Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

MEC302 > Lecture 1-4 > Flashcards

Lecture 1-4 Flashcards

1
Q

Give the two definitions for integrity

A
  1. An unimpaired condition

2. The quality of being whole and complete

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What are the dimensions of an axi-symmetric stress distribution?

A

3D stress distribution:

-Radial, Hoop, Axial

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What are the key components for which axi-symmetric stress is considered?

A
  • Thick disks subjected to rotation

- Thick cylinders subjected to pressure loading

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What is represented by R(B), sigma(theta), sigma(r) and dr?

A

R(B): body force
sigma(theta): hoop stress
sigma(r): radial stress
dr: thickness of element

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What is the first step in setting up axi-symmetrical calculations?

A

Set up equilibrium equation on element

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What assumptions are made to simplify the axi-symmetric equilibrium equation?

A
  • sin(dtheta/2) = dtheta/2
  • Second order terms can be neglected
  • Stress field is asymmetric
  • Stresses vary only with radius
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What must be insured due to the deformation of the material of the element?

A

Compatibility of displacements

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

How is compatibility of displacements ensured?

A

Considering the geometry of a typical displacement/deformation using ELASTIC HOOKE’S LAW relationships

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is represented by:

u, du, r, dr?

A

u: radial displacement at r
du: deformation
r: distance from centre to inner edge
dr: original thickness

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Give the strains (not in terms of stresses) for E(r), E(A), E(theta)
(Where E is epsilon)

A 
E(r) = du/dr
E(A) = dw/dA
E(theta) = u/r
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Give the equation and units for R(B) in relation to centrifugal force

A

R(B) = rhoomega^2r

In rad/s

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What assumption is made about E(A) in a THICK DISK and why?

A

The axial strain is constant with radius

The plane sections are assumed to remain plane

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

How many boundary conditions are required to solve for A and B?

A

Two, as there are two unknowns

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What does the assumption of E(A) being constant lead to?

A

dE(A)/dr = 0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What assumption is made about axial stress in a THIN DISK?

A

Sigma(A) = 0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What does assuming sigma(A) = 0 lead to?

A

A different set of integration constant equations (Jim pls fix this wording I’ve forgotten maths)

17
Q

What boundary conditions are used for a solid rotating shaft?

A 
sigma(Ro) = 0
B = 0
18
Q

Explain the boundary conditions for a solid rotating shafts

A

At Ro there is nothing to ‘push’ against, so there is no area for a stress to occur
In the centre, B/0 would be infinite if B=/= 0

19
Q

What are the boundary conditions for a hollow rotating shaft?

A

Sigma(Ro) and sigma(R1) are 0

20
Q

Explain the boundary conditions for a hollow rotating shaft

A

There is no stress as there is nothing to ‘push’ against- no area for force to be applied to

21
Q

How do you solve the equations for sigma(R1) and sigma(R0)?

A

Sigma(R1) - sigma(R0)

22
Q

What do the Lame equations apply to?

A

Thick cylinders subjected to internal and external pressure

23
Q

What happens to the body force term in the Lame equations?

A

Body forces are 0 as omega = 0

24
Q

What happens to the radial and hoop stresses as r decreases?

A

They both increase

25
Q

What sign do hoop and radial stresses have for internal pressure conditions?

A

Hoop: positive
Radial: negative

26
Q

What are the hoop and radial stresses also, due to the problems being axisymmetric?

A

They are principal stresses
sigma(1) = hoop stress
sigma(2) = radial stress

27
Q

How can max shear stress be calculated using the principal stress equivalents?

A

tau(max) = (sigma(1)-sigma(2)

28
Q

What does k represent in an internally pressurised cylinder?

A

r(o)/r(i)

29
Q

Why would an initial compressive hoop stress be induced in a cylinder?

A

Compression is negative, so initial pressurisation (which is tensile, so positive) overcomes the initial negative, bringing hoop stress to 0

30
Q

How can one contain a higher pressure in practice?

A
  • Shrink fit
  • Wind wire onto cylinder under tension
  • Overstrain once with a pressure beyond yield, to leave compressive residual stress distribution near bore
31
Q

How does the appearance of the hoop strress vs r graph change from a single to compound cylinder?

A

Initially lower, then spikes at the interface to above

32
Q

What is needed to produce a shrink fit?

A

Outer diameter of inner cylinder must be slightly greater than inner diameter of outer cylinder
Called ‘diametral interference’

33
Q

What equation can be used to calculate diameter change in a shrink fit?

A 
deltaD = D epsilon(theta) 
Where epsilon(theta) is hoop strain
34
Q

What happens to the calculation for diametral interference when both cylinders are the same material?

A

Poisson’s ratio can be ignored and E can be factored out

35
Q

For an interference fit of a sleeve on a solid shaft, what are the initial conditions?

A 
sigma(r) = sigma(theta) = C = -P (uniform across shaft)
B = 0 to avoid infinite stress at r = 0

MEC302 (13 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions