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BMSc SB > Structural Mechanics Unit 1 > Flashcards

Structural Mechanics Unit 1 Flashcards

1
Q

what is the difference between a structural material and a structure

A

structure - is an arrangement of one or more materials in a way that is designed to sustained loads

structural material - any material that may be used to construct a structure

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2
Q

what are the symbols for stress, strain and co-efficient of viscosity

A

stress - σ (sigma)

strain - ε (epsilon)

co-efficient of viscosity - η (eta)

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3
Q

what is stress denied as, the equation and units

A

force per cross-sectional area

stress = force/area

units = newton per metre squared or Pascal

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4
Q

what would handle more force, a bar with a bigger or small cross-sectional area

A

bar with a bigger cross-sectional area

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5
Q

in regards to strain, what would the difference be in elongation of 2 bars, 1 of which is longer than the other

A

the longest bar would elongate more

if bar 1, is twice the length of bar 2, it will elongate twice as much

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6
Q

what does the stress-strain curve show

A

how the material deforms/behaves as it is loaded

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7
Q

on a stress-strain curve, what does the letters P,E,Y,H,V and R represent

A 
P = proportional limit
E = elastic limit
Y = yield strength
H = strain hardening
V = ultimate stress
R = rupture
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8
Q

in regards to the stress-strain curve, was is the relationship between stress and strain at very small loads

A

there is a linear relationship between stress and strain

i.e. if stress doubles, strain doubles

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9
Q

what happens at P = proportional limit

A

relationship between stress and strain is not proportional anymore

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10
Q

what happens at E = Elastic limit

A

before here, if the load is removed from the material, the material will recover back to its original shape and size

this is the elastic region

after the elastic limit, the material will NOT return to its original shape and size after the load is removed

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11
Q

what happens at Y = Yield point

A

after this point, the material will undergo considerable elongation without an increase in stress

  • highlighted by the flatness of the region on the graph
  • material is displaying perfect plastic behaviour (no elastic recovery)
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12
Q

what happens after the E = Elastic limit

A

material is in the plastic region

material deforms instantly under applied load

material may partially recover to original size and shape when load is removed, but NOT completely like in the elastic region

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13
Q

what are the section of the stress-strain curve in order they happen

A

elastic region
plastic region
strain hardening
necking

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14
Q

what is happening in the strain hardening region

A

the material is undergoing changes in its atomic and crystalline structure

results in an increased resistance to further deformation

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15
Q

what is U = ultimate strength point on the stress-strain curve

A

occurs at highest point on the graph

after this point, strain increases with a reduction in stress and ‘necking’ happens

the stress the bar can withstand decreases, NOT sue to any loss of material but due to reduction in cross-sectional area of the bar

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16
Q

how can the true stress-strain curve be obtained

A

calculate the stress at the narrowest part of the neck

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17
Q

what is the rupture point, R

A

point at which the material breaks

stress at this point is called the rupture strength

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18
Q

what is a material that can only handle a small amount of strain before breaking described as

A

brittle

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19
Q

what is a material that deformed plastically before breaking described as

A

ductile

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20
Q

what is the difference between ductile and brittle materials

A

a brittle material ruptures after a small amount of strain whilst a ductile material can deform considerably before rupturing

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21
Q

what is Hooke’s Law

A

Up to a certain level of stress (the proportional limit), the strain is proportional to the applied stress

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22
Q

what is the equation for Young’s modulus and the other name for it

A

Youngs Modulus (E) = stress/strain

Unit = N m-2 or Pa

modulus of elasticity

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23
Q

what does a large young modulus mean

A

that the material requires a large amount of stress is required to produce a small strain i.e. material is stiff

vice versa, a small young’s modulus means only a small amount of stress is needed to produce a big strain i.e. material is flexible

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24
Q

what is the definition of rigidity and equation

A

ability to resist axial deformation

rigidity = E x cross sectional area

[rigidity = EA]

Unit = Newton (N)

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25
Q

what is stiffness (k) defined as and what is the equation

A

Force required to produce a unit deflection (i.e.. force required to elongate or shorten the bar by 1 metre)

stiffness = applied force/change in length

[k = F/trianglel]

unit = N m-1

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26
Q

how can the equation of stiffness be rearranged using young’s modulus

A

k = F/trianglel

To

k = EA/l

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27
Q

what is the definition of flexibility, equation and unit

A

Deflection under a unit load

Flexibility = length / stiffness

f = l / EA or l / k

Units = m N -1

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28
Q

in regards to flexibility and stiffness, what would in increase in the length of a bar mean

A

reduction in stiffness

increase in flexibility

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29
Q

what does it mean when a material displays viscous behaviour

A

material does not deform instantaneously when a load is applied

the strain [stretching] is prolonged

the material will not return to its original shape and size after the load is removed

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30
Q

can viscous behaviour be represented by Hooke’s Law or Young’s modulus

A

No

as viscous materials are dependant upon the strain rate not the stress

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31
Q

equation for viscous behaviour

A

η (Coefficient of Viscoscity) = stress/strain rate

Strain rate = change in strain/change in time

unit = N m-2 .s [Newton per metre squared second] or Pa .s [pascal per seconds]

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32
Q

what is viscoelastic behaviour

A

a combination of both elastic and viscous behaviour

e.g. cartilage and cortical bone

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33
Q

what is meant when a material displays ‘creep’

A

the material continues to deform over time when a CONSTANT LOAD is applied

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34
Q

what are examples of materials that creep

A

wood - will creep noticeably at only a few hours at room temp

[materials which are exposed to high temperatures are vulnerable to creep and may even fracture because of it]

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35
Q

what is meant by ‘stress relaxation’

A

if a material is kept under CONSTANT STRAIN then the STRESS in it will gradually diminish over time

[due to the change in the ordering of the atoms in the material]

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36
Q

what are the types of loadinf

A

Axial ( tension and compression)
Shear
Bending
Torsion

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37
Q

in axial strain, what does it mean if the strain is positive and negative

A

positive = elongation

negative = compression

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38
Q

what is shear stress

A

slippage of surfaces or planes within a material

caused by forces acting in OPPOSITE directions

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39
Q

what is 2 examples of shear stress in orthopaedics

A

a screw being sheared by a fracture fixation plate and bone

bone cement being sheared by the hip prosthesis and bone

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40
Q

what is the symbol, equation and unit for shear stress

A

tau = τ

V = shearing force 
A = shearing area

τ = V/A
unit = Pa

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41
Q

what is shear strain and how would you calculate it

A

angle sheared [in radians]

tan φ = x / d

where φ = angle
x = distance tilted forward
d = length

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42
Q

what is the definition of shear strength and the equation for it

A

the max shear stress a material can withstand before failing

shear strength = shear force at failure / sheared area

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43
Q

what is the value for the relationship between shear stress and shear strain called and what is the equation

A

Modulus of Rigidity (G) =
shear stress / shear strain

units = N m-2 or Pa

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44
Q

at what angle does the largess shear stress occur

A

at 45 degrees TO THE AXIAL LOADING

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45
Q

what is the equation to calculate max shear stress

A

max shear stress =
axial stress / 2

Or

τmax = σ / 2

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46
Q

what happens to cortical bone when it is applied with an AXIAL COMPRESSIVE LOAD

A

as cortical bone is less than half as strong in shear than in compression, it will tend to break at 45 degrees to an axial compressive load

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47
Q

what is bending stress and the 2 types we will looks at

A

Application of loading tending to cause bending results in both tension and compression

Cantilever (think of a diving board)
3 point bending

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48
Q

what is the neutral plane in regards to bending stress

A

plane where there is neither tensile or compressive stresses

i.e. no changes

[neutral axis maintains the same length when a beam is bent, neither compressed or elongated\

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49
Q

if you were to put a bending force on a bar, where would the strain and stress be greatest

A

at the surface

since elongation and compression is greater at the surfaces

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50
Q

what is the definition of a bending moment

A

a measure of the bending effect of an applied load at any point in a structure

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51
Q

what is the bending moment dependent on

A

the applied bending force and its displacement from the point of application of the bending force

[page 10 of the unit 2 notes to see bending moment diagrams]

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52
Q

what is the equation for calculation bending moment

A

M = FL

F = applied bending force
L = length of the bar
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53
Q

what is a positive and negative bending moment called

A

positive = sagging
[happy face]

negative = hogging
[think of a diver when they jump on a diving board and it curves in a sad face]

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54
Q

what is bending strength of a beam dependant on

A

strength of a material
cross sectional area
cross sectional shape

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55
Q

what is the Second Moment of Area

A

quantifies resistance of a substance to bending

i.e. the further the material of a beam is concentrated away from its neural axis, the larger its second moment of area

unit = m ^4
symbol = I
56
Q

what is the equation for calculating the second moment of area for a rectangle, a circle, and a circle with a hollow centre

A

Rectangle:

I =bd^3 / 12
[where b = breadth and d= depth]

Circle:

I = pie x D^4 / 64
[where D = diameter]

Circle with a hollow centre”

I = pie (D^4 - d^4) / 64
[where D = diameter and d = second diameter]

57
Q

what structure is best at bending

A

the more hollow a structure, the better it is a bending

58
Q

what is the general equation for bending

A

M/I = sigma/y = E/r

M = moment 
I = second moment of area
sigma = stress
y = displacement from the neutral axis 
E = young's modulus 
r = radius of the circle
59
Q

what is the aid memoir to remember the general equation for bending

A

MISYER

60
Q

what is the equation to calculate the maximum bending moment

A

Mmax = sigma x I / ymax

sigma = maximum bending stress
I = second moment of area 
ymax = max displacement of the extreme layer of the beam from the neutral axis

unit = Nm [Newton Metre]

61
Q

what is the ymax values for a rectangle, a circle and a circle with a hollow centre

A

rectangle:
ymax = 1/2d

circle:
ymax = 1/2d

circle w/ hollow centre
ymax = 1/2d outer

62
Q

what is an example of a bending fracture in bones

A

Boot top fracture seen in skiers

63
Q

what causes torsional stresses

A

twisting due to the application of a moment

one end is fixed, the other end is being twisted

64
Q

when is a circular bar said to be in pure torsion

A

when its cross-section retains its shape

i.e. remains circular and its radius is unchanged

65
Q

the angle of twist varies along the length of the bar, when is it at its maximum

A

at the outer surface

[further you get away from the neutral axis, the higher the stress/strain]

66
Q

what is the angle of twist measured

A

radians

67
Q

what is the shear strain equal to

A

equal to the angle of shear

[constant along the length go the bar]

68
Q

what is the equation to calculate torsional strain

A

angle of twist x radius / length

69
Q

what is the equation to calculate torsional stress

A

modulus of rigidity x angle of twist x radius / length

70
Q

how do you calculate modulus of rigidity

A

shear stress / shear strain

units = N m^-2 or Pa

[higher the number, harder it is to generate shear/strain]

71
Q

what is the Polar Second Moment of Area [J] a measure of

A

a measure of the distribution of the material about the central axis

unit = m^4

72
Q

what is the equation for the applied twisting moment

A

M = J [G x angle of twist/lenght of the bar]

73
Q

what is the general equation for torsion

A

M/J = τ/R = Gθ/L

where:
M=Twisting moment
J= polar second moment of area 
τ=shear stress
R= radius of cross section
G= modulus of rigidity 
θ= angle of twist
L= length
74
Q

what is the equation for polar second moment of area for circle and a hollow circle

A

Circle:
J = pie x d^4 / 32

Hollow Circle:
J = pie(d^4 outer - d^4 inner) /32

75
Q

what is the shear stress inversely proportional to

A

the length

76
Q

where is the maximum shear stress in a bar located

A

at the outer surface

77
Q

where is the minimum shear strain in the bar located

A

at the centre

78
Q

how are bones structured to resist torsional loads

A

hollow with strong cortical bone on the outer layer

maximises strength-to-weight ratio

79
Q

the tibia is most likely to fracture due to torsional loads - most fractures are found distally, why is this?

A

the distal polar second moment of area of the tibia is SMALLER than the proximal polar second moment of area

amount of bone tissue is the SAME, the distal part is less able to resist torsional loads and therefore, most likely to fracture

80
Q

how does muscle activity reduce the chance of fracture

A

muscles contract to alter stress distribution within the bone

muscle contracts > produces a compressive load on a bone and eliminates any tensile loading

[bones stronger in compression than tension]

81
Q

what do strain gauges do and whats an advantage of them

A

offer a means of measuring strain, and thus the stress, at the surfaces of a structure

consist of a very thin metal foil located between 2 pieces of thin insulating film

they can be applied to the actual surface under study

82
Q

what are the methods to perform stress analysis on a structure

A

strain gauges
photo-elasticity
Finite Element methods (FEA)

83
Q

how does FEA modelling work

A

done on a computer

  • blue = compressive stress
  • red = tensile stress
84
Q

what factors are important in material failure

A

magnitude of the applied load

rate of speed at which the load is applied

no. of times that the load is applied

85
Q

what is the difference between ductile and brittle fractures

A

ductile

  • fracture occurs AFTER plastic deformation
  • material shows “necking”

brittle

  • fracture occurs W/OUT plastic deformation
  • i.e. no ‘necking’
86
Q

what test allows the stress-strain curve to be drawn

A

tensile test

87
Q

what is the name given to the point on a stress-strain curve where a material fractures

A

rupture strength of the material

88
Q

how does the rupture strength and the ultimate strength of a material differ

A

rupture strength - stress when a material will fracture

ultimate - maximum stress calculated [calculate at the point of necking in a ductile material]

89
Q

to summerise when will a material fracture

A

when it is subjected to a load greater than its ultimate strength

90
Q

how do ductile fractures form

A
  • application of tensile load
  • formation of microscopic voids (small holes) at the centre of the bar
  • stress increases, voids grow
  • voids connect with each other to form cavities
  • actual metal to metal contact is reduced
  • unable to support applied load and complete fracture occurs
91
Q

what causes the formation of the voids

A

high stress causes separation of the metal at grain boundaries or at the interfaces between the metal grains and inclusions

92
Q

what is the characteristic look of a ductile fracture

A

“necking” and a small shear lip [gives a cup and cone appearance]

93
Q

when will a ductile material act like a brittle one

A

if it has been exposed to fatigue loading

94
Q

how do brittle fractures vary from ductile fractures

A

occurs suddenly

fracture surface is flat, perpendicular to the load and has a granular appearance

has CHEVRON pattern

95
Q

summarise the difference in appearance between ductile and brittle fractures

A

ductile - cup and cone appearance with granulated central portion

brittle - flat, granular cross-section with a chevron fracture

96
Q

why are sharp corners, i.e. on a boat, more prone to failing

A

the stress is concentrated on 1 area

[curved corner solve this problem]

97
Q

what areas are likely to be points of high stress in a structure

A

places where there is a SHARP CHANGE in shape

[the sharper the change, the higher the stress conc]

98
Q

what shapes are prone to fracture

A

at the tip of cracks or notches

[phenomenon of concentrated stress at the tip of a crack or notch is called NOTCH SENSITIVITY]

99
Q

what is an impact loading

A

a sudden intense blow/load

Impacts by masses create loads that are greater than equivalent mass static loading conditions.

[i.e. a impact load = to a static load may result in fracture, but the gradually applied static load may not]

100
Q

what is the name of the test used to test a structures resistance to an impact load and how does it work

A

Charpy Impact Test

  • Heavy pendulum is released from a known height
  • as pendulum reaches bottom of its trajectory it strikes and breaks the test specimen
  • then continues until it reaches the peak of its swing
  • the height reached by the pendulum at the end of the swing is lower than the height from which is was released
  • thus the difference is the energy absorbed by the specimen as it if fractured
101
Q

what is the equation for the charpy impact test

A

calculating potential energy

PE = W (ho - hf)

ho = original height
hf = final height 
W = weight of pendulum

or PE = mg (ho - hf)

m = mass
g = gravity

Unit = Joules [J]

102
Q

what can influence a materials ability to absorb energy and how

A

the temperature

  • a material will be able to absorb more energy as the temp increases
  • due to an increasing temperature changing the material from BRITTLE TO DUCTILE
  • yield strength decreases
  • ultimate tensile strength decreases
  • strain increases

[ductile material is tougher than a brittle one]

103
Q

when testing a material, how could you take account for the difference in ability to absorb energy at difference temperatures

A

a series of impact tests at different temperatures

104
Q

what is a fatigue fracture

A

a fracture caused by repeated loading

Load required is lower than for failure due to application of a steady load

[Failure due to combination of magnitude of load and repeated no. of loadings]

[orthopaedic implants are prone to fatigue fractures]

105
Q

what is the appearance of a fatigue fracture

A

2 regions:

  • a relatively smooth region marked by concentric markings that may allow the origin of the fracture to be found [sometimes called clam shell markings]
  • then either a granular or fibrous region
  • granular appearance indicates a brittle fracture
  • fibrous appearance indicates a ductile fracture
106
Q

what is fatigue life

A

Expressed in cycles
- is the number of cycles a structure can withstand before a fracture

Dependent on applied stress
Reduced by surface defects
Below Endurance Limit = no failure

107
Q

what are factors influencing fatigue life

A 
Stress
Geometry
Surface quality
Material Type
Residual stresses

Internal defects:
• Direction of loading
• Grain size
• Environment

108
Q

how can corrosion be prevented

A

creating an alloy

  • put a layer on that metal that is already corroded and cannot be corroded anymore
  • called PASSIVATION LAYEr
109
Q

what parts of metal are particularly prone to attack from corrosions

A

imperfections on the surface of the metal

- the imperfections develop to crevices after being corroded

110
Q

what happens at the crevice that has developed from corrosion

A

gives rise to stress concentrations in the structure

eventually leads to fracture

111
Q

how does corrosion affect the fatigue behaviour of metal

A

reduces the fatigue resistance of metals, results in a lower fatigue life and no endurance limit

[endurance limit = range of cyclic stress that can be applied to the material w/out causing fatigue failure]

112
Q

what are the 2 groups of metals

A

ferrous metal

non-ferrous metal

113
Q

what is the most common ferrous alloys

A

steel
- alloy of iron and carbon

[stainless steel

  • allow of iron, chromium, nickel and carbon
  • corrosion resistant]
114
Q

what part of the stainless steel alloy gives it its corrosion resistant property

A

chromium

115
Q

what are examples of non-ferrous metals and alloys used in biomechanics

A

titanium

titanium based alloys
- used in heart value components, joint replacement endoprostheses, # fixation plate

116
Q

what are the main advantages of titanium based alloys

A

lower density compared to steel

higher strength-to-weight ratios compared to Aluminium

excellent corrosion resistance

117
Q

what are the main disadvantages of titanium based alloys

A

high material cost compared to steel and aluminium

low young’s modulus (110 GPa) compared to steel (200 GPa)
- i.e. will deform more under a given load

118
Q

what is 316L

A

stainless steel used in orthopaedics

[10.6 - 18 % chromium, 10 - 14 % nickel, 2 % manganese, 0.035% carbon]

119
Q

what is the difference in properties between low carbon and high carbon steels

A

Low carbon steels- Low strength and hardness but good ductility

High carbon steels-High strength and hardness but brittle

120
Q

what are properties of polymers

A 
light weight
corrosion resistant
low tensile strength 
easily manufactured 
low density

based on long chains of monomers

121
Q

what is the stress-strain behaviours of polymers

A

non-linear and time dependent

exhibit both elastic and plastic behaviour

122
Q

what are the 2 main subtypes of polymers

A

plastics

elastomers

123
Q

what are the 2 main categories of plastics

A

thermoplastic

thermoset

124
Q

what are features of thermoplastic

A

display plastic behaviour at high temperatures

there structure is stable at high temps, so can be heated, cooled, re-heated or reformed w/out altering their behaviour

125
Q

examples of thermoplastics and there uses in orthopaedics

A

Polyethylene - acetabular cups

Polypropylene - orthoses

Polymethyl methacrylate [PMMA] - bone cement

126
Q

what are elastomers better known as and why

A

rubbers

can deform by enormous amounts w/out permanent shape change

e.g. a normal rubber can be stretched to 7 times its original length, 700% strain, and still return to its original shape/size

127
Q

what is the structure of ceramics and an example of one

A

Crystalline in structure

e.g. Diamonds

128
Q

what are properties of ceramics

A 
very hard but brittle 
high melting point 
low electrical and thermal conductivity 
good chemical and thermal stability 
high compressive strength

[Diamond E=1200 GN m-2. Highest known young’s modulus]

129
Q

what property does ceramics not exhibit

A

creep

130
Q

what is the use for ceramics in orthopaedics

A

used for heads of hip prostheses

131
Q

when are composite materials formed

A

when 2 or more materials are joined to give a combination of properties that can not be obtained from original materials

132
Q

what are the 3 categories of composite materials

A

particulate e.g. concrete

fibre e.g. fibreglass

laminar e.g. plywood

133
Q

what is features of particulate composite materials

A

hard brittle material dispersed within a softer more ductile material

e.g. concrete, mixture of gravel and cement

134
Q

what is features of fibre composite materials

A

fibres of strong, stiff brittle material within a softer, more ductile material

improves strength, fatigue resistance, stiffness and strength-to-weight ratio

e.g. fibreglass, contains glass fibres embedded in a polymer

135
Q

what is features of laminar composite materials

A

several different forms

very thin coating may cover a material to improve corrosion resistance

thick layers may be laminated together to improve strength i.e. plywood

136
Q

compare properties of bone cement and cortical bone

- in compression, in tension, young’s modulus, which is more ductile, fatigue cycles, overall

A

Both are stronger in compression than in tension
- but cortical bone in 3-5 times strong than bone cement

Cortical bone has higher young’s modulus
- i.e. is more stiffer

Bone cement elongates further at fracture
- more ductile than cortical bone

Cortical bone is able to withstand more than twice as many fatigue cycles as bone cement

Overall
- cortical bone is stronger, stiffer and more brittle material than bone cement.

BMSc SB (18 decks)

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