Elementary Surveying: An Introduction to Geomatics (15th Edition)
15th Edition
ISBN: 9780134645964
Author: GHILANI
Publisher: PEARSON
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Chapter 1, Problem 1.18P
To determine
About GIS in flood emergency planning.
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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 1 Solutions
Elementary Surveying: An Introduction to Geomatics (15th Edition)
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- 4. 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_forward
- Read 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_forwardplease explain step by step and use the ACI codearrow_forwardFind: 1. The support reactions 2. Internal forces (shear, and moments) 3. Deflectionarrow_forward
- 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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