Analysis of Engineering Structures and Material Behavior E-Book

Josip Brnic

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 663

Veröffentlichungsjahr: 2018

Beschreibung

Theoretical and experimental study of the mechanical behavior of structures under load

Analysis of Engineering Structures and Material Behavior is a textbook covering introductory and advanced topics in structural analysis. It begins with an introduction to the topic, before covering fundamental concepts of stress, strain and information about mechanical testing of materials. Material behaviors, yield criteria and loads imposed on the engineering elements are also discussed. The book then moves on to cover more advanced areas including relationships between stress and strain, rheological models, creep of metallic materials and fracture mechanics. Finally, the finite element method and its applications are considered.

Key features:

• Covers introductory and advanced topics in structural analysis, including load, stress, strain, creep, fatigue and finite element analysis of structural elements.
• Includes examples and considers mathematical formulations.
• A pedagogical approach to the topic.

Analysis of Engineering Structures and Material Behavior is suitable as a textbook for structural analysis and mechanics courses in structural, civil and mechanical engineering, as well as a valuable guide for practicing engineers.

Leseprobe

Analysis of Engineering Structures and Material Behavior

Josip Brnić

University of Rijeka – Faculty of Engineering, Department of Engineering Mechanics, Rijeka, Croatia

This edition first published 2018© 2018 John Wiley & Sons Ltd

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Josip Brnić to be identified as the author of this work has been asserted in accordance with law.

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Library of Congress Cataloging‐in‐Publication Data

Names: Brnić, Josip, 1951– author.Title: Analysis of engineering structures and material behavior / by Josip Brnić University of Rijeka.Description: First edition. | Hoboken, NJ : Wiley, 2018. | Includes bibliographical references and index. |Identifiers: LCCN 2017042809 (print) | LCCN 2017048581 (ebook) | ISBN 9781119329107 (pdf) | ISBN 9781119329060 (epub) | ISBN 9781119329077 (cloth)Subjects: LCSH: Structural analysis (Engineering)Classification: LCC TA645 (ebook) | LCC TA645 .B659 2018 (print) | DDC 624.1/7–dc23LC record available at https://lccn.loc.gov/2017042809

Cover Design: WileyCover Image: © Photo ephemera/Gettyimages

“Theory and the real process are referred to each other; theory teaches understanding of the process and the process testifies to the real event.”Let this book be dedicated to the memory of my parents, who instilled in me respect towards people.

Frequently Used Symbols and the Meaning of Symbols

Symbol

Meaning

A

Cross‐sectional area

A

0

Initial cross‐sectional area

A

1

Cross‐sectional area after deformation

A

e

Finite element area

a

Crack length

a, b, c, d, e, t

Constants in stiffness matrix

a

, [

a

]

Polynomial matrix

[

a

]

Transformation matrix

a

0

, (

a

i

)

Initial crack length

a

b

, [

a

b

]

Polynomial matrix at the boundary of finite element

a

eff

Effective crack length

a

f

Failure crack length

B

Strain‐displacement matrix

B, N

Parameters

b

Width of rectangular

C

Constant, contour of considered curve, compliance

C

Elasticity matrix (matrix of elastic constants), structural damping matrix

C, m

Constants in Paris equation(“m” is strain hardening coefficient)

C, n, p, q

Experimentally derived constants in Forman‐Newman –Koning equation

C

b

Generalized elasticity matrix (bending of plate)

C

F

, m

F

Constants in Forman equation

C

ijkl

Fourth‐order tensor (elasticity tensor, elastic matrix or stiffness matrix)

CVN

Charpy impact energy(specimen with V‐notch)

C

S

Elasticity matrix refers to shear stresses

c

e

Finite element damping matrix (local coord. System)

D

Diameter

D

Plate flexural rigidity

D, p, r

Parameters

d

ε

Differential operator

d

A

n

Differential area of an arbitrary sloping section (plane)

d

A

x

, d

A

y

, d

A

z

Differential area on x, y, z direction

d

a

Increase in crack length (length of crack:

a

)

dλ

Coefficient

E

Modulus of elasticity

E

x

,

E

y

,

E

z

Young moduli for orthotropic materials

e

Position of shear center, distance between the centroid and the neutral axis, distance

e

i

Invariants of strain deviator

e

ij

, [

e

]

Deviator strain tensor

F

Force (intensity)

F

Force, loading

F

, [

F

]

Force vector, concentrated force vector

F

cr

Critical force

F

i

,

M

i

Nodal forces

F

m

Known components of

F

R

F

R

Vector of structure nodal forces.

t

F

R

Vector of externally applied nodal forces in the considered structure at time

t

F

r

Unknown components of

F

R

F

V

Vector of volume forces

t

F

σ

Vector of nodal forces that corresponds to the element stresses at the time

t

f

Yield function, crack opening parameter (in Forman‐Newman‐de Koning Equation)

f

e

Finite element nodal forces vector (local coord. system)

f

ij

Dimensionless function

f

v

,

f

x

,

f

y

,

f

z

Volume force vector and components forces(unit)

G

Shear modulus (modulus of rigidity)

G

xy

,

G

yz

,

G

zx

Shear moduli for orthotropic materials

h

Height of rectangular

I

min

Minimum moment of inertia

I

p

Polar moment of inertia

I

t

Torsion moment of inertia

I

x

,

I

y

Axial moment of inertia (area moment of inertia about an in‐plane axis)

I

xy

Centrifugal/deviation moment of inertia(product of areas)

I

1

,

I

2

Principal (principal centroidal) moments of inertia

I

1

, 

I

2

, 

I

3

Stress tensor invariants

i

min

Minimum radius of inertia

J

J‐

integral (contour integral)

J

Jacobi matrix

J

e

Elastic part of

J

J

Ic

Fracture toughness

J

pl

Plastic part of

J

J

1

,

J

2

,

J

3

Invariants of deviator stress tensor

K

Bulk modulus, kinetic energy, stress intensity factor

K

Global stiffness matrix (structural matrix)

K/SIF, K

I

, K

II

,

K

III

Stress intensity factor, stress intensity factors for three opening modes (I, II, III)

K

*

Cyclic strength coefficient

K

c

,

K

Ic

, K

IIc

,

K

IIIc

Critical stress intensity factor

K

eff

Effective stress intensity factor

K

Ic

Fracture toughness (Plane strain fracture toughness)

K

tot

Total stress intensity factor (as effect of assembled load)

k

Constant

k

e

Finite element stiffness matrix (local coord. system)

Condensed stiffness matrix

,

, [ū

e

]

Finite element stiffness matrix, vector of nodal forces and vector of nodal displacements in global coordinate system

L

Length (of beam, element)

L

e

Effective (or free) buckling length

L

i

(i = 1,2,3)

Natural coordinates

L

0

(= G)

Gage length

L

1

Length of considered element after loading

l

Length

l, m, r

Direction cosines

l

i

(

z

),

l

i

(

L

i

),

l

i

(ξ),

l

i

(η),

l

i

(ζ)

Lagrange interpolating polynomials

M

Structural mass matrix

M

f

Bending moment (flexural moment)

M

t

Torsion moment(torque)

M

x

,

M

y

Bending moment (flexural moment) about in‐plane axis of cross‐section of element (beam), moments in the plate related to the unit of the length of plate.

M

xy

Twisting moment in plate

m

e

Finite element mass matrix (local coord. system)

N

Axial force, number of cycles, shape function

N

Axial force (internal)

N

, [

N

]

Interpolation matrix(matrix of interpolation functions, shape functions matrix)

n

Strain hardening exponent (in Holloman‐Ludwig equation), normal to the considered section (plane), degree of polynomial, number of nodes

n

*

Cyclic hardening exponent

P

Larson‐Miller parameter

P

n

(

x

)

Polynomial

Vector of an average stress

,

p

nx

,

p

ny

,

p

nz

Vector of total stress and its intensity components

R

p

,

r

p

Radius of plastic zone around crack tip

Q

Shear force, heat

Q

xz

,

Q

yz

Shear force in plate

q

Shear flow, distributed load intensity

q

i

Eigenvectors (shape vectors)

q

v

Body force

R

Radius, stress ratio

S

ij

, [

S

]

Deviator stress tensor

S

ijkl

Fourth‐order tensor(compliance tensor)

S

x

,

S

y

First (static) moment of the area with respect to axis

x

,

y

S

1

,

S

2

,

S

3

Principal values of deviator tensor

T

Temperature

T

i

Traction vector

T

m

Melting temperature

t

Wall thickness, time, thickness

t

0

, [

t

0

]

Basic transformation matrix (rotational matrix)

t

e

Finite element transformation matrix

U

Vector of structure nodal displacements

u

, [u], {

u

}

Displacement vector

u, v, w

Displacements, on x, y, z

Structural velocity vector

[

Ü

]

Structural acceleration vector

U

i

,

V

i

,

W

i

,

Φ

i

Nodal displacements

U

m

Unknown components of

U

U

r

Known components of

U

U

0

Strain energy density

U

0

D

Distortional energy density

u

e

, [

u

e

], {

u

e

}

Finite element nodal displacements vector (local coord. system)

V

Volume

V

Potential of external load

W

Work done by external forces, elastic strain energy density

W

p

Polar moment of resistance

W

t

Torsion moment of resistance

W

x

,

W

y

Section modulus

x, y, z

Cartesian coordinates

α

Angle of neutral axis, angle of principal stresses / strain

{

α

},

α

Vector of constants(vector of generalized coordinates)

α

,

β

,

γ

Functions with respect to ratio

h

/

b

of rectangular

α

T

(or

α

)

Coefficient of thermal dilatation

α

x

,

α

y

Rotation about x,y axes

β

Factor

Strain energy release rate (

crack extension force

or

crack driving force

)

.

γ

Shear strain, material constant

γ

xy

,….

γ

zx

Shear strain components

γ

R

,

γ

ρ

Angle

ΔK

th

Fatigue crack growth threshold

ΔK

Difference between

K

max

and

K

min

ΔL

,

Δ

l

Elongation

ΔT

Change in temperature

ΔV

Change in volume

ε

Strain

Strain rate

ε

, [

ε

],

ε

ij

Strain tensor

ε

i

Principal strains (dilatations)

ε

ij

Strain components

, [

ε

0

]

Mean strain tensor

ε

max

Maximum principal strain (dilatation)

)

Volumetric strain

ε

x

, 

ε

y

, 

ε

z

Normal strain components‐dilatations (directions: x, y, z)

ε

0

Mean strain (average dilatation)

ε

1

, 

ε

2

, 

ε

3

Principal strains (dilatations)

η

Coefficient of viscosity

θ

Twisting angle per unit length

κ

Curvature

κ

x

,

κ

y

Curvature of the midsurface

λ

Slenderness, introduced substitute

λ, μ

Lame constants

μ

Coefficient of friction

ν

Poisson ratio

ν

xy

,

ν

xz

,

ν

yx

,

ν

yz

,

ν

zx

,

ν

zy

Generalized Poisson ratio (orthotropic materials)

ξ, η, ζ

Coordinates, dimensionless coordinates

Π

Total potential (total potential energy)

ρ

Radius

σ

, [

σ

],

σ

ij

Stress tensor

σ

a

Stress amplitude

σ

all

Normal stress allowable

σ

cr

Critical stress

σ

e

Equivalent stress

σ

ij

Stress components

Mean (spherical) stress tensor

, [

σ

0

]

Mean (spherical) stress tensor

σ

m

,

UTS

,

US, σ

US

Ultimate tensile strength, mean stress

σ

max

,

σ

min

Stress maximum, minimum

σ

n

Normal stress on an arbitrary sloping section (plane)

σ

oct

Normal octahedral stress

σ

x

,

σ

y

, 

σ

z

Normal stress components(directions: x, y, z)

σ

0

Mean normal stress, initial stress in rheological models

σ

0.2

,

YS, σ

YS

,

σ

Y

0.2 offset yield strength

σ

1

,

σ

2

,

σ

3

Principal stresses, stresses in rheological models

τ

all

Shear stress allowable

τ

I

,

τ

II

Extreme values of shear stresses at the directions I, II (plane stress state)

τ

max

Shear stress maximum

τ

n

Shear stress on an arbitrary sloping section (plane)

τ

oct

Shear octahedral stress

τ

x

,…..

τ

zx

Shear stress components

τ

y

Shear stress associated with yielding in uniaxial tension

τ

1

, 

τ

2

, 

τ

3

or

τ

I

, 

τ

II

, 

τ

III

Extreme values of shear stresses at three –dimensional state of stress

Φ

Prandtl stress function

φ

Angle, twisting angle, angle of an arbitrary plane (section) with respect to perpendicular plane

φ

x

,

φ

y

,

φ

z

Rotational displacement

ψ

Reduction in area(contraction of cross‐sectional area), radius ratio, S. Venant warping function

ω

i

Eigenvalues (free vibration frequencies)

Principal SI Units and the US Equivalents

Quantity

SI Unit

US Equivalent

length

meter (m)

39.370079 inch (in)

meter (m)

3.2808399 feet (ft)

area

millimeter

2

(mm

2

)

0.001549907 in

2

meter

2

(m

2

)

10.7639104 feet

2

(ft

2

)

mass

kilogram (kg)

2.2045855 lb – mass

kilogram (kg)

0.06852177 slug (lb s

2

/ft)

volume (solid)

meter

3

(m

3

)

35.3146667 feet

3

(ft

3

)

meter

3

(m

3

)

61012.8 inch

3

(in

3

)

volume (liquid)

liter (l)

0.03531566 feet

3

(ft

3

)

liter (l)

0.26417944 gallon (gal)

force

newton (N = kg m/s

2

)

0.22480894 pound (lb, lbf)

kilonewton (kN)

0.22480894 kilopound (kip)

stress/pressure

pascal (Pa = N/m

2

)

0.855470208 pound/foot

2

(psf)

kilopascal (kPa/m

2

)

0.145037944 pound/inch

2

(psi)

megapascal (MPa = N/mm

2

)

0.145037944 kilopound/inch

2

(ksi)

moment of a force

newton meter (N · m)

8.8507456 pound inch (lb · in)

newton meter (N · m)

0.73756215 pound · foot (lb ft)

energy/work

joule (newton meter)

0.73756215 pound · foot (lb ft)

velocity

meters per second (m/s)

39.37 inches per second (in/s)

meters per second (m/s)

3.2808399 feet per second (ft/s)

density

kilograms per cubic meter (kg/m

3

)

0.06238 pounds per cubic foot (lb/ft

3

)

stress intensity factor

SIF

(

K

); fracture toughness (

K

Ic

)

(MPa

);… (

K

)

1.099 ksi

…(

SIF

)

SI Prefixes, Basic Units, Physical Constants, the Greek Alphabet

SI Prefixes

Prefix

tera

giga

mega

kilo

centi

milli

micro

nano

pico

SI symbol

T

G

M

k

c

m

μ

n

p

Factor

10

12

10

9

10

6

10

3

10

−2

10

−3

10

−6

10

−9

10

−12

Basic Units

Quantity

SI

US

length

meter (m)

foot (ft)

mass

kilogram (kg)

slug (

)

time

second (s)

second (sec)

force

newton (

)

pound (lb)

temperature

degree:     Kelvin (K)         Celsius (°C)

degree:     Fahrenheit (°F)         Rankine (°R)

T

K

 = 

T

°

C

 + 273.15

T

°F

 = 

T

°R

 + 459.67

Physical Constants

Quantity

SI

US

acceleration of gravity(

g

)

9.80665 m/s

2

32.1740 ft/s

2

density (

ρ

), unit weight of water (at 4 °C = 39.2 °F)

1000 kg/m

3

62.43 pcf

Normal atmospheric pressure (at)

101,325 kPa 0.101325 MPa

14.6960 psi

The Greek Alphabet

α

A

Alpha

ν

N

Nu

β

B

Beta

ξ

Ξ

Xi

γ

Γ

Gamma

ο

O

Omicron

δ

Δ

Delta

π

Π

Pi

ε

E

Epsilon

ρ

P

Rho

ζ

Z

Zeta

σ

Σ

Sigma

η

H

Eta

τ

T

Tau

θ

Θ

Theta

υ

Y

Upsilon

ι

I

Iota

φ

Φ

Phi

κ

K

Kappa

χ

χ

Chi

λ

Λ

Lambda

ψ

Ψ

Psi

μ

M

Mu

ω

Ω

Omega

Important Notice Before Reading the Book

The author and publisher of this book have invested reasonable efforts in its preparation. The book presents material that is the subject of the author's research and lectures and covers a wide spectrum of engineering disciplines. It provides a concise written guide to theories and applications, showing the methods for solving particular problems. However, the book contains the author’s interpretations of the above and not facts. The material in the book is provided as a study aid for the reader and not for business‐related activity. Since the book may contain different types of error, the author and the publisher make no warranty of any kind with regards to any of the content of the book or its usage. The author and the publisher shall not be liable in any event for any damages in connection with the usage of any contents of this book. By proceeding to read this book, the reader agrees with the above. This note is a part of this book.

Preface

This book, in its concise but clear form, provides to students, engineers and researchers an insight into the analysis of possible stresses and strains on engineering components which can arise when these components are subjected to loads. It also provides an insight into experimental investigations of the properties of materials from which the components are made. As such, the book is organized in such a way as to encourage, in engineering students and engineers, development of the ability to analyze an existing problem and solve it in a simple but logical way.

The contents of this book refer to matters related to the strength of materials, the theory of stress and strain, the theory of elasticity, the testing of materials, fracture mechanics, creep and the finite element method. In other words, the book covers topics related to structural analysis and the selection of materials, in order to create optimal designs and products.

Engineering components are intended to carry load, to conduct heat, to be exposed to wear and/or corrosive environments and so on. Whatever their predicted service conditions, the components need to be shaped and, of course, manufactured. The designer and manufacturer of a structure should be familiar with all of the above requirements relating to the stress and strain analysis of a structure as well as with the behavior of materials under load.

This book is intended as a reference of lasting value. The author would be grateful to anyone who wishes to contribute suggestions through which to improve the content of the next edition of this book.

Josip BrnićRijeka, November 2017.

About the Author

Josip Brnić, DSc, is a Professor in the Department of Engineering Mechanics at the Faculty of Engineering, University of Rijeka, Croatia. He graduated in Mechanical Engineering at the Faculty of Engineering, University of Rijeka. He received his MSc in Mechanical Engineering from the Faculty of Mechanical Engineering, University of Ljubljana, Slovenia in 1983 and his DSc in Mechanical Engineering from the Faculty of Engineering, University of Rijeka in 1988. He received the title of Consulting Professor from the Harbin Institute of Technology, Harbin, China in 2012, and the title of Honorary Professor from the Henan Polytechnic University, Jiaozuo, China in 2011.

At the beginning of his career, he worked in parallel on the “Brodoprojekt”, dealing with structural analysis and design, mainly of underwater objects, and at the Faculty of Engineering, dealing with research and teaching. After this period (1978–2000), he moved to permanent employment at the Faculty of Engineering. He was Vice Dean and Dean of the Faculty of Engineering of the University of Rijeka, Vice Rector and Rector of the University of Rijeka. He has also been a member of the National Council for Science of the Republic of Croatia.

In addition, Professor Brnić is an Associate member of the Croatian Academy of Sciences and Arts. He is the reviewer of papers for several prestigious international journals indexed in CC. His research, teaching and publications are in the areas of computational and experimental mechanics, finite element structural analysis and materials testing. He has authored more than 300 scholarly articles and ten books. For achievements in his research he has received several awards, including the Award of the Croatian Academy of Arts and Sciences in the field of Engineering in 2010 and a Lifetime Achievement award from the University of Rijeka in the field of Engineering Sciences in 2012.

Acknowledgements

During the years of my work in teaching, research, design and writing, I have met a lot of respectable people to whom I am grateful for everything that I have learned from them. We have shared beautiful but also hard times and temptations. My experience and knowledge I have tried to convey to others, and now, in writing this book, I am trying to record certain facts and results and leave them to future generations.

Among those whose contributions to my education are unforgettable are professors from the days of my primary, secondary and university education, professors from my masters and doctoral degree education, professors and friends from Croatian and foreign universities, many colleagues and friends from industry and many others.

A particular source of inspiration when choosing material and methods of presentation were my students, who always find a specific approach to problem solving.

In terms of encouragement and support in the preparation of this book and cooperation in research, my gratitude goes to my friends and colleagues with whom I have worked for many years. My special thanks go to Assistant Professor Sanjin Krscanski, DSc, for the creation and preparation of the figures in this book. I also thank those at Wiley who have been involved in the preparation, editing and production of this edition.

1Introduction

1.1 The Task of Design and Manufacture

The design of structures and machines that need to be safe, reliable and economical, and the estimation of their service life at some point in time, has recently been based on iterative procedures, capacitive computers and numerical analysis. In recent times, a very powerful tool in the aforementioned analysis has been the finite element method.

Practically all fields of human activity are involved in design processes. Problems that need to be solved relate to transportation, buildings, water systems, communication systems, and so on [1]. The same goes for the production processes and metal‐forming processes by which products are created.