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Design of reinforced concrete 6th edition solution manual pdf |
Design of reinforced concrete 6th edition solution manual pdf
A continuous pattern of mortar cracks begins to form. As a result there are few undamaged portions to carry load and the stress-strain curve is highly nonlinear. At the critical stress the lateral strain begins to increase rapidly. This causes the concrete core within the spiral to expand, stretching the spiral. The tension in the spiral is equilibrated by a radial compression in the core.
This in turn, biaxially compresses the core, and thus strengthens it. When concrete is subjected to sustained loads greater than the critical stress, it will eventually fail. Because both of these exceed psi, the concrete satisfies the requirements of ACI Code Section 5. All rights reserved.
This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. This is sample only, Download all chapters at: testbankreal. Use the maturity concept to estimate its strength as a fraction of the day strength under standard curing.
From Fig. As this fraction increases, shrinkage increases. As this increases, shrinkage decreases. As the water content increases, the aggregate fraction decreases, causing an increase in shrinkage. Shrinkage increases for finely ground cement that has more surface area to attract and absorb water. As this ratio increases, the shrinkage occurs more slowly and the total shrinkage is likely reduced. The average ambient relative humidity is 70 percent.
The concrete was moist-cured for 7 days. A compression load of kips was applied to the column at 30 days. Compute the ultimate shrinkage strain coefficient, , using Eqs. This publication is protected by Copyright and written [ ] permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.
Compute the creep coefficient for the time since loading, , using Eq. Compute the total stress-dependent strain, , using Eqs. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries. Hearing is one of the most crucial means of survival in the animal world, and speech is one of the most distinctive characteristics of human development and culture.
Accordingly, the science of acoustics spreads across many facets of human society—music, medicine, architecture, industrial production, warfare and more. Likewise, animal species such as songbirds and frogs use sound and hearing as a key element of mating rituals or marking territories. Art, craft, science and technology have provoked one another to advance the whole, as in many other fields of knowledge. Robert Bruce Lindsay's 'Wheel of Acoustics' is a well accepted overview of the various fields in acoustics.
The Latin synonym is "sonic", after which the term sonics used to be a synonym for acoustics[5] and later a branch of acoustics.
The fundamental and the first 6 overtones of a vibrating string. The earliest records of the study of this phenomenon are attributed to the philosopher Pythagoras in the 6th century BC. In the 6th century BC, the ancient Greek philosopher Pythagoras wanted to know why some combinations of musical sounds seemed more beautiful than others, and he found answers in terms of numerical ratios representing the harmonic overtone series on a string.
He is reputed to have observed that when the lengths of vibrating strings are expressible as ratios of integers e. If, for example, a string of a certain length would sound particularly harmonious with a string of twice the length other factors being equal.
In modern parlance, if a string sounds the note C when plucked, a string twice as long will sound a C an octave lower. In one system of musical tuning, the tones in between are then given by for D, for E, for F, for G, for A, and for B, in ascending order. Aristotle — BC understood that sound consisted of compressions and rarefactions of air which "falls upon and strikes the air which is next to it In about 20 BC, the Roman architect and engineer Vitruvius wrote a treatise on the acoustic properties of theaters including discussion of interference, echoes, and reverberation—the beginnings of architectural acoustics.
He described the ascending seats in ancient theaters as designed to prevent this deterioration of sound and also recommended bronze vessels of appropriate sizes be placed in theaters to resonate with the fourth, fifth and so on, up to the double octave, in order to resonate with the more desirable, harmonious notes.
Principles of acoustics have been applied since ancient times : A Roman theatre in the city of Amman. The physical understanding of acoustical processes advanced rapidly during and after the Scientific Revolution. Mainly Galileo Galilei — but also Marin Mersenne — , independently, discovered the complete laws of vibrating strings completing what Pythagoras and Pythagoreans had started years earlier.
Galileo wrote "Waves are produced by the vibrations of a sonorous body, which spread through the air, bringing to the tympanum of the ear a stimulus which the mind interprets as sound", a remarkable statement that points to the beginnings of physiological and psychological acoustics. Experimental measurements of the speed of sound in air were carried out successfully between and by a number of investigators, prominently Mersenne.
Meanwhile, Newton — derived the relationship for wave velocity in solids, a cornerstone of physical acoustics Principia, Age of Enlightenment and onward The eighteenth century saw major advances in acoustics as mathematicians applied the new techniques of calculus to elaborate theories of sound wave propagation. Also in the 19th century, Wheatstone, Ohm, and Henry developed the analogy between electricity and acoustics. The twentieth century saw a burgeoning of technological applications of the large body of scientific knowledge that was by then in place.
Underwater acoustics was used for detecting submarines in the first World War. Sound recording and the telephone played important roles in a global transformation of society. Sound measurement and analysis reached new levels of accuracy and sophistication through the use of electronics and computing.
The ultrasonic frequency range enabled wholly new kinds of application in medicine and industry. New kinds of transducers generators and receivers of acoustic energy were invented and put to use. At Jay Pritzker Pavilion, a LARES system is combined with a zoned sound reinforcement system, both suspended on an overhead steel trellis, to synthesize an indoor acoustic environment outdoors.
The study of acoustics revolves around the generation, propagation and reception of mechanical waves and vibrations. The fundamental acoustical process The steps shown in the above diagram can be found in any acoustical event or process. There are many kinds of cause, both natural and volitional.
There are many kinds of transduction process that convert energy from some other form into sonic energy, producing a sound wave. There is one fundamental equation that describes sound wave propagation, the acoustic wave equation, but the phenomena that emerge from it are varied and often complex. The wave carries energy throughout the propagating medium. The final effect may be purely physical or it may reach far into the biological or volitional domains.
The five basic steps are found equally well whether we are talking about an earthquake, a submarine using sonar to locate its foe, or a band playing in a rock concert. The central stage in the acoustical process is wave propagation. This falls within the domain of physical acoustics.
In fluids, sound propagates primarily as a pressure wave. In solids, mechanical waves can take many forms including longitudinal waves, transverse waves and surface waves. Acoustics looks first at the pressure levels and frequencies in the sound wave and how the wave interacts with the environment.
This interaction can be described as either a diffraction, interference or a reflection or a mix of the three. If several media are present, a refraction can also occur. Transduction processes are also of special importance to acoustics. Spectrogram of a young girl saying "oh, no" In fluids such as air and water, sound waves propagate as disturbances in the ambient pressure level.
While this disturbance is usually small, it is still noticeable to the human ear. The loudness of these disturbances is related to the sound pressure level SPL which is measured on a logarithmic scale in decibels. Wave propagation: frequency Physicists and acoustic engineers tend to discuss sound pressure levels in terms of frequencies, partly because this is how our ears interpret sound. What we experience as "higher pitched" or "lower pitched" sounds are pressure vibrations having a higher or lower number of cycles per second.
In a common technique of acoustic measurement, acoustic signals are sampled in time, and then presented in more meaningful forms such as octave bands or time frequency plots. Both of these popular methods are used to analyze sound and better understand the acoustic phenomenon.
The entire spectrum can be divided into three sections: audio, ultrasonic, and infrasonic. The audio range falls between 20 Hz and 20, Hz.
This range is important because its frequencies can be detected by the human ear. This range has a number of applications, including speech communication and music. The ultrasonic range refers to the very high frequencies: 20, Hz and higher. This range has shorter wavelengths which allow better resolution in imaging technologies.
Medical applications such as ultrasonography and elastography rely on the ultrasonic frequency range. On the other end of the spectrum, the lowest frequencies are known as the infrasonic range.
These frequencies can be used to study geological phenomena such as earthquakes. Analytic instruments such as the spectrum analyzer facilitate visualization and measurement of acoustic signals and their properties. The spectrogram produced by such an instrument is a graphical display of the time varying pressure level and frequency profiles which give a specific acoustic signal its defining character. In an electroacoustic context, this means converting sound energy into electrical energy or vice versa.
Electroacoustic transducers include loudspeakers, microphones, hydrophones and sonar projectors. These devices convert a sound pressure wave to or from an electric signal. The most widely used transduction principles are electromagnetism, electrostatics and piezoelectricity. The transducers in most common loudspeakers e.
Electret microphones and condenser microphones employ electrostatics—as the sound wave strikes the microphone's diaphragm, it moves and induces a voltage change. The ultrasonic systems used in medical ultrasonography employ piezoelectric transducers.
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