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Ortho BMSc > Deformable body Mechanics Unit 2: stress analysis (class) > Flashcards

Deformable body Mechanics Unit 2: stress analysis (class) Flashcards

1
Q

What is shear stress?

A

slippage of surfaces or planes within a material

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2
Q

What is shear stress equal to?

A

shearing force/ sheared area

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3
Q

What are the units of shear stress?

A

pascal

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4
Q

What does shear strain quantify?

A

the angular deformation of a material undergoing shear stress

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5
Q

What unit do we use for shear strain?

A

radians

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6
Q

What is shear strength?

A

the maximum shearing force a material can withstand before it fractures

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7
Q

How do we calculate shear strength?

A

shear force at failure / sheared area

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8
Q

What is the modulus of rigidity equal to

a) as equation?
b) in shear stress-shear strain curve?

A

a) shear stress/ shear strain

b) the gradient up to a limiting stress

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9
Q

What symbol represents modulus of rigidity?

A

G

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10
Q

Where does the maximum shear stress occur?

A

45 degrees to axial loading

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11
Q

How do we calculate max shear stress?

A

axial stress/ 2

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12
Q

How can we relate modulus of rigidity to Young’s modullus?

A

G = E / 2 (1+v)

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13
Q

What is 1+v?

A

Poisson ratio

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14
Q

What is the modulus of rigidity equal to?

A

the gradient of a shear-stress/shear-strain curve up to a limiting stress

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15
Q

What does application of a load that tends to cause bending result in?

A

tension and compression so one side of the material will be elongated and the other compressed

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16
Q

give the two types of bending

A

cantilever

3 point fixation

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17
Q

If a bar is subjected to a bending load where will the stress be greatest?

A

on the outer surfaces

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18
Q

What do we call the area of a bar where there is neither tensile nor compressive stresses?

A

the neutral axis

- it stays the same length

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19
Q

What is the bending moment?

A

the internal moment within a bar that balances the external moments when a bending load is applied

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20
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

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21
Q

When does the maximum magnitude for bending moment occur?

A

at the maximum displacement

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22
Q

What is the bending resistance of a beam dependent on?

A

resistance of material (its E)
cross-sectional area
cross-sectional shape

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23
Q

How do we quantify the cross-sectional shape?

A

use the second moment of area (I)

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24
Q

Will a beam resist bending moments better if its mass is distributed

a) further from the neutral axis?
b) closer to the neutral axis?

A

A

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25
Q

What is the general bending equation for a beam?

A

MISYER

M = Sigma = E
I y R

bending moment = stress
2nd mom of area displacement of layer from neutral
axis

= youngs modulus
radius of circle containing neutral axis

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26
Q

what symbol represents shear stress?

A

τ tau

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27
Q

what is tan ϕ and therefore sheer strain equal to?

A

distance sheared / distance between two shearing forces

28
Q

what is the unit for the modulus of rigidity?

A

pa

29
Q

what causes torsional stress?

A

twisting due to the application of a moment

30
Q

What is a bar under the action of a twisting moment in?

A

torsion

31
Q

How does deformation and therefore shear strain of a bar under torsion vary?

A

zero at central axis and maximum at outer surface

32
Q

Is it harder to twist a shorter or longer bar at a given moment?

A

shorter bar

33
Q

What does
a) φ
b) θ
represent in torsion?

A

a) shear strain

b) angle of twist

34
Q

What quantifies the resistance to shearing force in torsion?

A

modulus of rigidity (G): the higher it is the more resistance

35
Q

What are the units for modulus of rigidity?

A

N/m2 or Pa

36
Q

how can we calculate shear strain of a bar in torsion?

A

φ = θ x radius / length

37
Q

how do we converts degrees to radians ?

A

multiply by π/180

38
Q

How can re-distribution of material in a bar help to resist torsion?

A

hollow bar is more resistant than a solid bar

39
Q

What is the polar second moment of area?

A

a measure of distribution of the material about a central axis

40
Q

What symbol represents polar second moment of area?

A

J

41
Q

What are the units for polar second moment of area?

A

metres to the power of 4

42
Q

How do we calculate polar second moment of area for a solid circle?

A

J = π d4 / 2

43
Q

What is the general equation for torsion?

A

M/J = T/R = Gθ/L

44
Q

in the general equation for torsion what is

a) M?
b) T?
c) R?
d) G?
e) θ?
f) L?
g) J?

A

a) twisting moment
b) shear stress
c) radius of the cross section
d) modulus of rigidity
e) angle of twist
f) length of the bar
g) polar second moment of area

45
Q

What is the angle of twist measured in?

A

radians

46
Q

What is shear stress

a) proportional to?
b) inversely proportional to?

A

a) modulus of rigidity, angle of twist and distance of point of interest
b) length

47
Q

How are long bones designed to resist torsional loads?

A

hollow with stronger outer cortex to maximise strength:weight ratio

48
Q

Where do tibia fractures due to torsional loads tend to occur? why?

A

distally where there is a smaller J so it is less able to resist torsional loads and therefore is more likely to fracture

49
Q

explain how a strain gauge works

A

gauge is stuck on to a surface and deforms with it to produce electrical resistance that is proportional to the strain and can be measured using an electrical circuit

50
Q

give a positive and a negative for a strain gauge

A

+ve apply straight to structure so no need for a model
-ve work on a few points measuring a few directions so
no overall idea of a complete structure

51
Q

explain photoelasticity

A

model of the structure is made from a polymer and polarised light is shone through while it is loaded in different ways to analyse patterns of stress

52
Q

explain the finite element method

A

uses computer to make a mathematical model of something where a complex structure is broken down into small parts and loads can be analysed using equations

53
Q

In the general bending equation what does y stand for?

A

displacement from neutral axis

54
Q

How do we calculate polar second moment of area for a hollow circle?

A

J = π (d4outer - d4inner)/ 32

55
Q

how do we calculate second moment of area for a circle?

A

I = πd4/64

ymax =1/2d

56
Q

how do we calculate second moment of area for a rectangle?

A

I = bd3/12 ymax =1/2d

57
Q

What does I stand for in the bending equation?

A

second moment of area

58
Q

What does the polar second moment of area of a structure indicate?

A

how resistant the material is to axial twisting

59
Q

What beam has the largest bending strength?

A

the I shaped beam

60
Q

What does the moment of area indicate about a structure?

A

how resistant the structure is to bending

61
Q

Which is more resistant to bending and twisting
a) hollow tube
b) solid bar
of the same diameter. Why?

A

hollow tube almost as resistant as solid bar because its mass is distributed further from the neutral axis so it has a greater second moment of area and polar second moment of area

62
Q

Which characteristic of a twisted bar indicates its strength:weight ratio? Why?

A

polar second moment of area
hollow bar stronger per weight
material in the centre of a bar is effectively redundant

63
Q

Why are hollow bars not stronger than solid bars in axial tension and compression?

A

changing to a hollow bar reduces the cross sectional area the force is applied on so axial strength would be reduced

64
Q

What quantifies a materials ability to resist elongation and compression ?

A

ie its stiffness

young’s modulus

65
Q

What is the symbol for shearing force?

A

V

Ortho BMSc (14 decks)

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