Materials- Fatigue, Bending and Twisting

Question 1

What is fatigue?

Answer 1

Failure at relatively low stress levels of structures that are subjected to fluctuating and cyclic stresses.

Question 2

Describe fatigue

Answer 2

Where a material is weakened due to repeatedly applied loads. It is the progressive and localised structural damage that occurs when a material is subjected to cyclic loading.

Question 3

What is fatigue life?

Answer 3

The total number of stress cycles of a specified character that will cause a fatigue failure at some specified stress amplitude

Question 4

What is fatigue limit (endurance limit)?

Answer 4

The maximum stress amplitude level below which a material can endure an essentially infinite number of stress cycles and not fail

Question 5

What is fatigue strength?

Answer 5

The maximum number of stress level that a material can sustain without failing for some specified number of cycles

Question 6

What is stress amplitude?

Answer 6

The stress a material can withstand before plastic deformation occurs.

Question 7

Describe the S-N curve

Answer 7

y axis is S (stress amplitude). x axis is N (number of stress cycles to failure) and is logarithmic scale, e.g 10^3, 10^4, etc. For a material that displays a fatigue limit, the line goes diagonally down from top left (quite straight) and then curves to horizontal at the endurance limit. For a material that doesn’t display a fatigue limit, it is shaped like an exponential decrease curve.

Question 8

Define creep and describe the conditions necessary for it

Answer 8

The time-dependent and permanent deformation of materials when subjected to a constant load or stress. This occurs when the material is placed in service at elevated temperatures and exposed to static mechanical stresses.

Question 9

What is bending?

Answer 9

It characterises the behaviour of a slender structural element subjected to an external load applied perpendicular to the longitudinal axis of that element.

Question 10

What is the curvature of a slender object being bent?

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Answer 10

κ=2nd partial derivative u respect to x
Equal to 1/R
u is distance moved by object from its original position which will be a function of x (the horizontal axis through the length of the object).
κ is curvature
R is radius of curvature which is radius of circle formed if you continue the curve all the way around (assumed constant).

Question 11

Assumptions made in the Euler-Bernoulli theory of bending

Answer 11

The beam is initially straight, unstressed and symmetric. The material of the beam is linearly elastic, homogeneous and isotropic. No plastic deformation occurs. The Young’s modulus for the material is the same in tension and compression. All deflections are small so that the planar cross-sections remain planar before and after bending. The applied load is in pure bending moment (no twisting).

Question 12

What is a homogeneous material?

Answer 12

One that has a uniform composition throughout and can not be mechanically separated into different materials.

Question 13

Describe how stress in a bending material varies through its cross-section

Answer 13

At one surface (top or bottom) of the CSA there is maximum tension stress and at the opposite surface there is maximum compressive stress. On a y against stress graph, line is of form y=mσ and the stress is negative for the compression side. y is distance from the neutral axis to the point where you measure the stress (not same as u).

Question 14

What is the neutral axis in a bending material?

Answer 14

The line, surface or region of zero stress between the two surfaces of the material through the material

Question 15

How do we determine if the bending moment is positive or negative?

Answer 15

If it causes compression at the top surface, by convention this is a positive moment. Causes a smiley face.

Question 16

What are the beam theory equations?

Answer 16

σ/y = M/I = Eκ
Where σ is stress (at either end)
y is distance from neutral axis
M is bending moment (at either end)
I is second moment of area (m^4)
E is Young’s modulus 
κ is curvature

Question 17

What is flexures rigidity?

Answer 17

M/κ

Equal to EI

Question 18

What is bending stiffness?

Answer 18

The resistance offered by a structure while undergoing bending.
Formula of S=F/δ=C1EI/L^3
S is bending stiffness
δ is maximum deflection (or u)
C1 is geometry constant for the shape of the beam.

Question 19

What is the sending moment of area (I)?

Answer 19

The integral of y^2 with respect to the CSA across the cross-section

Question 20

Describe the I beam cross section

Answer 20

For an upright I shape, centre vertical bit is web, the two horizontal bits at top and bottom are flanges. Flanges and web have same thickness (T). The overall height is H. The width is B.

Question 21

What is torsion?

Answer 21

Twisting due to an applied torque

Question 22

What is a shaft?

Answer 22

A long and slender structural member that is subject to a torque (moment) about its long axis.

Question 23

How does the cross section of a circular shaft vary when subjected to torsion?

Answer 23

It doesn’t, every cross section remains plane and undistorted

Question 24

When a torque is applied to the end of a circular bar, what does the angle the end twists (θ) depend on?

Answer 24

The length of the bar, the magnitude of torque, the shear modulus (G). It is a function of the length of the bar or the distance between the cross section in question and the other end face (x)

Question 25

For a circular bar under torsion, how does the inner cone angle (γ) vary across its length?

Answer 25

It is constant along the length. It is not the same as θ.

Question 26

What are the torsion equations?

Answer 26

τ/r=T/J=Gθ/L
τ is shear stress
r is radius (from point in question to centre of circle cross-section)
T is torque
J is polar second moment of area
G is shear modulus

Question 27

How does shear stress for a circular bar under torsion vary with radius from the centre of its cross-section?

Answer 27

Graph of r against τ is of form y=mx. So maximum shear stress at the circumference of the circular cross-section

Question 28

At what angle in the profile cross-section of a circular beam under torsion is the shear stress at a maximum?

Answer 28

45°