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Asserts are checks that you can put in your app that cause the application to halt if it fails a condition. C++ has a built-in call that you can use, as does Objective-C. For example, in C++, the following assert checks to see whether the condition is true:

Thermal stresses in the structure are caused by the temperature gradient in the wall and accompanying dimensional changes. In order to develop the thermal stresses, the structural member must be restrained in some way. The constraints in the thermal-stress problems in the design of vessels are usually divided into external and internal constraints. Whenever there is a significant temperature gradient across the vessel wall, thermal expansion takes place. Generally, the effects of the externally applied loads and the effects of thermal expansion or contraction are independently analyzed, and the final effects of the total combined stresses are considered additive when comparisons are made with maximum allowable stresses. It is usually assumed that thermal stresses are within the elastic range on the stress-strain curve of the vessel material. If the temperature is very high, the creep may become significant and must be considered. The induced thermal stresses often exceed the yield strength of the vessel material. Since thermal stresses are self-limiting, local plastic relaxation will tend to reduce the acting load.

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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.

The basic equations for thermal stresses can be developed by considering that a body is composed of unit cubes of uniform average temperature T. If the temperature of the unit cube is changed to T1 such that T1 > T and is restricted, then there are three distinct cases according to the nature of restriction. If a cartesian coordinate system x, y, z is considered, then restrictions can be imagined in (1) the x direction, (2) in the x and y directions, and (3) in all three directions, i.e., in the x, y, and z directions. The corresponding thermal stresses are given by the following expressions: x = E(T1 T) x = y = E (T1 T) (1 ) E (T1 T) (1 ) (39.41) (39.42) (39.43)

TABLE 11-1 1209

where = coefficient of thermal expansion = Poisson s ratio E = modulus of elasticity The equations are basic for direct thermal stresses under external or internal constraints and give the maximum thermal stress for the specific constraint. The internal constraint is due to nonuniform temperature distribution in the body of the structure such that it does not allow free expansion of the individual body elements according to the local temperatures. In such a case, stresses are induced in the body in the absence of any external constraints. A thick cylindrical shell may be assumed to consist of thin, mutually connected, concentric cylindrical shells. Whenever a temperature gradient exists in the vessel wall due to heat transfer, the cylindrical elements will be at different average temperatures and will expand at different rates. The individual cylindrical elements will be constrained by each other, and consequently, thermal stresses will be induced in the otherwise nonrestrained cylinder wall. Detailed treatments of the general analytical methods for solving thermal stresses caused by internal constraints are given by Gatewood [39.6], Bergen [39.7], and Goodier [39.8]. Most cylindrical shell and pressure-vessel problems can be reduced to twodimensional stress problems. Generally, analytical solutions are possible for relatively simpler cases.

assert(myVariable == someOtherVariable);

39.6.1 Thermal Stresses in Thin Cylindrical Vessels Consider a hollow, thin cylindrical vessel (Fig. 39.8) subjected to a linear radial temperature gradient. The temperature at the inner wall is T1 and is greater than temperature T2 at the outer wall. If the vessel is long and restrained at the ends, then the longitudinal stress z is given by z = E (T1 T2) 2(1 ) (39.44)

where = coefficient of thermal expansion, and = Poisson s ratio. Estimation of thermal stresses in composite cylinders is quite involved. Faupel and Fisher [39.10] consider the thermal stresses in a multishell laminate of different materials with thermal gradients through each shell.

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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.

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