POINT ESTIMATE METHODS in Visual Studio .NET Generator UCC - 12 in Visual Studio .NET POINT ESTIMATE METHODS POINT ESTIMATE METHODSUPC A Recognizer In .NET FrameworkUsing Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in .NET applications.Table 15.1 Results from point-estimate method for vertical cut Point 1 2 3 4 c (kPa) 70 130 70 130 (kN/m3 ) 18 18 22 22 M (kPa) 25 85 15 75 p pM pM 2 234.375 903.125 28.125 2109.375 3275.000 = 27.84Universal Product Code Version A Generation In Visual Studio .NETUsing Barcode creator for .NET framework Control to generate, create UPC A image in .NET applications.0.375 9.375 0.125 10.625 0.125 1.875 0.375 28.125 Sum = 50.000 Var = 3275 (50)2 = 775 3 H = 10 m, c = 100 kPa, c = 30 kPa, c = 20 kN/m , c = 2 kN/m3Reading UPC-A Supplement 5 In Visual Studio .NETUsing Barcode scanner for VS .NET Control to read, scan read, scan image in VS .NET applications.is 50. Similarly, the products of the entries in column 5 and the square of the entries in column 4 give the entries in column 7, and the sum of these gives the estimate of E[M 2 ]. The difference between this and the square of the estimate of the mean gives the estimate of the variance. The square root of the variance is the standard deviation. The calculations in the next-to-last row show that this gives 27.84. The values of the mean and the standard deviation of M agree exactly with the theoretical values. These give a reliability index = 1.796, and, if M is Normally distributed, a probability of failure pf = 3.6 10 2 . When the correlation coef cient is set to zero, M is unchanged, and M in both the exact and Rosenblueth calculations becomes 30.41 kPa. Then = 1.644, and pf = 5.0 10 2 .Encode Bar Code In VS .NETUsing Barcode generator for .NET framework Control to generate, create barcode image in .NET framework applications.15.3.2 Example Culmann Failure Mechanism along a Plane Barcode Recognizer In .NETUsing Barcode reader for .NET framework Control to read, scan read, scan image in .NET framework applications.A more complicated example is the margin of safety of a slope against sliding on a single plane, otherwise known as the Culmann analysis (Taylor 1948). The margin of safety is M =c+ 1 H sin( ) cos [tan tan ] 2 sin (15.29)UPC Code Maker In Visual C#Using Barcode maker for .NET framework Control to generate, create UPC Symbol image in VS .NET applications.where is the inclination of the failure plane, is the inclination of the front of the slope, H is the vertical distance from the crest to the toe of the slope, and the other variables have the conventional soil mechanics meanings. If the only uncertain variables are the unit weight, the cohesion, and the tangent of the friction angle ( , c, and tan ), and if these variables are mutually independent, the mean and variance of M can be expressed exactly. For the following values of the parameters: H = 10 m, = 20 , = 26 c = 5 kPa, c = 0.5 kPa tan = 0.267949( = 15 ), tan = 0.018756( the exact analytical results are M = 2.633 kPa M = 0.722 kPa (15.31)GS1 - 12 Generator In VS .NETUsing Barcode maker for ASP.NET Control to generate, create UCC - 12 image in ASP.NET applications. = 22 kN/m3 , = 2.2 kN/m3 = 0.07) (15.30)UPC Code Generator In VB.NETUsing Barcode generation for .NET Control to generate, create UPC-A Supplement 5 image in VS .NET applications.RELATION TO ORTHOGONAL POLYNOMIAL QUADRATURE GTIN - 12 Encoder In .NET FrameworkUsing Barcode creation for .NET Control to generate, create UPC-A image in .NET framework applications.Table 15.2 Point 1 2 3 4 5 6 7 8 Create EAN 13 In .NET FrameworkUsing Barcode drawer for .NET Control to generate, create GS1 - 13 image in .NET framework applications.Results from point-estimate method for Culmann slope c (kPa) 5.5 5.5 4.5 4.5 5.5 5.5 4.5 4.5 tan( ) 0.286706 0.249193 0.286706 0.249193 0.286706 0.249193 0.286706 0.249193 M (kPa) 3.405 2.388 2.405 1.388 3.786 2.954 2.786 1.954 p pM pM 2 1.4493 0.7128 0.7230 0.2408 1.7917 1.0908 0.9702 0.4773 7.4559 = 0.7222Drawing Barcode In VS .NETUsing Barcode drawer for .NET Control to generate, create barcode image in .NET applications. (kN/m3 ) 24.2 24.2 24.2 24.2 19.8 19.8 19.8 19.8Universal Product Code Version E Maker In Visual Studio .NETUsing Barcode generation for Visual Studio .NET Control to generate, create UPC-E Supplement 5 image in VS .NET applications.0.125 0.4256 0.125 0.2985 0.125 0.3006 0.125 0.1735 0.125 0.4733 0.125 0.3693 0.125 0.3483 0.125 0.2443 Sum = 2.6333 Var = 7.4559 (2.6333)2 = 0.52160 H = 10 m, = 20 deg, = 26 degUPC-A Supplement 5 Encoder In JavaUsing Barcode generation for Java Control to generate, create UCC - 12 image in Java applications.Table 15.2 shows the calculations for Rosenblueth s method with three independent variables. The arrangement is similar to that of Table 15.1. In this case all the weights are the same (0.125) because the variables are uncorrelated. The results are the same as the exact values to the limit of computational precision. In both cases = 3.647, and pf = 1.3 10 4 . It is much easier to carry out the Rosenblueth point estimates than to derive the exact expressions for the mean and variance of M. Further, in the cases not considered here that the variables were correlated or that some of the other xed variables were uncertain, an analytical expression would be very dif cult or impossible to derive, and an approximate approach would be necessary. These results inspire some con dence in the point-estimate method.Code 39 Reader In VS .NETUsing Barcode decoder for VS .NET Control to read, scan read, scan image in Visual Studio .NET applications.UCC - 12 Drawer In Visual Basic .NETUsing Barcode drawer for VS .NET Control to generate, create UCC-128 image in .NET applications.Generating Code 3/9 In Visual C#.NETUsing Barcode encoder for VS .NET Control to generate, create ANSI/AIM Code 39 image in VS .NET applications.Barcode Encoder In Visual C#Using Barcode drawer for VS .NET Control to generate, create bar code image in .NET framework applications.