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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

[queuedCondition lock]; self.playQueueDataRecs[0].inUse = YES; [queuedCondition unlock]; // Get the magic cookie (for compressed formats like MPEG 4 AAC) // from the file stream and set it on the audio queue err = AudioFileStreamGetPropertyInfo(inAudioFileStream, kAudioFileStreamProperty_MagicCookieData, &propertySize, NULL); void *magicCookie = calloc(1, propertySize); err = AudioFileStreamGetProperty(inAudioFileStream, kAudioFileStreamProperty_MagicCookieData, &propertySize, magicCookie); if (err == noErr) { err = AudioQueueSetProperty(playQueue, kAudioFileStreamProperty_MagicCookieData, magicCookie, propertySize); } free(magicCookie); } }

38.1 BENDING IN THE PLANE OF CURVATURE / 38.2 38.2 CASTIGLIANO S THEOREM / 38.2 38.3 RING SEGMENTS WITH ONE SUPPORT / 38.3 38.4 RINGS WITH SIMPLE SUPPORTS / 38.10 38.5 RING SEGMENTS WITH FIXED ENDS / 38.15 REFERENCES / 38.22

A B C E e F G I K M P Q R r r T U V W w X Area, or a constant Constant Constant Modulus of elasticity Eccentricity Force Modulus of rigidity Second moment of area (Table A.1) Shape constant (Table 36.1), or second polar moment of area Bending moment Reduced load Fictitious force Force reaction Ring radius Centroidal ring radius Torsional moment Strain energy Shear force Resultant of a distributed load Unit distributed load Constant

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38.1 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

Listing 9-1

Constant Deflection Constant Load angle Span angle, or slope Normal stress Angular coordinate or displacement

The property listener callback starts by checking its inPropertyID argument to see what new property information is available. If it s not kAudioFileStreamProperty_ReadyToProducePackets, it does nothing. When the stream is ready to produce packets, it finishes the setup that wasn t possible earlier when the stream was created. First it looks up the audio format property and creates the play queue. This makes use of the self variable both to set the play queue on the streaming object and to pass self along in AudioQueueNewOutput so that it will be available in the postPlayCallback() function. Next the callback creates the audio buffers, since you now have enough information to do so. You ll create the buffers once and reuse them as many times as needed. It sets self s currentBufferIndex to 0 so that the first buffer in the array will be current and marks that buffer as being in use. Now, the playback queue has been created, and you re ready to start playing audio. As new data comes in, you ll continue to pass it to AudioFileStreamParseBytes(). This will lead to calls to the audio data callback, the aptly named audioDataCallback(). Listing 318 shows this function.

Methods of computing the stresses in curved beams for a variety of cross sections are included in this chapter. Rings and ring segments loaded normal to the plane of the ring are analyzed for a variety of loads and span angles, and formulas are given for bending moment, torsional moment, and deflection.

The distribution of stress in a curved member subjected to a bending moment in the plane of curvature is hyperbolic ([38.1], [38.2]) and is given by the equation = My Ae(r e y) (38.1)

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where r = radius to centroidal axis y = distance from neutral axis e = shift in neutral axis due to curvature (as noted in Table 38.1) The moment M is computed about the centroidal axis, not the neutral axis. The maximum stresses, which occur on the extreme fibers, may be computed using the formulas of Table 38.1. In most cases, the bending moment is due to forces acting to one side of the section. In such cases, be sure to add the resulting axial stress to the maximum stresses obtained using Table 38.1.

A complex structure loaded by any combination of forces, moments, and torques can be analyzed for deflections by using the elastic energy stored in the various components of the structure [38.1]. The method consists of finding the total strain energy stored in the system by all the various loads. Then the displacement corresponding to a particular force is obtained by taking the partial derivative of the total energy with respect to that force. This procedure is called Castigliano s theorem. General expressions may be written as yi = U Fi i = U Ti i = U Mi (38.2)

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