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section in comparison to the spokes, the spokes act as guided cantilevers and have a maximum bending stress that is half the value given by Eq. (7.38). Example 7. A cast-iron flywheel with a rectangular rim 5 in thick and 11 in wide has an average radius of 48 in. If the hub has a 5.2-in radius and each of the 8 spokes has an area of 11 in2, what are the maximum stresses at a speed of 400 rpm The maximum torque possible is 4000 lb ft at full speed. The area A = (5)(11) = 55 in2, = 2 (400)/60 = 41.9 rad/s, I = 11(5)3/12 = 114.6 in4, and Zr = 11(5)2/6 = 45.8 in 3. The angle is 22.5 degrees, or /8, and the maximum rim stress occurs at the inner surface of the rim with = /8. From Eqs. (7.34) through (7.36), using a density of 0.283 lb/in3, f1 = 1 2 sin2 ( /8) sin ( /4) /8 + = 1.274 4 2 (7.39) (7.40) (7.41)

The most common place I ve run into this kind of mem stomp is with animation systems. The usual sequence of events is something like this: 1. 2. 3. 4. 5. 6. 7. 8. 9. Object A creates an animation instance. Object A sets a callback to itself so that it is notified when the animation completes. Object A triggers the animation. The animation runs. The animation completes and calls Object A s callback. Inside the callback, Object A causes an app state change that requires that the animation gets deleted. The animation object gets deleted. The callback completes and returns into the animation object (which has now been deleted). The animation object does some cleanup code, which involves modifying some member variables.

* *** * * ** 0 ** * * **** ** * * * ** * * * * * *

1 = 7.600 10 4 /4

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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.

f4 = =

cos ( /8) = 0.340 7.11 sin ( /8) 1 0.283(48)2(41.9)2 55(48) 0.340 1 + 0.340 32.2(12) 7.11 /8 3( 45.8) 3 = 3660 psi

01000010 10000100 10100100 10000011 00000001 00100100 11000011 00000100 00000010 01110100 10100011 01000100 11000010 10000010 11100011 01100100 11010100 01000011

10. What it s actually doing is changing memory that has been allocated to something else now. I have typically run into these kinds of problems when transitioning between front-end menu screens and in-game state (and vice versa) in games. It s not uncommon for an animation to play in response to user input and at the end of the animation trigger a state change. For a simplified example, see Figure 4-7. Of course, this kind of mem stomp can occur in other ways, so just be aware of it.

(7.42) (7.43)

Table 7.5 shows the values for points P1, P2 , P3, and P4 , giving additional digits for checking computer programs. Although the stress formulation was based on a spoke of length ra, the maximum tension stress in the spoke is found for the hub radius, 5.2 in. From Eq. (7.37), = 4(55) 3(5.2)2 0.283(48)2(41.9)2 3+ = 2850 psi 6(32.2)(12) 7.11(11) (48)2 (7.44)

If the spokes are of standard design, an elliptical cross section twice as long in the direction of motion as in the axial direction, the dimensions for an 11-in2 spoke would be 2(11)/ = 2.65 in by 5.29 in. The section modulus is then Zs = (2.65)(5.29)2/32 = 7.28 in3, and the bending stress in the spokes, from Eq. (7.38), would be = 4000(48 5.2) = 61 psi 7.28(8)(48) (7.45)

66 132 164 131 1 36 195 4 2 116 163 68 194 130 227 100 212 67

The combined stress for the spoke is then = 2850 + 61 = 2910 psi. 7.3.3 Thin Disk If a thin disk has a large radius in comparison to its thickness, the stress can be assumed constant across the thickness. Defining the stress function F as F = rz r the stress equation for a thin disk of variable thickness z(r) is r2 and t = 1 dF + 2 r 2 z dr (7.48) dF 2 r 3z r dz d 2F dF F + (3 + ) r F = 0 2 + r dr dr g z dr dr (7.47) (7.46)

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