Principles of Geotechnical Engineering (MindTap Course List)
9th Edition
ISBN: 9781337516877
Author: Das
Publisher: Cengage
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Textbook Question
Chapter 2, Problem 2.7P
Repeat Problem 2.4 with the following data.
2.4 The following are the results of a sieve analysis.
a. Determine the percent finer than each sieve and plot a grain-size distribution curve.
b. Determine D10, D30, and D60 for each soil.
c. Calculate the uniformity coefficient Cu.
d. Calculate the coefficient of gradation Cc.
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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…
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 .
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).
Chapter 2 Solutions
Principles of Geotechnical Engineering (MindTap Course List)
Ch. 2 - For a gravel with D60 = 0.48 mm, D30 = 0.25 mm,...Ch. 2 - Prob. 2.2PCh. 2 - Prob. 2.3PCh. 2 - The following are the results of a sieve analysis....Ch. 2 - Repeat Problem 2.4 with the following data. 2.4...Ch. 2 - Repeat Problem 2.4 with the following data. 2.4...Ch. 2 - Repeat Problem 2.4 with the following data. 2.4...Ch. 2 - The following are the results of a sieve and...Ch. 2 - Repeat Problem 2.8 using the following data. 2.8...Ch. 2 - Repeat Problem 2.8 using the following data. 2.8...
Ch. 2 - The grain-size characteristics of a soil are given...Ch. 2 - Repeat Problem 2.11 with the following data. 2.11...Ch. 2 - Repeat Problem 2.11 with the following data. 2.11...Ch. 2 - A hydrometer test has the following result: Gs =...Ch. 2 - Repeat Problem 2.14 with the following values: Gs...Ch. 2 - Three groups of students from the Geotechnical...Ch. 2 - Refer to Problem 2.C.1. Results of the sieve...
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- 1. A W10x60 with sections properties shown is to be used as a column. If the unsupported length is 5.0m, find the Safe Axial Load that can be carried by the section. Use Fy=248 MPa and K=1.50 (35pts) Section Properties: A = 11355 mm2 Ix = 142x106 mm4 rx = 111.51 mm Iy = 48 x 106 mm4 ry = 65.28 mm 2. A Steel Column will be required to carry a total load of 500KN. If a tubular section will be utilized and the required dimension must not exceed 400x400, what will be the required thickness of the section (tf=tw). Use Fy=248 MPa L=4.5m, K=1.0 and 80% of initial fa will be used. (50pts) Note: Plate thickness available are: 2mm, 3mm, 4mm, 6mm, 8mm and 10mm 3. A steel tension rod will be subjected to a tension load of 320 KN. What will be the required diameter of the rod if Fy=248 MPa (15pts)arrow_forwardfor purposes of orientation every contour may must display what?arrow_forwardDuring calibration of an LVDT, the data shown in the accompanying table were obtained. Using a spreadsheetprogram, plot the relation between the micrometer reading and voltage. What is the linear range of the LVDT? Determinethe calibration factor of the LVDT by obtaining the best fit line of the data within the linear range.arrow_forward
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