MAT.SCIENCE+ENGIN.(PERUSALL ACCESS)
10th Edition
ISBN: 2818440149658
Author: Callister
Publisher: PERUSALL
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Chapter 16, Problem 4QAP
To determine
To find:
- (a) The difference between cement and concrete.
- (b) The limitations of concrete being used as the structural material.
- (c) The techniques used to make concrete stronger by reinforcement.
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In a structural reliability problem, the resistance (capacity) R and load effect (demand) S random variables
associated with a failure mode of the structure of interest are normally distributed and statistically
independent with the following probability distribution parameters (or statistics) in consistent units:
MR = 12, σR = 3
μs = 5, σs = 2
(a) Determine the exact probability of failure pF ·
Please find Vo using Mesh analysis
(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…
Chapter 16 Solutions
MAT.SCIENCE+ENGIN.(PERUSALL ACCESS)
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- Based 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_forwardThe 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_forwardc) A RC circuit is given in Figure Q1.1. 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 the circuit. C₁ C₂ Vi(t) Vo(1) R₁ C₂ R-25 k C=C2=50 µF Figure Q1.1. RC circuit.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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