BITS Pilani Hyderabad Campus

CE G551 Dynamics of Structures Instructor: Mr. J S Kalyana Rama

Course Lecture-IV

Application of FEM to Structural Dynamics

BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama

Contents

Dynamic analysis of Water Tanks

Dynamic analysis of Bridges

BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama

Dynamic analysis of Water Tanks

Elephant-foot buckling of a tank wall (courtesy

of University of California at Berkeley)

Sloshing damage to upper shell of tank (courtesy of University of

California at Berkeley)

BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama

Liquid-filled tank modelled by generalized single-degree-of-

freedom systems

Method of Dynamic Analysis

• The dynamic analysis of a liquid-filled

tank may be carried out using the

concept of generalized single-degree-of

freedom (SDOF) systems representing

the impulsive and convective modes of

vibration of the tank-liquid system.

• For practical applications, only the first

few modes of vibration need to be

considered in the analysis.

• For a given earthquake ground motion,

the response of various SDOF systems

may be calculated independently and

then combined to give the net base

shear and overturning moment.

BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama

Solid model of experimental set-up

Water Sloshing in Rectangular Tanks – An Experimental Investigation &

Numerical Simulation: Mechanical Engineering, Petroleum Institute, P.O. Box

2533 Abu Dhabi, UAE

BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama

Actual experimental set-up

BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama

Schematic of the experimental setup

BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama

Image Processing

BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama

Comparison between experimental and numerical results for 50% fill level and 4.5 kg

BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama

Comparison between experimental and numerical results for 50% fill level and 4.5 kg

BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama

A STUDY ON SLOSHING FREQUENCIES OF FLUID-TANK SYSTEM

Visvesvaraya National Institute of Technology, Nagpur, India

Where, fc = Sloshing frequency (Hz), h = height of water in tank (m), L = length of rectangular tank along direction of excitation

(m), D= diameter of circular tank (m), g = acceleration due to gravity (m/s2)

For the circular and rectangular tanks, the first sloshing frequency is given by Housner, 1963): as

BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama

Details of tanks of other shapes

Circular tank of 170

mm diameter and

230 mm

height (Model 1);

square tank of plan

size 270mm x

270mm and 300

mm height (Model

2); rectangular tank

of plan size 270

mm x 135 mm and

300 mm height

BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama

First sloshing mode of liquid in tanks of different shapes

BITS Pilani, Hyderabad Campus Instructor: Mr. J S Kalyana Rama

• Clough and Penzein

• A K Chopra

• Slides from Different foreign Universities

• Wikipedia.org

• Technical University of Denmark-Material for Dynamics

References

BITS Pilani Hyderabad Campus

THANK YOU!