Postgraduate Course: Structural Dynamics and Earthquake Engineering (PGEE11051)
Course Outline
School  School of Engineering 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 11 (Postgraduate) 
Availability  Not available to visiting students 
SCQF Credits  10 
ECTS Credits  5 
Summary  Structures are often subjected to dynamic forces of one form or the other during their lifetime. This course introduces the theory of dynamic response of structures with emphasis on physical insight into the analytical procedures and with particular application to earthquake engineering. The structural dynamics component of the course includes free and forced vibration response of single and multidegree of freedom systems. The earthquake engineering component considers seismic analysis methods, earthquake resistant design philosophy and includes elements of engineering seismology. 
Course description 
Lectures  2 hours per week; Tutorials  1 hour per week
Lecture topics:
L1 Vibrations in Structures
Sources and classification of dynamic loads; basic definitions; structure idealisation.
L2 Equation of motion of SDOF Systems
Inertia, damping and elastic resistance forces on a vibrating SDOF (single degree of freedom) system; establishment of the general equation of motion for a SDOF system including situations of base excitation; deduction of the free vibration equation of motion from the general one.
L3 Free Vibration Response of SDOF Systems: 1
Characteristic equation for free vibrations; response evaluation for undamped free vibrations with examples; natural frequency and period; damped free vibrations; overdamped, critically damped and underdamped systems with examples.
L4 Free Vibration Response of SDOF Systems: 2
Different forms for expressing the response of underdamped systems; concept of damping ratio;
response of underdamped systems to initial conditions with examples; logarithmic decrement.
L5 Response of SDOF systems subjected dynamic forces
Solution of equations of motion under forced vibration  homogeneous and particular solutions; method of undetermined coefficients for evaluating the particular integral; response of an underdamped system to linearly varying forces.
L6 Response of SDOF systems to harmonic loading
Derivation of the response of a damped system subjected to harmonic excitation; special case of undamped system subjected to harmonic excitation when the exciting frequency equals the natural frequency; transient and steady state response; dynamic amplification under harmonic excitation; resonance; phase lag.
L7 Response of SDOF systems to impulsive and arbitrary loading: 1
Response of SDOF systems to step loading and load amplification; response to rectangular loading and variation of response for loads of different durations; examples; response to a triangular loading;
L8 Response of SDOF systems to impulsive and arbitrary loading: 2
Response of undamped SDOF systems to impulse loading; response of damped and undamped SDOF systems to an impulse; examples; analysis of SDOF systems under general dynamic loading  Duhamel integral; examples.
L9 MDOF systems: 1
Introduction to the analysis of simple multidegree of freedom (MDOF) dynamic systems; equations of motion.
L10 MDOF systems: 2
Analysis of vibration frequencies with examples;
analysis of vibration modes with examples; orthogonality of vibration modes ¿ derivation and examples.
L11 MDOF systems: 3
Practical evaluation of vibration modes; description of the free vibration response of complex MDOF systems; examples; introduction to dynamic response of MDOF systems under forced vibration.
L12 Lessons from past earthquakes
Different types of damage caused by earthquakes; typical planning and design weaknesses; design details that can prevent damage to lowrise structures; nonengineered construction.
L13 Seismology
Causes of earthquakes; seismic waves; focus, magnitude and intensity; terms used in seismology; role of a seismologist and an earthquake engineer; characteristics of strong ground motions; translational and rotational components of ground motions; introduction to earthquake measuring instruments.
L14 Response spectrum: 1
Response of SDOF systems to earthquake excitation; response quantities of interest; response history. The concept of response spectrum; deformation, pseudovelocity and pseudoacceleration response spectra.
L15 Response spectrum: 2
Combined DVA spectrum; construction of response spectrum; response spectrum characteristics; elastic design spectrum; difference between response and design spectra; design spectra in codes; peak structural response from the response spectrum; examples.
L16 Earthquake response analysis: 1
Concept of mode superposition analysis; generalized mass stiffness and force; uncoupled equations of motion.
L17 Earthquake response analysis: 2
Mode superposition analysis; modal expansion of earthquake excitation vector; examples.
L18 Earthquake response analysis: 3
Response/design spectrum analysis; combination of peak modal responses; examples.
L19 Earthquake response analysis: 4
Direct integration methods of analysis; example.
L20 Earthquake codes
Earthquake design philosophy; simplified design procedures.
L21 Revision
Tutorial Topics:
 Formulating equations of motion
 Free vibration analysis of SDOF systems
 Response of SDOF systems to harmonic loadings
 Response of SDOF systems to impulsive and arbitrary loadings
 Free vibration analysis of MDOF systems
 Response spectrum and earthquake response analysis of SDOF systems
 Earthquake response analysis of MDOF systems
 Time history analysis

Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  None 
Course Delivery Information
Not being delivered 
Learning Outcomes
On completion of this course, the student will be able to:
 Derive differential equations for single degree of freedom (SDOF) systems and for multidegree of freedom systems (MDOF) and evaluate their free vibration characteristics.
 Evaluate the response of SDOF and MDOF systems subjected to forced vibrations.
 Identify the possible causes of failure in a poorly designed structures subjected to earthquake loading.
 Describe basic concepts of engineering seismology.
 Describe the construction of response/design spectra and be able to apply these for seismic analysis.

Reading List
Anil K. Chopra  Dynamics of Structures: Theory and Application to Earthquake Engineering, Prentice Hall.
Ray W. Clough and Joseph Penzien ¿ Dynamics of Structures, McGraw Hill.
R.R. Craig  Structural Dynamics, John Wiley.
G.B. Warburton  Dynamical Behaviour of Structures, Pergamon Press. 
Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  Structural dynamics,Earthquake,seismic analysis of structures 
Contacts
Course organiser  Dr Pankaj Pankaj
Tel: (0131 6)50 5800
Email: Pankaj@ed.ac.uk 
Course secretary  Miss Margaret Robertson
Tel: (0131 6)50 5565
Email: margaret.robertson@ed.ac.uk 

