Structural Dynamics in Earthquake and Blast Resistant Design

BK Raghu Prasad

• Publisher: CRC Press
• Year: 2020
• Print ISBN:
  9780367519001
• eBook ISBN:
  9781351250504
• Topic: Technology & Engineering
• Subtopic: Industrial Design
• Index: Technology & Engineering

Focusing on the fundamentals of structural dynamics required for earthquake blast resistant design, Structural Dynamics in Earthquake and Blast Resistant Design initiates a new approach of blending a little theory with a little practical design in order to bridge this unfriendly gap, thus making the book more structural engineer-friendly. This is attempted by introducing the equations of motion followed by free and forced vibrations of SDF and MDF systems, D'Alembert's principle, Duhammel's integral, relevant impulse, pulse and sinusoidal inputs, and, most importantly, support motion and triangular pulse input required in earthquake and blast resistant designs, respectively. Responses of multistorey buildings subjected to earthquake ground motion by a well-known mode superposition technique are explained. Examples of real-size structures as they are being designed and constructed using the popular ETABS and STAAD are shown. Problems encountered in such designs while following the relevant codes of practice like IS 1893 2016 due to architectural constraints are highlighted. A very difficult constraint is in avoiding torsional modes in fundamental and first three modes, the inability to get enough mass participation, and several others. In blast resistant design the constraint is to model the blast effects on basement storeys (below ground level). The problem is in obtaining the attenuation due to the soil. Examples of inelastic hysteretic systems where top soft storey plays an important role in expending the input energy, provided it is not below a stiffer storey (as also required by IS 1893 2016), and inelastic torsional response of structures asymmetric in plan are illustrated in great detail. In both cases the concept of ductility is explained in detail. Results of response spectrum analyses of tall buildings asymmetric in plan constructed in Bengaluru using ETABS are mentioned. Application of capacity spectrum is explained and illustrated using ETABS for a tall building. Research output of retrofitting techniques is mentioned. Response spectrum analysis using PYTHON is illustrated with the hope that it could be a less expensive approach as it is an open source code. A new approach of creating a fictitious (imaginary) boundary to obtain blast loads on below-ground structures devised by the author is presented with an example.

Aimed at senior undergraduates and graduates in civil engineering, earthquake engineering and structural engineering, this book:

Explains in a simple manner the fundamentals of structural dynamics pertaining to earthquake and blast resistant design
Illustrates seismic resistant designs such as ductile design philosophy and limit state design with the use of capacity spectrum
Discusses frequency domain analysis and Laplace transform approach in detail
Explains solutions of building frames using software like ETABS and STAAD
Covers numerical simulation using a well-known open source tool PYTHON

1Introduction

In structural engineering practice, design for dynamic loads is important. Most common dynamic loads are those due to earthquake ground motion, wind, blast and machinery, etc. Vehicles travelling on a rough surface also undergo dynamic loading and in turn transfer those dynamic effects to the surface of the vehicle in which the passengers are seated. But the problem which generally an engineer encounters is the decision regarding whether the loads are dynamic or mere static.

As it strikes to common sense, generally speed controls dynamic effects. It is true that in all our experiments we do control the rate of loading which is also the speed of loading. Speed is a relative variable and, therefore, with respect to what we compare the rate of loading, to judge it as fast or slow is an important question. Here, the concept of theory of vibrations is considered. A system parameter called natural period (T in seconds), which is the reciprocal of natural frequency (f, in Hertz), comes in handy as a yard stick to compare the rate of loading as sudden or gradual. Various types of dynamic loading, like suddenly applied load, ramp load, pulse loads of different shapes, sinusoidal and random loadings, are common in practice.

A machine foundation supporting rotating machinery having an eccentric mass on the rotor will cause a sinusoidal force on the foundation. A tall building or a tall tower subjected to along and across wind oscillations is an example of sinusoidal load due to wind. The wind at certain velocities will cause resonant condition of the tower. Earthquake ground motion is an example of random base motion, which can cause severe damage to a structure if not properly designed. A distant blast or an explosion causes a triangular pulse load on a structure which is in the vicinity thus intercepting the over-pressure waves from the blast. Sudden fall of an object could be an example of an impulse. A suddenly applied load held constant over time can be a step load. Similarly, one can find examples of different types of pulse loadings. In all the examples cited above, the first mode natural period, T becomes important. Either the duration of the pulse in the case of pulse loads or the period of oscillation of the force in the case of sinusoidal load or reciprocal of the number of zero crossings per second in the case of random loading is compared with the natural fundamental period of the system. Their ratio is an important parameter which decides the severity of vibration.

1.1Types of Analysis

Static Analysis and Dynamic Analysis

In any problem dealing with either statics or dynamics, there is always a system with an input and output. Why we need to know static analysis while understanding dynamics is because in many cases a dynamic problem is solved as an equivalent static problem by converting dynamic loads as equivalent static loads and performing static analysis (Figs. 1.1 and 1.2).

Figure 1.1: System subjected to input and providing an output

Figure 1.2: Static and dynamic cases

Generally, the system and input are known to obtain the required output. Input consists of geometrical as well as material properties, boundary conditions and forces acting on the system (Fig. 1.1). The outputs generally are bending moments, shear and axial forces, displacements, stresses and strains. The system is defined by appropriate system equations which could either be differential or integral equations. The differential equations will be ordinary in the case of discrete systems and partial in the case of continuous systems. In the case of stochastic systems, either the input or the system or both can be stochastic which obviously means that the output will always be stochastic. In dynamic analysis, the input forces are time varying. In linear systems, system properties remain constant and the responses have linear variation. In non-linear systems, the response values will be non-linear. Further, there could be non-linear elastic as well as inelastic systems. In non-linear elastic systems, the response is non-linear from the beginning but can come back to the original position on the same path when the forces are released; while in the non-linear inelastic systems, the system is non-linear right from the beginning and the system does not come to original position along the same path when the loads are released, thus expending some energy in the process. There are non-linear hardening and softening systems. Yet another important fact to note is that even a dynamic problem can be treated as an equivalent static problem by the use of dynamic load factors.

Some examples of problems in structural dynamics are listed below:

1.Effects of earthquake ground motions on structures.

2.Wind effect.

3.Vehicle moving on a bridge causing vibrations of the bridge.

4.Vehicle negotiating a road hump suffering vibrations.

5.Foundation of machine.

6.A passenger train car undergoing vibration causing discomfort to the passengers due to roughness of the rail.

1.2Modelling of a Dynamic System

The dynamic response of a system can be defined by three quantities viz. displacement, velocity and acceleration. Knowing any one of the three, the remaining quantities can be obtained by either differentiation or integration depending on the case (Fig. 1.2). If displacement is determined first, the velocity and acceleration can be obtained by successive differentiation with respect to time. On the other hand, if acceleration is determined first, velocity and displacement can be obtained by successive integration with respect to time once and twice, respectively. In order to obtain the above quantities, the position of the system at any instant of time with respect to a reference coord...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Acknowledgments
• Author
• Symbols
• Chapter 1: Introduction
• Chapter 2: Single Degree of Freedom Systems.
• Chapter 3: Two Degree of Freedom Systems
• Chapter 4: Force Transmitted to the Support
• Chapter 5: Duhamel’s Integral
• Chapter 6: Modal Analysis
• Chapter 7: Earthquake Resistant Design
• Chapter 8: Inelastic Vibration Absorber Subjected to Earthquake Ground Motion
• Chapter 9: Inelastic Torsional Response of a Single-Storey Framed Structure: Two Degree of Freedom System
• Chapter 10: Inelastic Torsional Response of a Single-Storey Framed Structure: Three Degree of Freedom System
• Chapter 11: Earthquake Resistant Design as per IS 1893:2016
• Chapter 12: Miscellaneous Aspects
• References and Suggestions for Further Reading
• Index