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Hertz (1882, 1895) established the state of stress and strain between two contacting elastic bodies In this section we present two cases: (a) two crowned rollers and (b) two cylindrical rollers Figure 91 shows two crowned rollers of different sizes in elastic contact A plane tangent to each body at the touching point forms the tangent plane If the bodies are now pressed together so that the collinear force is normal to the tangent plane, deformation takes place and a small contact area will replace the contact point O of the unloaded state First, we will nd the size and shape of this contact area and distribution of normal pressure Then we can calculate the stresses and strains that the interfacial pressure induces in the contacting members Hertz assumed that (a) the two contacting bodies are isotropic and elastic in accordance with Hookes law, (b) the contact area is quite small compared to the radii of curvature of the undeformed bodies, and (c) only normal pressures that exist during contact are prevalent Displacements in the xy plane and shearing tractions are neglected In Fig 91, the pressure distribution between the two contacting bodies form a semiellipsoid, and the surface of contact traced on the tangent plane will have an elliptical boundary The intensity of pressure over the surface of contact is represented by the coordinates of the semiellipsoid x 2 y2 p = p0 1 - 2 - 2 a b

a & c is false a | b is true a | c is true Use short-circuit && and || a && b is true a && c is false a || b is true a || c is true

Many people get confused by fan traps and chasm traps These are two types of join problems that lead to incorrect results How they are different matters little In fact, I don t even like to discuss them, because if you really follow the rules in the other sections, you should never encounter either Further, if you use these terms with a SQL programmer, he or she will stare at you dumbfounded: a what trap However, the vendor uses these terms in education courses and help text, so I ll describe them briefly As discussed in the last section, a chasm trap occurs when you lose results by joining two fact tables to a common lookup table With a fan trap, the opposite happens: your results are overstated (spread like a fan) because a Cartesian product occurs when aggregates go across one-to-many joins (See 7, Figure 7-3 for an illustration of how this happens) A prime example of a fan trap is joining Order Header to Order Detail This is typically a oneto-many join relationship Freight exists on the Order Header table and Quantity exists on the Detail table The Freight will be fanned or overstated by however many line items there are in the Order Detail table

Let s look closely at how the & and | are implemented They are shown here:

(91)

// Overload | for short-circuit evaluation public static ThreeD operator |(ThreeD op1, ThreeD op2) { if( ((op1x != 0) || (op1y != 0) || (op1z != 0)) | ((op2x != 0) || (op2y != 0) || (op2z != 0)) ) return new ThreeD(1, 1, 1); else return new ThreeD(0, 0, 0); } // Overload & for short-circuit evaluation public static ThreeD operator &(ThreeD op1, ThreeD op2) { if( ((op1x != 0) && (op1y != 0) && (op1z != 0)) & ((op2x != 0) && (op2y != 0) && (op2z != 0)) ) return new ThreeD(1, 1, 1); else return new ThreeD(0, 0, 0); }

There seems to be a tendency for long-time BusinessObjects developers to avoid contexts at all costs This might have been valid with the earliest versions of BusinessObjects, but it is not a valid concern with XI, or really anything later than version 4 As described earlier, users are rarely prompted to choose a context The use of contexts prevents loops and, most important, allows users to formulate and answer valid business questions In an attempt to avoid contexts, some designers will turn to aliases as a way of breaking a loop and avoiding a context This is the wrong use of aliases While it might result in valid join statements, it can create an unnecessarily complicated universe and more objects (that really mean the same thing) Instead, try to understand the data from the business perspective Use contexts to group the related schemas and use aliases only when one table can have multiple meanings such as a Sold To Customer versus a Ship To Customer or a Manager who is also an Employee

Notice first that both now return an object of type ThreeD Pay attention to how this object is generated If the outcome of the operation is true, then a true ThreeD object (one in which at least one coordinate is non-zero) is created and returned If the outcome is false, then a false object is created and returned Thus, in a statement like this

if(a & b) ConsoleWriteLine("a & b is true"); else ConsoleWriteLine("a & b is false");

where a and b denote the semiaxes of the elliptical boundary The maximum pressure is situated at the center of the surface of contact above point O