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Design for DifferentType of Loading

Lecture NotesDr. Rakhmad Arief Siregar

Kolej Universiti Kejuruteraan Utara Malaysia

Machine Element in Mechanical Design

Fourth Edition in SI UnitRobert L. Mott

Chapter 5

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Chapter 5 Design for Different Types of Loading

Objectives: Identify various kinds of loading commonly

encountered by machine parts, including static, repeated and reversed, fluctuating, shock or impact and random

Define the term stress ratio and compute its value for the various kinds of loading

Define the concept of fatigue Define the material property of endurance strength

and determine estimates of its magnitude for different materials

Recognize the factors that affect the magnitude of endurance strength

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Chapter 5 Design for Different Types of Loading

Objectives: Define the term design factor Specify a suitable value for the design factor Define the maximum normal stress theory of failure

and the modified Mohr method for design with brittle materials

Define maximum shear stress theory of failure Define he distortion energy theory, also called the von

Mises theory or the Mises-Hencky theory Describe the Goodman method and apply it to the

design of parts subjected to fluctuating stresses Consider statistical approaches, finite life and damage

accumulation method for design

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Types of Loading & Stress Ratio

Types of loading: Static: when a part is subjected to a load that is

applied slowly, without shock, and is held at constant value.

Repeated and Reversed: when a part is subjected to a certain level of tensile stress followed by the same level of compressive stress

Fluctuating stress: when a load-carrying member is subjected to an alternating stress with a nonzero mean.

Shock or impact: loads applied suddenly and rapidly cause shock or impact, i.e., hammer blow, weight falling

Random: when varying loads are applied that are not regular in their amplitude

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Figures

See Fig. 5-1 for static stress See Fig. 5-2 for repeated, reversed

stress See Fig. 5-4 for Fluctuating stress

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Impact Load

Strain Gage A Strain Gage B

Signal Conditioner

Digital Oscilloscope

Striker Bar

Input Bar Output BarV

Photodiode velocity sensor

(a)

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Impact Load

-60

-40

-20

0

20

40

60

Str

ess

[ M

Pa

]

10008006004002000

Time [ sec ]

Incident wave Transmitted wave x 20%

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Stress ratio

Stress ratio is one of method to characterize variation of stresses.

Maximum stress, max Minimum stress, min Mean stress, m Alternating stress, a (stress amplitude)

max

min

RrationStress

m

aArationStress

2

minmax

m

2minmax

a

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Photographs of failed parts

Failure of a truck drive shaft spline due to corrosion fatigue

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Photographs of failed parts

Failure of a stamped steel bracket due to residual stresses

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Photographs of failed parts

Failure of an automotive drag link (steering wheel)

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Photographs of failed parts

Failure of bolt in the overhead-pulley

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Photographs of failed parts

Automotive rocker-arm articulation-joint fatigue failure

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Photographs of failed parts

Valve-spring failure caused by spring surge in an over speed engine

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Photographs of failed parts

Brittle facture of a lock washer in one-half cycle

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Failure resulting from static loading

Static loading Direct tension and compression Direct shear Torsional shear Vertical shearing stresses Bending Buckling

How to predict failure if the component is subjected to combine loading?

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Ductile materialsMaximum shear stress

Also known as Tresca theory The maximum shear stress hypothesis states

that yielding begin “whenever the maximum shear stress in any element becomes equal to the maximum shear stress in a tension test specimen of the same material when specimen begins to yield”

yy SorS

21max 2

ysy SS 5.0

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Triaxial shear stresses

221

2/1

232

3/2

231

3/1

The maximum shear stress graphically represented in three dimensions

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Biaxial stress1

2

-Sy

-Sy

Sy

Sy

yy SorS

21max 2

ysy SS 5.0

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Ductile materialsDistortion energy

Also known as von Misses – Hencky theory The maximum strain energy hypothesis

predicts failure by yielding occurs “when distortion energy in a unit volume equals the distortion energy in the same when uniaxially stressed to the yield strength”

yS

2

213

232

221

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Ductile materialsDistortion energy

Under the name of octahedral shear stress this theory predicts failure occurs “whenever the octahedral shear stress for any stress state equal or exceeds the octahedral shear stress for the simple tension test at failure”

yoct S

2132

322

213

1 oct

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Triaxial stress3

2

1

The distortion energy theory graphically represented in three dimensions

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Biaxial stress

1

2Sy

Sy

-Sy

-Sy

yS

2221

21

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Problem 1

A hot-rolled steel is subjected to principle stress 1 = 210 MPa, 1 = 480 MPa and 3 = 0 MPa. By utilizing UTM the hot-rolled steel has a yield strength of Syt=Syc = 690 MPa and a true strain at fracture of f = 0.55. Estimate the factor of safety.

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Solution

Maximum shear stress theory

Distortion energy theory

MPa8.416

2

48000210210480 222

66.18.416

690

ySSF

2402

0480

221

max

44.12402

690

2 max

ySSF

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Brittle materialsMaximum normal stress

Also known as Rankine theory The maximum normal stress hypothesis

predicts failure occurs “whenever one of the three principle stresses equals or exceeds the strength”

Suppose we arrange: 1 > 2 > 3

ycyt SnSn 31

Note: n = safety factor

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Brittle materialsModification of Mohr

Coulomb-Mohr

Mod. I-Mohr

ututut SSn

S 211 00

utucutuc

B

ut

SSSnSS

211 0

1

utututut SSSn

S 211 0

utucututcu

utuc

utcu

ut SSSSSn

SS

SS

S

21

21 0

)(

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Brittle materialsModification of Mohr

Mod. II-Mohr

utututut SSSn

S 211 0

utucututcu

ut

ut

SSSSS

Sn

S

n

21

2

11 01

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Problem 2

A cast iron is subjected to principle stress 1 = 210 MPa, 1 = 480 MPa and 3 = 0 MPa.

By utilizing UTM the cast iron has a yield strength of Sut=215 MPa and Suc = 750 MPa. Estimate the factor of safety by using:(1) Coulomb-Mohr failure model(2) Mod. I-Mohr failure model(3) Mod. II-Mohr failure model

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Solution

Maximum shear stress theory

Distortion energy theory

MPa8.416

2

48000210210480 222

66.18.416

690

ySSF

2402

0480

221

max

44.12402

690

2 max

ySSF

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Fatigue

A machine components often subjected to dynamic loading such as: variable, repeated alternating or fluctuating stresses.

In most cases machine members are found to have failed under the action of repeated or fluctuating stresses.

The analysis reveals that the actual maximum stresses were below the ultimate strength of the material and quite frequently even below the yield stress

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Fatigue

This kind failure CAN NOT be detected by naked eye and even quite difficult to locate in a Magnaflux or X-ray inspection

This failure called as fatigue failure. Begins with a small crack and develops a point

of discontinuity in materials such as change in cross section, a keyway or a hole.

Once developed, the stress-concentration effect becomes greater and crack progresses more rapidly

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Endurance strength

Endurance strength of material is its ability to withstand fatigue loads.

Endurance strengths are usually charted on a graph like shown in Fig. 5-7, called as S-N diagram.

Factors affecting endurance strength: Surface finish Material factor Type of stress factor Reliability Factor Size Factor