CE 809 - Structural Dynamics

Lecture 0: Course Introduction

Semester – Fall 2021

Dr. Fawad A. Najam

Department of Structural Engineering

NUST Institute of Civil Engineering (NICE)

National University of Sciences and Technology (NUST)

H-12 Islamabad, Pakistan

Cell: 92-334-5192533, Email: fawad@nice.nust.edu.pk

Prof. Dr. Pennung Warnitchai

Head, Department of Civil and Infrastructure Engineering

School of Engineering and Technology (SET)

Asian Institute of Technology (AIT)

Bangkok, Thailand

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Examples of Problems related to Structural Dynamics

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Tacoma Narrows bridge

• A classic example.

• A suspension bridge built in 1940s.

• The bridge was designed by one of the leading experts in suspension bridges at that time.

• Dead load, traffic load, and wind induced drag load (lateral force) were considered in the structural

design.

• However, the bridge collapsed during a wind storm in which the wind velocity was much lower than

the maximum wind speed used in the design.

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Flutter of Tacoma Narrows Bridge

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Tacoma Narrows bridge

• The design, based on static concept, was perfectly correct, but the dynamic effects were not

considered.

• From the recorded motion picture, we found that the bridge collapsed by a certain unstable dynamic

excitation mechanism (torsional flutter).

• Starting from small amplitude torsional oscillation, the motion grew up until suspended ropes broke

by fatigue, and then the bridge collapsed.

• After this failure, many studies on bridge dynamics were conducted, and every bridge engineer who

involves in the design of long-span bridges has to learn the theory of structural dynamics.

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Flutter of Tacoma Narrows Bridge

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Wind Effects on Structures

Static

effects

Deformation due to time-averaged aerodynamic force

Stress due to wind-induced pressure or force

Static

instability

Torsional divergence (negative stiffness)

Lateral buckling

Dynamic

effects

Forced

vibration

Buffeting (random

vibration)

due to atmospheric turbulenceLimited-

amplitude

response

due to body-induced turbulence (wake)

Vortex excitation

Dynamic

instability

(negative

damping)

Galloping

Divergent-

amplitude

response

Wake galloping

Torsional flutter

Coupled flutter

Rain-induced vibration

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A Hospital Building subjected to an earthquake

• Structural safety is the main concern.

• A hospital building was subjected to the San Fernando

earthquake in 1971, and it was severely damaged.

• The building vibrated like a large rigid mass shaking on

flexible columns. These columns had to resist large

cyclic shear force, and after few cycles they failed.

• The dynamic shear force is proportional to the product

of mass and acceleration of the building

𝐹 = 𝑚 𝑎

Olive View Hospital

(First story has a permanent displacement of 2 feet (61 cm)

Courtesy: P. C. Jennings and G. W. Housner

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Earthquake Loading on Structures

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A Hospital Building subjected to an earthquake (continued)

During the 9 February 1971 San Fernando earthquake the new Olive View Hospital building was

severely damaged. In response to very strong ground shaking. the building vibrated essentially as a

large mass on relatively flexible columns. The spirally reinforced concrete columns were deformed

far beyond the requirements of the building code.

Second story column fracture in Olive View Hospital

Collapsed first story of Psychiatric building at

Olive View HospitalOlive View Hospital after February 1971 San

Fernando earthquake

Courtesy: P. C. Jennings and G. W. Housner

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A Hospital Building subjected to an earthquake (continued)

• In many current seismic resistant design codes, a regular building may be designed by a static

method, that is, the building may be designed to resist an equivalent static lateral force (of

earthquake).

• Although the analysis involved is static analysis, the equivalent static force is entirely formulated

from the consideration of the dynamic behavior of the building.

• For the seismic design of complex structures and/or important structures, an explicit dynamic

analysis may be required.

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Wenchuan Earthquake (2008), China

Magnitude = 7.9

Death Toll > 70,000

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Balakot, Kashmir Earthquake (2005)

Magnitude = 7.6

Death Toll = 79,000

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Yogyakarta Earthquake (2006)

Magnitude = 6.2

Death Toll = 5,000

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Kobe Earthquake (1995)

Magnitude = 6.9

Death Toll > 6000

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Earthquake Motion: Kobe Earthquake, 1995

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Typical Commercial Concrete Buildings

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Building Response to EQ Ground Shaking

Lateral-Torsional Movement (period = 0.50 sec)

2121

First-story Collapse of Commercial Buildings The 1999 Chi-Chi Earthquake (Taiwan)

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Why This Course?

Location of Major Earthquakes in Last 100 Years

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Why This Course?

Seismic zonation of Pakistan as per Building Code of Pakistan (BCP). The areas in red color (Zone 4) are under severe threat of earthquakes.

The areas in dark blue and light blue are relatively less exposed to seismic threat.

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Tower Structures

• Marine observation towers, airport control towers, tall and slender buildings (see the following

slides).

• These structures are safe against wind and earthquake.

• But the wind-induced vibration may causes human discomfort – motion sickness, difficult to perform

desk work, furniture and fixtures make sounds

• Serviceability problems

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The Yokohama Marine

Tower (Japan, 1961)

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The Sydney Tower

(Australia, 1981)

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The CN Tower

(Canada, 1976)

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Tall Buildings - Dynamic Wind Effects need to be considered !

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Photo Courtesy: http://www.bangkok.com/magazine/baiyoke-tower-II.htmPhoto Courtesy: https://www.bangkokpost.com/learning/advanced/1073529/

Tall Buildings - Dynamic Wind Effects need to be considered !

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Response of a mid-rise

building with a high

natural frequency

Response of a high-rise

building with a low natural

frequency

Wind force (Drag)

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A Steel Stack

A Steel Stack

Pendulum Tuned Mass Damper

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Suspended Wire Rope

Steel Ring

Viscous Damper

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A Pedestrian Bridge

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A Pedestrian Bridge

• 2000 pedestrians walk across the bridge in the same time.

• The bridge is subjected to human-induced force in both vertical and horizontal directions.

• The bridge girder vibrates laterally, and the stay cables also vibrate with very large lateral vibration

amplitudes, says up to 50 cm.

• The dynamic stresses are so low that the structure will never fail.

• And the vibrations are too low to cause any difficulty on the walking mode of pedestrians.

• But many pedestrians are afraid to walk. Many people complain about the vibration, and many of

them think that the bridge was poorly designed and constructed.

• Problem of ‘human perception of vibration’

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Why This Course? - Course Objectives

• As modern structures are becoming slender and light, they are also becoming more susceptible to

dynamic loadings.

• Various examples of real-life dynamic problems that frequently confront civil engineers include:

• Aerodynamic stability of long-span bridges

• Earthquake response of multi-story buildings

• Impact of moving vehicles on highway structures, etc.

• The traditional engineering solutions to these problems, based on "static force" and "static response", are

no longer valid in most cases.

• Many of these problems have to be tackled by applying the knowledge of structural dynamics. Thus, a

basic understanding of the dynamic behavior of structures as well as the underlying principles is essential

for structural engineers.

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Learning Outcomes

• Develop the basic understanding of principles of structural dynamics

• Develop the ability to integrate the principles of structural dynamics in structural design of buildings and

structures

• Develop the ability to analyze and solve problems in dynamic response and behavior of buildings and

structures

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Course Outline

1) Dynamics of Simple Structures (single-degree-of-freedom systems)

a. Equation of motion

b. Free vibrations

c. Response to harmonic force

d. Response to periodic force

e. Response to arbitrary dynamic force

f. Nonlinear dynamic response

2) Multi-Degree-Of-Freedom Structures

a. Formulation of matrix equations of motion

b. Analysis of free vibrations

c. Modal analysis and forced vibrations

d. Nonlinear dynamic response

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Course Outline

3) Continuous Structures

a. Partial differential equations of motions (for strings, bars, beams)

b. Modal analysis

c. Wave propagation analysis

4) Earthquake Response

a. Response spectrum concept

b. Application to earthquake engineering

5) Random Vibrations

a. Probability theory, random processes

b. Correlation and spectral density functions

c. Response to stationary random excitations

d. Crossing, peak distributions, extreme value analysis, evaluation of fatigue life

e. Application to wind engineering

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Course Outline

6) Control of Dynamic Response

a. Overview of vibration control

b. Tuned Mass Dampers

c. Active vibration control

Chapter Topic Videos YouTube Link Duration

Introduction Introduction to the Course y2u.be/MCRX1KXQZBU 16:42

Dynamics of

Simple

Structures

SDF Systems Formulation of Mathematical Model of SDF Systems y2u.be/sbxf1D1Umvw 50:53

Free Vibration Free Vibration Response of SDF Systems y2u.be/_ZUp3c5IMIk 1:47:25

Harmonic Loading

Response of SDF Systems to Harmonic Loading - Part 1 y2u.be/qh47IyfCA9E 1:30:49

Response of SDF Systems to Harmonic Loading - Part 2 y2u.be/bh8DTlu3urU 1:24:59

Response of SDF Systems to Harmonic Loading – A Recap y2u.be/Li6Of0tlOjc 48:04

Periodic Loading

Response of SDF Systems to Periodic Loading – Part 1 y2u.be/9ueH32NpRkc 25:25

Response of SDF Systems to Periodic Loading – Part 2 y2u.be/1reOQ18—gQ 53:09

Solved Examples – Harmonic/Periodic Responses of SDF Systems y2u.be/YEg15kIaoF4 17:23

Impulse Loading Response of SDF Systems to Impulse Loading y2u.be/GVov4SyM2Nc 18:42

General Loading

Response of SDF Systems to General Dynamic Loading – Part 1 y2u.be/TWkCBCZiDuM 43:16

Response of SDF Systems to General Dynamic Loading – Part 2 y2u.be/Ow3V4tKQW9c 1:14:34

ETABS Modeling of a Single-Degree-of-Freedom (SDF) System y2u.be/iLlC0h6W6Oo 25:08

Earthquake

Response of SDF

Systems

Concept of Elastic Response Spectrum y2u.be/08FqAqrpbLc 36:51

Elastic Response Spectrum of a Ground Motion – An Introduction y2u.be/ckpzOp5ivrc 29:44

Basic Processing of Ground Motion Records using SeismoSignal y2u.be/cGEJ6yX9VsY 33:28

Dynamics and Earthquake Response of Simple (Elastic) Structures - A Quick Summary y2u.be/tjdMQs3ZmUc 1:20:46

The Concept of Elastic Design Spectrum y2u.be/DVt0R_0063Q 30:25

The Concept of Inelastic Response Spectrum y2u.be/BYjM7N8FOtI 1:39:20

Chapter Topic Videos YouTube Link Duration

Dynamics of

Simple

Structures

Generalized SDF

Systems

Generalized Single Degree of Freedom Systems - Part 1 y2u.be/73kwkfCG0yA 1:17:02

Generalized Single Degree of Freedom Systems - Part 2 y2u.be/pt6AnqqDvaI 1:11:57

Chapter Topic Videos YouTube Link Duration

Dynamics of

Discrete MDF

Structures

MDF Systems Formulation of Mathematical Model for MDF Systems y2u.be/YuD1gdpSbPs 31:09

Free Vibration

Free Vibration Response of MDF Systems y2u.be/XlEsGZ37vG0 1:11:27

Classical Modal Analysis of Building Structures and Interpretation of Results Using CSI

ETABSy2u.be/KZgTFseW3Kc 44:29

Orthogonality Property of Mode Shapes - ETABS Demonstration y2u.be/nrI50lhfv6A 26:49

Forced Vibration

Response of MDF

Systems

Mode Superposition Method for the Dynamic Analysis of Structures y2u.be/z16tSTs91PM 1:03:19

Modal Damping and Rayleigh Damping Models - ETABS Demonstration on Damping in

Dynamic Analysisy2u.be/4rgTdWGbmpQ 34:54

Numerical Evaluation of Dynamic Response of MDF Systems - Step-by-step Direct

Integration Methody2u.be/re_qK_UHStE 1:15:25

Determination of Mode Shapes and Natural Frequencies of MDF Systems using MATLAB y2u.be/MywS__AXBL8 12:38

Assignments - Dynamic Response of MDF Structures y2u.be/SohHK6Ax1AM 16:26

Dynamics of

Continuous

Structures

Continuous

Structures

Formulation of Equations of Motion and Free Vibration Response y2u.be/FdjtVdVHiyg 1:33:23

Modal Orthogonality and Forced Vibrations Response y2u.be/DBJVIB4WEgQ 39:45

SDF Systems – Discrete MDF Systems – Continuous Systems (A Quick Summary) y2u.be/O-eVoopUmRY 12:33

Wave Propagation Introduction to Wave Propagation y2u.be/0c5M1KlK3b8 1:23:12

Random Vibrations

Probability theory, random processes

Correlation and spectral density functions

Response to stationary random excitations

Crossing, peak distributions, extreme value analysis, evaluation of fatigue life

Control of Dynamic ResponseOverview of vibration control

Tuned Mass Dampers

Active vibration control

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Reference Books

• A. K. Chopra, (2017): Dynamics of Structures-Theory and Applications to Earthquake Engineering, ISBN

0134555120, 9780134555126, Prentice Hall international series, Pearson, 2017.

• R. W. Clough, and J. Penzien, (2003): Dynamics of Structures, Computers and Structures, Incorporated, ISBN

0923907505, 9780923907501.

• Roy R. Craig, (2010): Structural dynamics: An introduction to computer methods, ISBN 0471044997, Wiley.

• J. W. Smith, (1988): Vibration of Structures: Applications in Civil Engineering Design, Chapman and Hall,

London.

• T. R. Tauchert, (1974): Energy Principles in Structural Mechanics, McGraw-Hill, ISE.

• H. Bachmann, and W. Ammann, (1987): Vibrations in Structures-Induced by Man and Machines, Series:

Structural Engineering Documents. Vol. 3e. International Association for Bridge and Structural Engineering

(IABSE), Zurich, Switzerland.

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Reference Books

• D. E. Newland, (1993): An Introduction to Random Vibrations, Spectral and Wavelet Analysis,

Longman, 3rd Edition, London.

• S. H. Crandall, and W. D. Mark, (1963): Random Vibration in Mechanical Systems, Academic Press,

New York.

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Journals and Magazines

• Earthquake Engineering and Structural Dynamics, Wiley

• Engineering Structures, Elsevier

• Structural Design of Tall and Special Buildings, Wiley

• Journal of Structural Engineering, ASCE

• Soil Dynamics and Earthquake Engineering, Elsevier

• Journal of the engineering mechanics division, ASCE

• Magazine of Concrete Research, ICE

• Structures and Buildings, ICE

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Evaluation Scheme

• The final grade will be computed according to the following weight distribution:

• One Hour Tests: 30%

• Assignments: 10%

• Quizzes: 10%

• Final Exam: 50%

• Link for downloading course material.

www.structurespro.info

www.fawadnajam.com

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• Monday to Friday – Working Hours

• Office No. 14, Ground Floor, PG Wing Building, SCEE, NUST

Instructor and Contact

Fawad A. NajamDepartment of Structural Engineering

NUST Institute of Civil Engineering (NICE)

National University of Sciences and Technology (NUST)

H-12 Islamabad, Pakistan

Cell: 92-334-5192533, Email: fawad@nice.nust.edu.pk

Thank you