Structural Mechanics Unit 1 Flashcards Preview

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Flashcards in Structural Mechanics Unit 1 Deck (136):

what is the difference between a structural material and a structure

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


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

stress - σ (sigma)

strain - ε (epsilon)

co-efficient of viscosity - η (eta)


what is stress denied as, the equation and units

force per cross-sectional area

stress = force/area

units = newton per metre squared or Pascal


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

bar with a bigger cross-sectional area


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

the longest bar would elongate more

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


what does the stress-strain curve show

how the material deforms/behaves as it is loaded


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

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


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

there is a linear relationship between stress and strain
i.e. if stress doubles, strain doubles


what happens at P = proportional limit

relationship between stress and strain is not proportional anymore


what happens at E = Elastic limit

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


what happens at Y = Yield point

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)


what happens after the E = Elastic limit

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


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

elastic region
plastic region
strain hardening


what is happening in the strain hardening region

the material is undergoing changes in its atomic and crystalline structure

results in an increased resistance to further deformation


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

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


how can the true stress-strain curve be obtained

calculate the stress at the narrowest part of the neck


what is the rupture point, R

point at which the material breaks

stress at this point is called the rupture strength


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



what is a material that deformed plastically before breaking described as



what is the difference between ductile and brittle materials

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


what is Hooke's Law

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


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

Youngs Modulus (E) = stress/strain

Unit = N m-2 or Pa

modulus of elasticity


what does a large young modulus mean

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


what is the definition of rigidity and equation

ability to resist axial deformation

rigidity = E x cross sectional area

[rigidity = EA]

Unit = Newton (N)


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

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


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

k = F/trianglel


k = EA/l


what is the definition of flexibility, equation and unit

Deflection under a unit load

Flexibility = length / stiffness

f = l / EA or l / k

Units = m N -1


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

reduction in stiffness

increase in flexibility


what does it mean when a material displays viscous behaviour

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


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


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


equation for viscous behaviour

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]


what is viscoelastic behaviour

a combination of both elastic and viscous behaviour

e.g. cartilage and cortical bone


what is meant when a material displays 'creep'

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


what are examples of materials that creep

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]


what is meant by 'stress relaxation'

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]


what are the types of loadinf

Axial ( tension and compression)


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

positive = elongation

negative = compression


what is shear stress

slippage of surfaces or planes within a material

caused by forces acting in OPPOSITE directions


what is 2 examples of shear stress in orthopaedics

a screw being sheared by a fracture fixation plate and bone

bone cement being sheared by the hip prosthesis and bone


what is the symbol, equation and unit for shear stress

tau = τ

V = shearing force
A = shearing area

τ = V/A
unit = Pa


what is shear strain and how would you calculate it

angle sheared [in radians]

tan φ = x / d

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


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

the max shear stress a material can withstand before failing

shear strength = shear force at failure / sheared area


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

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

units = N m-2 or Pa


at what angle does the largess shear stress occur

at 45 degrees TO THE AXIAL LOADING


what is the equation to calculate max shear stress

max shear stress =
axial stress / 2


τmax = σ / 2


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

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


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

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

Cantilever (think of a diving board)
3 point bending


what is the neutral plane in regards to bending stress

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\


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

at the surface

since elongation and compression is greater at the surfaces


what is the definition of a bending moment

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


what is the bending moment dependent on

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]


what is the equation for calculation bending moment

M = FL

F = applied bending force
L = length of the bar


what is a positive and negative bending moment called

positive = sagging
[happy face]

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


what is bending strength of a beam dependant on

strength of a material
cross sectional area
cross sectional shape


what is the Second Moment of Area

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


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


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


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]


what structure is best at bending

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


what is the general equation for bending

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


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



what is the equation to calculate the maximum bending moment

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]


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

ymax = 1/2d

ymax = 1/2d

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


what is an example of a bending fracture in bones

Boot top fracture seen in skiers


what causes torsional stresses

twisting due to the application of a moment

one end is fixed, the other end is being twisted


when is a circular bar said to be in pure torsion

when its cross-section retains its shape
i.e. remains circular and its radius is unchanged


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

at the outer surface

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


what is the angle of twist measured



what is the shear strain equal to

equal to the angle of shear

[constant along the length go the bar]


what is the equation to calculate torsional strain

angle of twist x radius / length


what is the equation to calculate torsional stress

modulus of rigidity x angle of twist x radius / length


how do you calculate modulus of rigidity

shear stress / shear strain

units = N m^-2 or Pa

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


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

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

unit = m^4


what is the equation for the applied twisting moment

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


what is the general equation for torsion

M/J = τ/R = Gθ/L

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


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

J = pie x d^4 / 32

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


what is the shear stress inversely proportional to

the length


where is the maximum shear stress in a bar located

at the outer surface


where is the minimum shear strain in the bar located

at the centre


how are bones structured to resist torsional loads

hollow with strong cortical bone on the outer layer

maximises strength-to-weight ratio


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

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


how does muscle activity reduce the chance of fracture

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]


what do strain gauges do and whats an advantage of them

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


what are the methods to perform stress analysis on a structure

strain gauges
Finite Element methods (FEA)


how does FEA modelling work

done on a computer
- blue = compressive stress
- red = tensile stress


what factors are important in material failure

magnitude of the applied load

rate of speed at which the load is applied

no. of times that the load is applied


what is the difference between ductile and brittle fractures

- fracture occurs AFTER plastic deformation
- material shows "necking"

- fracture occurs W/OUT plastic deformation
- i.e. no 'necking'


what test allows the stress-strain curve to be drawn

tensile test


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

rupture strength of the material


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

rupture strength - stress when a material will fracture

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


to summerise when will a material fracture

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


how do ductile fractures form

- 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


what causes the formation of the voids

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


what is the characteristic look of a ductile fracture

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


when will a ductile material act like a brittle one

if it has been exposed to fatigue loading


how do brittle fractures vary from ductile fractures

occurs suddenly

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

has CHEVRON pattern


summarise the difference in appearance between ductile and brittle fractures

ductile - cup and cone appearance with granulated central portion

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


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

the stress is concentrated on 1 area

[curved corner solve this problem]


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

places where there is a SHARP CHANGE in shape

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


what shapes are prone to fracture

at the tip of cracks or notches

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


what is an impact loading

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]


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

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


what is the equation for the charpy impact test

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]


what can influence a materials ability to absorb energy and how

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]


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

a series of impact tests at different temperatures


what is a fatigue fracture

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]


what is the appearance of a fatigue fracture

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


what is fatigue life

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


what are factors influencing fatigue life

Surface quality
Material Type
Residual stresses

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


how can corrosion be prevented

creating an alloy
- put a layer on that metal that is already corroded and cannot be corroded anymore


what parts of metal are particularly prone to attack from corrosions

imperfections on the surface of the metal
- the imperfections develop to crevices after being corroded


what happens at the crevice that has developed from corrosion

gives rise to stress concentrations in the structure

eventually leads to fracture


how does corrosion affect the fatigue behaviour of metal

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]


what are the 2 groups of metals

ferrous metal
non-ferrous metal


what is the most common ferrous alloys

- alloy of iron and carbon

[stainless steel
- allow of iron, chromium, nickel and carbon
- corrosion resistant]


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



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


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


what are the main advantages of titanium based alloys

lower density compared to steel

higher strength-to-weight ratios compared to Aluminium

excellent corrosion resistance


what are the main disadvantages of titanium based alloys

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


what is 316L

stainless steel used in orthopaedics

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


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

Low carbon steels- Low strength and hardness but good ductility

High carbon steels-High strength and hardness but brittle


what are properties of polymers

light weight
corrosion resistant
low tensile strength
easily manufactured
low density

based on long chains of monomers


what is the stress-strain behaviours of polymers

non-linear and time dependent

exhibit both elastic and plastic behaviour


what are the 2 main subtypes of polymers




what are the 2 main categories of plastics




what are features of thermoplastic

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


examples of thermoplastics and there uses in orthopaedics

Polyethylene - acetabular cups

Polypropylene - orthoses

Polymethyl methacrylate [PMMA] - bone cement


what are elastomers better known as and why


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


what is the structure of ceramics and an example of one

Crystalline in structure

e.g. Diamonds


what are properties of ceramics

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]


what property does ceramics not exhibit



what is the use for ceramics in orthopaedics

used for heads of hip prostheses


when are composite materials formed

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


what are the 3 categories of composite materials

particulate e.g. concrete

fibre e.g. fibreglass

laminar e.g. plywood


what is features of particulate composite materials

hard brittle material dispersed within a softer more ductile material

e.g. concrete, mixture of gravel and cement


what is features of fibre composite materials

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


what is features of laminar composite materials

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


compare properties of bone cement and cortical bone
- in compression, in tension, young's modulus, which is more ductile, fatigue cycles, overall

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

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