Deformable body Mechanics Unit 2: stress analysis (class)

Question 1

What is shear stress?

Answer 1

slippage of surfaces or planes within a material

Question 2

What is shear stress equal to?

Answer 2

shearing force/ sheared area

Question 3

What are the units of shear stress?

Answer 3

pascal

Question 4

What does shear strain quantify?

Answer 4

the angular deformation of a material undergoing shear stress

Question 5

What unit do we use for shear strain?

Answer 5

radians

Question 6

What is shear strength?

Answer 6

the maximum shearing force a material can withstand before it fractures

Question 7

How do we calculate shear strength?

Answer 7

shear force at failure / sheared area

Question 8

What is the modulus of rigidity equal to

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

Answer 8

a) shear stress/ shear strain

b) the gradient up to a limiting stress

Question 9

What symbol represents modulus of rigidity?

Answer 9

G

Question 10

Where does the maximum shear stress occur?

Answer 10

45 degrees to axial loading

Question 11

How do we calculate max shear stress?

Answer 11

axial stress/ 2

Question 12

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

Answer 12

G = E / 2 (1+v)

Question 13

What is 1+v?

Answer 13

Poisson ratio

Question 14

What is the modulus of rigidity equal to?

Answer 14

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

Question 15

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

Answer 15

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

Question 16

give the two types of bending

Answer 16

cantilever

3 point fixation

Question 17

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

Answer 17

on the outer surfaces

Question 18

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

Answer 18

the neutral axis

- it stays the same length

Question 19

What is the bending moment?

Answer 19

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

Question 20

What is the bending moment dependent on?

Answer 20

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

Question 21

When does the maximum magnitude for bending moment occur?

Answer 21

at the maximum displacement

Question 22

What is the bending resistance of a beam dependent on?

Answer 22

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

Question 23

How do we quantify the cross-sectional shape?

Answer 23

use the second moment of area (I)

Question 24

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

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

Answer 24

A

Question 25

What is the general bending equation for a beam?

Answer 25

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

Question 26

what symbol represents shear stress?

Answer 26

τ tau

Question 27

what is tan ϕ and therefore sheer strain equal to?

Answer 27

distance sheared / distance between two shearing forces

Question 28

what is the unit for the modulus of rigidity?

Answer 28

pa

Question 29

what causes torsional stress?

Answer 29

twisting due to the application of a moment

Question 30

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

Answer 30

torsion

Question 31

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

Answer 31

zero at central axis and maximum at outer surface

Question 32

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

Answer 32

shorter bar

Question 33

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

Answer 33

a) shear strain | b) angle of twist

Question 34

What quantifies the resistance to shearing force in torsion?

Answer 34

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

Question 35

What are the units for modulus of rigidity?

Answer 35

N/m2 or Pa

Question 36

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

Answer 36

φ = θ x radius / length

Question 37

how do we converts degrees to radians ?

Answer 37

multiply by π/180

Question 38

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

Answer 38

hollow bar is more resistant than a solid bar

Question 39

What is the polar second moment of area?

Answer 39

a measure of distribution of the material about a central axis

Question 40

What symbol represents polar second moment of area?

Answer 40

J

Question 41

What are the units for polar second moment of area?

Answer 41

metres to the power of 4

Question 42

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

Answer 42

J = π d4 / 2

Question 43

What is the general equation for torsion?

Answer 43

M/J = T/R = Gθ/L

Question 44

in the general equation for torsion what is a) M? b) T? c) R? d) G? e) θ? f) L? g) J?

Answer 44

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

Question 45

What is the angle of twist measured in?

Answer 45

radians

Question 46

What is shear stress a) proportional to? b) inversely proportional to?

Answer 46

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

Question 47

How are long bones designed to resist torsional loads?

Answer 47

hollow with stronger outer cortex to maximise strength:weight ratio

Question 48

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

Answer 48

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

Question 49

explain how a strain gauge works

Answer 49

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

Question 50

give a positive and a negative for a strain gauge

Answer 50

+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

Question 51

explain photoelasticity

Answer 51

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

Question 52

explain the finite element method

Answer 52

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

Question 53

In the general bending equation what does y stand for?

Answer 53

displacement from neutral axis

Question 54

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

Answer 54

J = π (d4outer - d4inner)/ 32

Question 55

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

Answer 55

I = πd4/64 | ymax =1/2d

Question 56

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

Answer 56

I = bd3/12 ymax =1/2d

Question 57

What does I stand for in the bending equation?

Answer 57

second moment of area

Question 58

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

Answer 58

how resistant the material is to axial twisting

Question 59

What beam has the largest bending strength?

Answer 59

the I shaped beam

Question 60

What does the moment of area indicate about a structure?

Answer 60

how resistant the structure is to bending

Question 61

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

Answer 61

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

Question 62

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

Answer 62

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

Question 63

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

Answer 63

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

Question 64

What quantifies a materials ability to resist elongation and compression ?

Answer 64

ie its stiffness young's modulus

Question 65

What is the symbol for shearing force?

Answer 65

V