CE-5113:
DYNAMICS OF
STRUCTURES
By: Dr. Mohammad Ashraf
([email protected])
Office: CE: B109
Department of Civil Engineering, University of
Engineering and Technology, Peshawar
Course Contents
Introduction to SDOF, MDOF and Continuous Systems
Formu
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 4
Last Time:
Inertia and damping elements
Equivalent mass (inertia)
Harmonic motion
Definitions: Cycle, Amplitude and Perio
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 12
Last Time:
Today:
Start Chapter 3, Harmonically Excited Vibrations
Response of Undamped Systems under Harmonic Force
Res
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 18
Last Time:
Lagranges Equations
Examples of free vibrations of 2dof Undamped systems
Today:
Coordinate Coupling, General
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 3
Last Time:
Examples of finding equivalent spring constant
Series, parallel and structural members
Non-Linear Springs
Toda
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 17
Last Time:
Free vibrations of 2dof Undamped systems
Today:
Lagranges Equations
Examples of free vibrations of 2dof Undam
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 16
Last Time:
Started chapter 5, Two-degrees of Freedom systems
Matrix Notation
Linear Algebra
Free vibrations of 2dof Unda
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 6
Last Time:
Started Chapter 2,
Free Vibrations of Single Degree of Freedom Systems
Deriving governing equation of SDoF und
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 8
Last Time:
Examples of finding natural frequencies and damping ratios for
damped systems
Today:
Graphical Representation
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 14
Last Time:
Response of damped system under the harmonic motion of base (support)
Today:
Response of damped system under
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 21
Last Time:
Start Chapter 6, Multidegree of Freedom Systems
Influence Coefficients
Today:
Matrix Algebra
Matrix algebra t
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 11
Last Time:
Coulomb Damping
Today:
Start Chapter 3, Harmonically Excited Vibrations
Response of Undamped Systems under Ha
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 22
Last Time:
Matrix Algebra
Matrix algebra techniques on 2dof systems
Decoupling of equations of motion
Today:
Modal analy
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 25
Last Time:
Control of Vibration
Controlling natural frequency
Preventing large amplitudes at resonance by introducing da
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 7
Last Time:
Examples of writing GE and finding natural frequencies for undamped
systems
Today:
Deriving governing equation
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 5
Last Time:
Equivalent damping
Definitions: Oscillation frequency, Phase angle and Natural frequency
Harmonic analysis
Tod
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 23
Last Time:
Modal Analysis
Today:
Start of Chapter 9, Vibration Control
Vibration Nomograph
Rotor Balancing
2
Vibration C
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 15
Last Time:
Response of damped system under rotating unbalance
Flow induced vibrations
Today:
Start chapter 5, Two-degree
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 20
Last Time:
Semidefinite Systems
Forced Vibration Analysis
Today:
Start Chapter 6, Multidegree of Freedom Systems
Influen
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
This Course
Lecture Plan
Be active, pay attention
A rather intense class
Reading the text is important
The class builds on itself e
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 19
Last Time:
Coordinate Coupling, General and Principal Coordinates
Examples of Coordinate Coupling
Today:
Semidefinite Sy
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 13
Last Time:
Examples of finding steady state response
Today:
Response of damped system under the harmonic motion of base
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 24
Last Time:
Start of Chapter 9, Vibration Control
Vibration Nomograph
Rotor Balancing
Today:
Control of Vibration
Control
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 10
Last Time:
Graphical Representation of Roots
Root Locus
Logarithmic Decrement
Stability of Systems
Today:
Coulomb Dampin
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 8
Last Time:
Deriving governing equation of SDoF damped systems
Solving governing equation of SDoF damped systems
Today:
Ex
ME-475
Mechanical Vibrations
Fall 2016
Department of Mechanical Engineering
University of Engineering and Technology Lahore
Lecture 2
Last Time:
Started Chapter 1, Fundamentals of Vibrations
Elements of a vibrating system (elastic, inertia and friction/vi
Daniel
T. Li
PROJECT :
CLIENT :
JOB NO. :
PAGE :
DESIGN BY :
REVIEW BY :
DATE :
WF Base Plate Design Based on AISC-ASD 9th Edition
INPUT DATA & DESIGN SUMMARY
AXIAL LOAD OF COMPRESSION
P =
fc' =
CONCRETE STRENGTH
COLUMN SIZE
BASE PLATE SIZE
600
3
=>
W21X7
Daniel
Tian Li
PROJECT :
CLIENT :
JOB NO. :
DATE :
Group Fasteners in Combined Stresses Based on ACI 530-02 & CBC 2001
PAGE :
DESIGN BY :
REVIEW BY :
INPUT DATA & DESIGN SUMMARY
MASONRY STRENGTH
fm'
=
1.5
ksi
=
60
ksi
=
0.42
kips / ft
1
kips / ft
=
0.85
k
Daniel
Tian Li
PROJECT :
CLIENT :
JOB NO. :
PAGE :
DESIGN BY :
REVIEW BY :
DATE :
Single Tension Fastener Away from Edges Based on ACI 318-02
INPUT DATA & DESIGN SUMMARY
fc'
=
4
ksi
fut
SPECIFIED STRENGTH OF FASTENER
=
60
ksi
(The strength of most fasteni
BASE PLATE DESIGN
P = AXIAL LOAD ON COLUMN
Fy = YEILD STRENGTH OF PLATE
fc = CONCRETE COMPRESSIVE STREGTH
b=
d=
Fp = 0.25 fc
Fb = ALLOWABLE BENDING STRESS (0.75Fy)
A = REQUIRED AREA OF PLATE
410.00
36.00
4.00
15.65
15.22
1.00 ksi
27.00 ksi
15.18519 in2
B