7. Q4 Timber studs in a timber-framed wall are usually 100 x 50 mm. The framing includes one or two rows of noggings. What do the noggings do? The studs would tend to buckle in the weaker direction The noggings support the studs in the weaker direction This results in a slenderness ratio roughly equal in both directions

8. a) the beam bends - the bottom face comes under tension due to bending concrete is weak in tension the beam cracks due to bending b) the beam bends - shear produces diagonal tension concrete is weak in tension the beam cracks due to shear Q5 What happens to an unreinforced concrete beam when loaded?

9. b) a) c) compression tension shear Q6 Name the three basic states of stress: state of stress where material pulled apart state of stress where material crushed state of stress where parts of material slide relative to each other

10. bending C T Q7 Name another very important state of stress: state of stress where compression and tension exist in different fibres of same element (producing a moment effect)

11. buckling Q7 Name another very important state of stress: state of stress where compression acts on slender member

12. Q8 What happens to an element that is stressed: it deforms changes in shape or dimensions or both results in strain change may be reversible or irreversible (elastic or inelastic)

13. a) b) what is stress? what are the units of stress? Q9 Give units where applicable internal forceintensity as result of external forces force per unit area Pa, kPa, MPa 1Pa = 1 N / m2 1MPa = 1 N / mm2

14. c) d) what is strain? what are the units of strain? Q9 Give units where applicable change in size or shape relative to original state, e.g. change in length relative to original length e = DL / L - dimensionless

15. a) b) what is the stress in the cable? what is the strain in the cable? Q10 a 20mm dia. high-strength steel cable 5 m long has a weight of 50 kN added to its end. Neglecting the self-weight of the cable and given that the cable lengthens by 4mm: area of cable = p x 20 x 20 / 4 = 314.16 mm2 stress = F / A stress = 50 / 314.16 (keep units to Newtons, MPa and mm2 for simplicity) stress = 50000 / 314.16 = 159.2 N/mm2 = 159.2 MPa strain = DL / L strain = 4 / 5000 = 0.0008 (8 x 10-4)

16. c) Given that the maximum allowable tensile stress for high-strength steel is 1000MPa, is the cable strong enough? Q10 stress in cable = 159.2 MPa maximum allowable stress of steel = 1000 MPa stress in cable < maximum allowable stress yes - the cable is strong enough

17. a) What factors do we have to take into consideration? b) What is the first means of failure we should check for? Q11 When a column is under load: (i) whether buckling will occur (the slenderness ratio of the column) (ii) whether it is strong enough to take the load w.r.t its compressive strength (material strength and x-sectional area) whether buckling will occur

18. a) What is the stress in the column? Q12 A reinforced concrete column 400 x 400 mm and 3.5 m high is subject to a load 160 kN. Given that the column shortens by 0.07 mm: stress = Force / Area = 160 / (0.4 x 0.4) = 1000 kN/m2 = 1000 kPa (1 MPa)

19. b) What is the strain in the column? c) Given that the maximum allowable stress of the concrete is 20MPa, is the column strong enough? Q12 Given that the column shortens by 0.07 mm: strain = DL / L = 0.07 / 3500 = 0.00002 = 2 x 10 -5 max allowable stress = 20 MPa actual stress = 1 MPa since actual stress < max allowable stress yes column is strong enough as regards compressive strength

20. d) Could you reduce the area of the column? Q12 Considering strength only - max allowable stress = 20 MPa Min Area = Force / Max Allow stress = 160 (kN) / 20 (MPa) (keep units to Newtons, MPa and mm2 for simplicity) = 160,000 (N) / 20 (MPa = N / mm2 ) = 8000 mm2 e.g 90 x 90 mm However a 90 x 90 mm column, apart from being difficult to build, would be very slender and subject to buckling