Instructor’s Solutions Manual
for
Dynamics of Structures: Theory and
Applications to Earthquake
Engineering, 6th edition,
ST
By Anil Chopra
(All Chapters 1-24, 100% Original
U
Verified, A+ Grade)
D
YL
This is The Only Original and
AB
Complete Instructor’s Solutions
Manual.
Instant Download.
, Table of Content
PART I: SINGLE-DEGREE-OF-FREEDOM SYSTEMS
Equations of Motion, Problem Statement, and Solution Methods
Free Vibration
Response to Harmonic and Periodic Excitations
Response to Arbitrary, Step, and Pulse Excitations
Numerical Evaluation of Dynamic Response
Earthquake Response of Linear Systems
Earthquake Response of Inelastic Systems
Generalized Single-Degree-of-Freedom Systems
PART II: MULTI-DEGREE-OF-FREEDOM SYSTEMS
ST
Equations of Motion, Problem Statement, and Solution Methods
Free Vibration
Damping in Structures
Dynamic Analysis and Response of Linear Systems
U
Earthquake Analysis of Linear Systems
Analysis of Nonclassically Damped Linear Systems
Reduction of Degrees of Freedom
D
Numerical Evaluation of Dynamic Response
Systems with Distributed Mass and Elasticity
YL
Introduction to the Finite Element Method
PART III: EARTHQUAKE RESPONSE, DESIGN, AND EVALUATION OF
MULTISTORY BUILDINGS
Earthquake Response of Linearly Elastic Buildings
AB
Earthquake Analysis and Response of Inelastic Buildings
Earthquake Dynamics of Base-Isolated Buildings
Earthquake Dynamics of Building–Soil Interaction
Structural Dynamics in Building Codes
Structural Dynamics in Building Evaluation Guidelines
, CHAPTER 1
Problem 1.1
Starting from the basic definition of stiffness, determine
the effective stiffness of the combined spring and write the
equation of motion for the spring–mass systems shown in
Fig. P1.1.
Figure P1.1
ST
Solution:
If ke is the effective stiffness,
fS = keu
u
k1 u
U
fS fS
k2 u
D
Equilibrium of forces: fS = (k1 + k2 ) u
YL
Effective stiffness: ke = fS u = k1 + k2
Equation of motion: mu + keu = p(t )
AB
1
Copyright © 2023 Pearson Education, Inc.
, Problem 1.2
Starting from the basic definition of stiffness, determine
the effective stiffness of the combined spring and write the
equation of motion for the spring–mass systems shown in
Fig. P1.2.
Figure P1.2
Solution:
If ke is the effective stiffness,
ST
fS = keu (a)
u
fS
U
If the elongations of the two springs are u1 and u2 ,
u = u1 + u2 (b)
Because the force in each spring is fS ,
D
fS = k1u1 fS = k2u2 (c)
Solving for u1 and u2 and substituting in Eq. (b) gives
f 1 1 1
= S + kS
fS f = +
YL
2
ke k1 ke k1 k2
k1 k2
ke = k + k
1 2
Equation of motion: mu + keu = p(t ).
AB
2
Copyright © 2023 Pearson Education, Inc.
for
Dynamics of Structures: Theory and
Applications to Earthquake
Engineering, 6th edition,
ST
By Anil Chopra
(All Chapters 1-24, 100% Original
U
Verified, A+ Grade)
D
YL
This is The Only Original and
AB
Complete Instructor’s Solutions
Manual.
Instant Download.
, Table of Content
PART I: SINGLE-DEGREE-OF-FREEDOM SYSTEMS
Equations of Motion, Problem Statement, and Solution Methods
Free Vibration
Response to Harmonic and Periodic Excitations
Response to Arbitrary, Step, and Pulse Excitations
Numerical Evaluation of Dynamic Response
Earthquake Response of Linear Systems
Earthquake Response of Inelastic Systems
Generalized Single-Degree-of-Freedom Systems
PART II: MULTI-DEGREE-OF-FREEDOM SYSTEMS
ST
Equations of Motion, Problem Statement, and Solution Methods
Free Vibration
Damping in Structures
Dynamic Analysis and Response of Linear Systems
U
Earthquake Analysis of Linear Systems
Analysis of Nonclassically Damped Linear Systems
Reduction of Degrees of Freedom
D
Numerical Evaluation of Dynamic Response
Systems with Distributed Mass and Elasticity
YL
Introduction to the Finite Element Method
PART III: EARTHQUAKE RESPONSE, DESIGN, AND EVALUATION OF
MULTISTORY BUILDINGS
Earthquake Response of Linearly Elastic Buildings
AB
Earthquake Analysis and Response of Inelastic Buildings
Earthquake Dynamics of Base-Isolated Buildings
Earthquake Dynamics of Building–Soil Interaction
Structural Dynamics in Building Codes
Structural Dynamics in Building Evaluation Guidelines
, CHAPTER 1
Problem 1.1
Starting from the basic definition of stiffness, determine
the effective stiffness of the combined spring and write the
equation of motion for the spring–mass systems shown in
Fig. P1.1.
Figure P1.1
ST
Solution:
If ke is the effective stiffness,
fS = keu
u
k1 u
U
fS fS
k2 u
D
Equilibrium of forces: fS = (k1 + k2 ) u
YL
Effective stiffness: ke = fS u = k1 + k2
Equation of motion: mu + keu = p(t )
AB
1
Copyright © 2023 Pearson Education, Inc.
, Problem 1.2
Starting from the basic definition of stiffness, determine
the effective stiffness of the combined spring and write the
equation of motion for the spring–mass systems shown in
Fig. P1.2.
Figure P1.2
Solution:
If ke is the effective stiffness,
ST
fS = keu (a)
u
fS
U
If the elongations of the two springs are u1 and u2 ,
u = u1 + u2 (b)
Because the force in each spring is fS ,
D
fS = k1u1 fS = k2u2 (c)
Solving for u1 and u2 and substituting in Eq. (b) gives
f 1 1 1
= S + kS
fS f = +
YL
2
ke k1 ke k1 k2
k1 k2
ke = k + k
1 2
Equation of motion: mu + keu = p(t ).
AB
2
Copyright © 2023 Pearson Education, Inc.
