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212 Ketter Hall, North Campus, Buffalo, NY 14260 civil.buffalo - PowerPoint PPT Presentation

212 Ketter Hall, North Campus, Buffalo, NY 14260 www.civil.buffalo.edu Fax: 716 645 3733 Tel: 716 645 2114 x 2400 Control of Structural Vibrations Lecture #4 MDOF Structures Analysis Instructor: Andrei M. Reinhorn P.Eng. D.Sc. Professor of Structural Engineering.

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www.civil.buffalo.edu

Fax: 716 645 3733 Tel: 716 645 2114 x 2400

Control of Structural Vibrations

Lecture #4

MDOF Structures Analysis

Instructor:

Andrei M. Reinhorn P.Eng. D.Sc.

Professor of Structural Engineering

T1

T2

T3

Modal Analysis

Review of MDOF response

using ortho-normalized modes

Modal Response Calculations:

_______________________________________________________

Spectral Displacement:

Spectral Acceleration:

_______________________________________________________

Modal Floor Displacement (u or  )

Modal (Floor) Inertia Force

Modal Reaction- BASE SHEAR

_______________________________________________________

Total Response can be obtained from all modes

by superposition:

SRSSn (xi) = ( SUMn (xi2))1/2

Approximations in highly damped structures:

1. Use of undamped mode shapes

2. Use of proportional damping

Capacity (Curve) of StructureCapacity is a function, not a single value, indicating the strength of the system at a deformed position of the structure

• The static procedure is an equivalent instantaneous approximation of MDOF response to determine internal stresses and other …..

Nonlinear Static Analysis (Procedure)

Perform static analysis with increasing lateral forces, Fi,

(applied at each floor) incrementally, proportional to the

distribution of inertia forces which appear in the dynamic

analysis

Step-by-step DC Procedure[DC = Demand Capacity]

Step-by-step DC Procedure[DC = Demand Capacity]

INCLUDING A NUMBER OF MODAL SHAPES:

Spectral Evaluation - Linearized Procedure

Linearized procedures uses equivalent period

and damping to evaluate response

Spectral Evaluation - Inelastic Spectrum Procedure

Inelastic Spectrum Procedure uses no approximations

but require inelastic spectrum to evaluate response

Note that it is necessary to adjust the inelastic spectra fro the

increased damping: