BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, Pilani Pilani Campus
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1 First Semester Instruction Division Course Handout (Part II) Date: 02/08/2017 In addition to Part I (General Handout for all courses appended to the Time Table), this portion gives further specific details regarding the course. Course No. Course Title Instructor In-charge : CE G551 : DYNAMICS OF STRUCTURES : DIPENDU BHUNIA 1. Course Description Introduction and Scope of dynamic analysis of structures; origins of vibration theory and experiment; review of earlier concepts: d Alembert s principle, equations of motion. Elements of a structural system: springs, dashpot, mass; Springs in parallel and series; methods to formulate equations of motion; Formulation (equation of motion) and solution of undampe d and damped free vibration analysis of S.D.O.F system; Formulation (equation of motion) and solution of undamped and damped forced vibration analysis of S.D.O.F system; Forced vibration under harmonic, periodic, impulse, step, ramp, general dynamic forces (time and frequency domain analysis) and response spectrum load, support excited vibration, seismic pickups; Numerical techniques for evaluation of dynamic response of SDOF system; time domain analysis; direct integration techniques; finite difference method (Central Difference method); Newmark beta method; average and linear acceleration method; Development of equation of motion and solution for two degree of freedom systems; Free vibration analysis of MDOF systems; frequencies; mode shapes and response; orthogonality condition of mode shapes; Approximate methods for obtaining natural frequencies and mode shapes; Holzer method; Stodola s method; Rayleigh s method; Rayleigh-Ritz method; Inverse iteration method; Vector iteration method; Rayleigh s Quotient iteration method; Matrix iteration method; Generation of damping matrix for MDOF; dynamic properties; modal damping; classical damping; damped response with Rayleigh and Caughey damping.mode superposition method; mode acceleration method; modal combination rules using absolute sum, SRSS and CQC method. Response Spectrum, continuous system. 2. Scope and Objectives Natural phenomena and human activities impose forces of time-dependent variability on various civil engineering structures. This course deals with analysis and design of structures subjected to dynamic loads which involve consideration of time-dependent forces. Therefore, this course is necessary for students desirous of joining design offices/ industry related to buildings, industrial plants, bridges, tanks, offshore structure, tall chimneys etc. At the end of the course
2 work students will be able to determine the behavious of structures under dynamic loading and design a structure which is resistant to dynamic loading such as seismic, wind, seawave, vehicle induced vibration force etc. 3. Prescribed Text Book T1. Anil K. Chopra, Dynamics of Structures: Theory and applications to earthquake engineering, Prentice Hall India Ltd., Reference Books R1. R.W. Clough and J. Penzien, Dynamics of Structures, McGraw Hill International edition, R2. Mukhopadhyay,M., Structural Dynamics: Vibrations Systems Ane Books Pvt. Ltd., R3. Paz,M., Structural Dynamics: Theory Computation CBS Publishers Distributors, Course Plan Module Number Lecture session/practice Session. Reference Learning Outcome 1. Importance of the course. L1. Introduction and Scope of T1-1, Understand the dynamic analysis of structures; Importance of the origins of vibration theory and experiment; review of earlier concepts: d Alembert s principle, equations of motion. course 2. Fundamentals of Dynamics of Structures L2.1. Elements of a structural system: springs, dashpot, mass; Springs in parallel and series; L2.2. methods to formulate equations of motion T1-1,2, T1-1,2, Understand about the Fundamentals of Dynamics of Structures. 3. Free vibration analysis of L3. Formulation (equation of motion) and solution of undamped and damped free vibration analysis of T1-2, Understand Free vibration analysis of P3. Practice problems Class notes 4. Forced vibration analysis of S.D.O.F system L4. Formulation (equation of motion) and solution of undamped and damped forced vibration analysis of T1-3, Understanding the Forced vibration analysis of S.D.O.F
3 P4. Practice problems. Class notes system. 5. Forced vibration analysis (evaluation of response to general dynamic loading). L5.1. Forced vibration under harmonic, periodic, impulse, step, ramp, general dynamic forces (time and frequency domain analysis). T1-4, 6,7, Acquiring knowledge about the evaluation of response to general dynamic loading L5.2. response spectrum load, support excited vibration, seismic pickups. T1-4, 6,7, P5. Practice problems. Class notes 6. Numerical methods for free and forced vibration analysis (evaluation of dynamic response). L6. Numerical techniques for evaluation of dynamic response of SDOF system; time domain analysis; direct integration techniques; finite difference method (Central Difference method); Newmark beta method; average and linear acceleration method. T1-5, Acquiring knowledge about the Numerical methods for free and forced vibration analysis. P6. Practice problems. Class notes 7. Analysis of two degree of freedom. L7.1. Development of equation of motion. L7.2. Solution for two degree of freedom systems. T1-9, 11, T1-9, 11, Understanding the Analysis of two degree of freedom. P7. Practice problems. Class notes 8. Free vibration (Eigen L 8. Free vibration analysis of MDOF R1-11,13, Free vibration (Eigen
4 value) analysis of lumped MDOF systems. systems; frequencies; mode shapes and response; orthogonality condition of mode shapes. P8. Practice problems. Class notes value) analysis of lumped MDOF systems. 9. Method of solving Eigen value problems. L9.1 Approximate methods for obtaining natural frequencies and mode shapes; Holzer method; Stodola s method; Rayleigh s method; Rayleigh-Ritz method. R1-13, Method of solving Eigen value problems. L9.2 Inverse iteration method; Vector iteration method; Rayleigh s Quotient iteration method; Matrix iteration method. R1-13, P 9. Practice problems. Class notes 10. Forced vibration analysis of MDOF systems. L10. Generation of damping matrix for MDOF; dynamic properties; modal damping; classical damping; damped response with Rayleigh and Caughey damping.mode superposition method; mode acceleration method; modal combination rules using absolute sum, SRSS and CQC method. Response Spectrum, continuous system. R1-12, Understanding of Forced vibration analysis of MDOF systems. P 10. Practice problems. Class notes
5 6. Evaluation Scheme: Evaluation Weightage Component (Marks) Date Time Remarks Mid-Sem. 30% (60) 11/10 4:00-5:30 PM Open Book Comprehensive 40% (80) 7/12 AN Closed Book Project along with seminar 20% As per the schedule to be announced 10% Every week Closed Book Test: No reference material of any kind will be permitted inside the exam hall. Open Book Exam: Use of any printed / written reference material (books and notebooks) will be permitted inside the exam hall. Loose sheets of paper will not be permitted. Computers of any kind will not be allowed inside the exam hall. Use of calculators will be allowed in all exams. No exchange of any material will be allowed. Note: It shall be the responsibility of the individual student to be regular in maintaining the self study schedule as given in the course handout, attend lectures and in time assignments submission as per the schedule announced in Nalanda/lecture class. Mid Semester Test and Comprehensive Examination are according to the Evaluation Scheme given in the respective Course Handout. If the student is unable to appear for the Regular Test/Examination due to genuine exigencies, the student must refer to the procedure for applying for Make-up Test/Examination. No make up for the assignments/projects seminar. (DIPENDU BHUNIA) Instructor In charge CE G551
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