
Interpretation:
The amount of nickel in grams that must be added to copper is to be calculated to give an alloy of desired properties. Also, the ratio of the number of nickel atoms to copper atoms in this alloy is to be determined.
Concept Introduction:
On the temperature-composition graph of an alloy, the curve above which the alloys exist in the liquid phase is the liquidus curve. The temperature at this curve is maximum known as liquidus temperature at which the crystals in the alloy can coexist with its melt in the
Solidus curve is the locus of the temperature on the temperature composition graph of an alloy, beyond which the alloy is completely in solid phase. The temperature at this curve is minimum known as solidus temperature at which the crystals in the alloy can coexist with its melt in the thermodynamic equilibrium.
Percentage of a component in an alloy is calculated as:

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Chapter 10 Solutions
Essentials of Materials Science and Engineering, SI Edition
- (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…arrow_forwardBased on the results obtained, comment on the relative importance of the body and the tails of thedistributions of R and S on the probability of failure with increasing central safety factor CSF .arrow_forwardFind Vo using mesh analysisarrow_forward
- The resistance R and load effect S for a given failure mode are statistically independent random variables with marginal PDF's 1 fR (r) = 0≤r≤100 100' fs(s)=0.05e-0.05s (a) Determine the probability of failure by computing the probability content of the failure domain defined as {rarrow_forward1. 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).arrow_forward4. EI is constant in the beam below (a = 12 ft, b = 5 ft, E = 29,000 ksi, I = 800 in¹ (W18x50), P = 2 kip): b Р C a. Sketch the deflected shape. b. Determine the equations of the slope and the elastic curve using the coordinates x1 and x2. c. For the AB segment, determine the maximum deflection and its location. Hint: at maximum deflection, the slope is zero. d. Specify the slope (in radians) and deflection at point C.arrow_forward3. EI is constant in the beam below (a = 10 ft, b = 5 ft, E = 29,000 ksi, I = 340 in (W14x34), Mo = 50 k. ft): Mo Mo a. Sketch the deflected shape. X2 b. Determine the equations of the slope and the elastic curve using the coordinates x1 and x2. Due to symmetry, only the left side is sufficient. Hint: symmetry requires the slope to be zero at mid span. c. Determine the maximum deflection. d. Specify the slope (in radians) at point A.arrow_forward2. EI is constant in the beam below (L = 10 ft, E = 29,000 ksi, I = 350 in (W12x45), W = 500 lb/ft): a. Sketch the deflected shape. b. Determine the equations of the slope and the elastic curve using the coordinates x1 and X2. c. Specify the slope (in radians) and deflection at point C. d. Specify the slope (in radians) at point B. -x- L 2 W C X27 L 22 Barrow_forwardPlease solve this problem as soon as possible My ID# 016948724arrow_forwardRead the paper of Khalili et al. (2004). Describe the issue raised by Jennings and Burland in using the single-value effective stress to quantify the problem of wetting-induced collapse. Use the discussion in Khalili et al. (2004) on the different ways that effective stress and yield stress change with suction to explain how wetting-induced collapse can be modeled with the single-valued effective stress. Comment on whether the soil tested by Jotisankasa (2003) would be collapsible based on the discussionarrow_forwardc) An RC circuit is given in Figure Q1.1, where Vi(t) and Vo(t) are the input and output voltages. (i) Derive the transfer function of the circuit. (ii) With a unit step change of Vi(t) applied to the circuit, derive the time response of Vo(t) with this step change. Vi(t) C₁ Vo(1) R₂ C2 C3 | R = 20 ΚΩ = 50 ΚΩ C=C2=C3=25 μF Figure Q1.1. RC circuit.arrow_forwardc) An RC circuit is given in Figure Q1. vi(t) and vo (t) are the input and output voltages. (i) Derive the transfer function of the circuit. (ii) With a unit step change vi(t) applied to the circuit, derive and sketch the time response of the circuit. R₁ R2 v₁(t) R3 C₁ v₁(t) R₁ = R₂ = 10 k R3 = 100 kn C₁ = 100 μF Figure Q1. RC circuit.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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