Using Excel, create a table showing the viscosity of water as a function of temperature in the range of 0 ° C ( 273.15 K ) to 100 ° C ( 373.15 K ) and also plot the graph showing the value of viscosity as a function of temperature.

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(a) Determine the Nataf model for the joint PDF fxx, (xx) of the basic (physical) random variables X₁ and X, with marginal PDF's fx(x)=e, 0≤x (Exponential distribution) fx₁ (x2)=x2e-0.5x, 0≤x (Rayleigh distribution) and correlation coefficient Pxx=0.50 Note: Use Table 6 of paper by Liu and Der Kiureghian, 1986. (b) Generate a 3D surface plot and contour plot of the joint PDF fxx, (x,x) using Matlab or any other software of your choice. (c) What is the standard deviation of X2? (d) Construct a transformation from the physical X space (defined by random variables X, and X,) to the standard normal U space (defined by the statistically independent standard normal random variables (U, and U₂), i.e., U=T(X). Also describe the inverse transform X=T(U) and the Jacobian matrices J = ди θα and Ju Ox ди (e) According to the inverse transformation X = T¹ (U) and using Matlab, generate 1,000 samples from the Nataf joint PDF fxx, (x1,x2) derived in part (a). Start by generating samples of U using a…

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Chapter 14, Problem 4P

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Using Excel, create a table showing the viscosity of water as a function of temperature in the range of 0° C (273.15 K) to 100° C (373.15 K) and also plot the graph showing the value of viscosity as a function of temperature.

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(a) Determine the Nataf model for the joint PDF fxx, (xx) of the basic (physical) random variables X₁ and X, with marginal PDF's fx(x)=e, 0≤x (Exponential distribution) fx₁ (x2)=x2e-0.5x, 0≤x (Rayleigh distribution) and correlation coefficient Pxx=0.50 Note: Use Table 6 of paper by Liu and Der Kiureghian, 1986. (b) Generate a 3D surface plot and contour plot of the joint PDF fxx, (x,x) using Matlab or any other software of your choice. (c) What is the standard deviation of X2? (d) Construct a transformation from the physical X space (defined by random variables X, and X,) to the standard normal U space (defined by the statistically independent standard normal random variables (U, and U₂), i.e., U=T(X). Also describe the inverse transform X=T(U) and the Jacobian matrices J = ди θα and Ju Ox ди (e) According to the inverse transformation X = T¹ (U) and using Matlab, generate 1,000 samples from the Nataf joint PDF fxx, (x1,x2) derived in part (a). Start by generating samples of U using a…

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1. The beam is supported by a roller constraint at B, which allows vertical displacement but resists axial load and moment. If the bar is subjected to the loading shown and constant El (L = 12 ft, E = 3100 ksi, I = 1728 in (rectangular section 12"x12"), w = 1 klf). Caution: pay attention to unit conversion between ft and in) x W B a. Sketch the deflected shape. L b. Determine the equations of the slope and the elastic curve using the coordinate x. First, solve this problem parametrically, and then substitute the numerical values for L, E, I, w at the end. There will be a significant penalty for solutions that do not calculate the slope and deflection as parametric functions. c. Specify the slope (in radians) at point A (parametrically and numerically). d. Specify the vertical displacement at point B (parametrically and numerically).