Unit 2 - Stress analysis

Question 1

Name the 2 types of axial loading

Answer 1

Tensile

Compressive

Question 2

Describe shear stress

Answer 2

When forces act in opposite directions to shear/slip surfaces within a material

Question 3

What is the formula for shear stress?

Answer 3

Shear stress (τ - tau) = shearing force (V)/shearing area (A)

Pa

Question 4

What is shear strain equivalent to?

Answer 4

Φ = Angle sheared (in rads)

Question 5

What is shear strength & how is it calculated?

Answer 5

Maximum shear stress a material can withstand before failing

Shear strength = shear force at failure/sheared area

Question 6

What is the modulus of rigidity?

Answer 6

G = shear stress/shear strain

Pa

Higher G = more resistant to shearing

Question 7

Shear stress can also occur during axial loading

Where does the greatest shear stress occur in this instant & how is it calculated?

Answer 7

Largest shear stress occurs at 45 degrees to axial loading

Max shear stress = axial stress/2

Cortical bone <1/2 as strong in shear than compression & tends to break at 45 degrees to axial load

Question 8

How are modulus of rigidity & Young’s modulus related?

Answer 8

G = E / 2(1+v)

v = Poisson ratio

Question 9

Name 2 types of bending

Answer 9

Cantilever

3-point

Question 10

What happens to the surfaces of a material when it is bent?

Answer 10

One side is compressed & the other elongated (tensile load)

Question 11

What is the neutral plane of a material that is being bent?

Answer 11

An axis where there is no compressive or tensile stresses

Question 12

What equation would you use to find variation in stress of a bent beam (bending stress)?

Answer 12

σ = εE = yE/r

E = Young’s modulus
y = displacement of segment under examination from neutral axis
r - radius of circle containing neutral axis

Question 13

Where is a bent material most likely to fail?

Answer 13

At the surfaces

Question 14

What is a bending moment?

Answer 14

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

M = Fd

Question 15

When does the maximum bending moment of a bar occur?

Answer 15

When F is applied at largest distance possible (i.e. length of bar)

Question 16

When is a bedning moment:

• positive?
• negative?

Answer 16

Positive = sagging bar )

Negative = hogging bar (

Question 17

What 3 things is the bending strength of a beam dependent on?

Answer 17

Strength of material

Cross-sectional area

Cross-sectional shape

Question 18

How would a beam with its mass distributed away from its neutral axis resist bending moments compared to once with mass closer to axis?

Answer 18

Better able to resist when mass distributed away from neutral axis

Question 19

What is the second moment of area (I)?

Answer 19

A geometrical property of an area which reflects how its mass is distributed from neutral axis

Larger I = further material of the beam is concentrated away from neutral axis

Question 20

How do you calculate the maximum bending moment that a beam can resist?

Answer 20

M(max) = σI / y(max)

σ = bending stress
I = second moment of area
y(max) = max displacement of extreme layer of beam neutral axis

Question 21

What is the general equation for bending?

Answer 21

M/I = σ/y = E/r

MISYER

Question 22

What is the equation for the second moment of area for:

• rectangular cross section
• circular cross section

Answer 22

I = bd^3 / 12
y(max) = d/2

I = πd^4 / 64
y(max) = d/2

(learn these 2 and can work out the rest)

Question 23

What is torsional stress?

Answer 23

Stress caused by twisting due to application of a moment

Question 24

Where is maximal torsional stress experienced?

Answer 24

At outer surface

Question 25

How do you calculate shear stress in a bar being twisted?

Answer 25

t = Gθr / L

Question 26

What is the equation for shear strain in a bar that is being twisted?

Answer 26

Φ = θr / L

Equal to angle of shear (constant along bar)

Question 27

What is the polar second moment of area (J)?

Answer 27

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

Units = m^4

Question 28

What is the equation for the twisting moment of a bar?

Answer 28

M = JGθ / L

J = polar second moment of area
G = modulus of rigidity
θ = angle of twist (rads)
L = length of bar

Question 29

What is the polar second moment of area for a circular cross-section?

Answer 29

J = πd^4 / 32

Take away d^4 of inner tube from outer for hollow

Question 30

What is the general equation for torsion?

Answer 30

M/J = t/r = Gθ/L

M = twisting moment
J = polar second moment of area
t = shear stress
R = radius of cross section
G = modulus of rigidity
θ= angle of twist (in rads)
L= length

Question 31

Why is it better to have hollow bars if they are being twisted?

Answer 31

Outer surface place of greatest stress & at centre there is zero deformation therefore in a solid bar most of the material is being stressed below max allowable

When weight reduction and material saving are important, the material near the centre is effectively redundant.

To hollow the bar increases the strength to weight ratio

Question 32

How are bones designed to resist torsional loads?

Answer 32

Hollow with strong cortical bone forming outer layer (maximising strength-weight ratio)

Question 33

Why is distal tibia more prone to fractures from torsional loads?

Answer 33

Distal polar second moment of area of the tibia is smaller than the proximal

Although amount of bone tissue is the same the distal part is less able to resist torsion

Question 34

Why may muscles contract if not causing a movement?

Answer 34

To alter the distribution of stress within bone

Muscles may contact to produce compressive loading on a bone and eliminate tensile loading (since bone is stronger in compression)

Question 35

Why are tired athletes more likely to fracture?

Answer 35

Fatigued muscles less able to control distribution of stress within their bones

Question 36

Name 3 methods of stress analysis that can be used for more complicated structures

Answer 36

Strain gauge

Photoelasticity

Finite element method

Question 37

How does a strain gauge work?

Answer 37

A thin metal foil between 2 insulating films is cemented to surface of material required to measure strain

As material changes dimension with changes in stress, the length of the gauge will also change, altering resistance of foil (proportional to strain)

Question 38

Describe photoelasticity

Answer 38

Useful for structures with complicated geometry/complicated loading

When certain plastics are subjected to force, some of their optical properties change to the stresses developed. Material becomes birefringent. Polarised light passing through material splits into 2 beams creating a fringe pattern

Stress can be quantified by counting number of fringes

Question 39

Describe finite element modeling

Answer 39

Creates mathematical model & is reliant on power of modern computing to perform vast number of operations quickly

Splits structure up into various small sub-regions (elements)

Elements associated with a number of nodes for which equations are created and solved to calculate stress