University of Waterloo
CivE 331
Compute the Fourier Series expansion of the following periodic function. Plot the expansion for =3, 5, and 10.
-20
By inspection, the period of the function is =16 and l = T / 2 = 8 . Substitute l into the general expressio
University of Waterloo
CivE 331
Consider the following function, which could represent ramp loading with decay:
x +1 ; 0 < x < 4 f (x ) = -k ( x - 4 ) where ; 4< x <L 5e
is a degradation constant.
Graphically, ( ) with = 0.26824 and = 10 is:
6.00 5.00
University of Waterloo
CivE 331
Determine the Fourier Series representation of the following function using the half-range cosine expansion. Graph the expansion for n = 10.
6.00 5.00 4.00 3.00 2.00 1.00 0.00 0 1 2 3 4 5 6 7 8 9 10
f (x ) = 5e - k ( x - 4
University of Waterloo
CivE 331
Periodic Loading of a Railway Foundation Consider a stationary train in which every other car is loaded with cargo:
empty empty empty
Track Bed
Track
The train and its cargo exert a force (per unit length) on the track bed
University of Waterloo
CivE 331
Complete the following table.
Differential Equation
ODE IndeDeHomogeneous Linear or pendent pendent or Nonor PDE Order variables variables homogenous non-linear
(a)
yx = x2 + 5y
(b) y xx - 4 y x - 5 y = e3 x
(c) ut = 4u xx
University of Waterloo
CivE 331
Classify the following linear 2nd order PDEs.
Differential Equation
IndeDeHomogeneous Parabolic, pendent pendent or nonhyperbolic, Order variables variables homogenous or elliptic
(a) utt = e -t u xx + sin (t )
2 (b) u xx +
Flow of Water Through Soils
A ball on a Hill
Ball on top of hill will not move if surface flat (horizontal) Mg Mg Ball on slope will roll down hill
Movement of ball due to gravity requires a change in slope or a gradient
1
Water also flows downhill
Soil
Soil Structure
Das Chapter 2
Geotechnical Engineering
Soil Rock
Water
1
Key Soil Engineering Properties
Compressibility
Settlement Ability to carry load Flow of water through soils
Strength
Permeability (hydraulic conductivity)
Settlement Failure
2
Pala
Seepage
Sheet pile walls and Cofferdams
Sheet piling is a form of driven piling using thin interlocking sheets of steel to obtain a continuous barrier in the ground. The main application of steel sheet piles is in retaining walls and cofferdams erected to
1/4/2010
CIVE 353 Geotech Engineering I
Winter 2010 Dr. M k K i ht D Mark Knight
Geotechnical Engineer
CIV E 353 Knight
1
1/4/2010
Geotechnical Engineer?
Course Instructors
Lectures:
Dr. Mark Knight g E2-2343A
Laboratory Sessions:
Rashid Rehan Ken Bowman
CIVE 353 - Geotechnical Engineering I ASSIGNMENT 2
De p a r t m e n t o f Ci v i l En g i n e e ri n g
Posted Date: Monday, Jan 18, 2010 Due Date: Monday, Jan 25, 2010 @4PM
1. Explain why cohesive and cohesionless soils have different: compressibility, st
Tarun Rampersad 20265813
Assignment 2
25/01/2010 CIVE 375
1. Cohesive soils refer to claylike soils and cohesionless refers to very bulky soils such as cobble. The main difference between these two types of soils is the diameter size of the particle. The
CIVE 353 - Geotechnical Engineering I ASSIGNMENT 4
Department of Civil Engineering
Posted Date: Monday, February 1, 2010 Due Date: Wednesday, February 10, 2010 @ 4pm
1. A soil sample was taken from the site of a proposed borrow pit and a standard Proctor
CIVE 353 - Geotechnical Engineering I ASSIGNMENT 1
Department of Civil Engineering
Posted Date: Monday January 11, 2010 Due Date: Monday January 18, 2010 @ 4pm in the COURSE BOX 1. Name the three soil mass engineering properties that will be discussed thr
Metric Sieve Size 25mm 19 mm 9.5 mm 4.76 mm 2.38 mm 0.84 mm 420 mm 250 mm 150 mm 75 mm Pan
US Sieve Size 1 in 3/4 in 3/8 in No.4 No.8 No.20 No.40 No.60 No.100 No.200 Pan
Metric Sieve Size (mm) 25.000 19.000 9.500 4.760 2.380 0.840 0.420 0.250 0.150 0.075
CIV E 353 Geotechnical Engineering I Assignment 3
Department of Civil Engineering
Posted Date: Friday January 22, 2010 Due Date: Monday, February 1, 2010 @ 4pm 1. Soil is excavated from a pit that is to be used for the construction of a landfill liner and