Assignment03
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Florida International University *
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Course
4012
Subject
Civil Engineering
Date
Dec 6, 2023
Type
Pages
2
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FLORIDA INTERNATIONAL UNIVERSITY
NAME: ______________
DEPARTMENT OF CIVIL & ENVIRONMENTAL ENGINEERING
DATE: _______________
1
CEG 4012 Fall 2023
–
ASSIGNMENT #3
Due: Nov. 14, 2023 at 1:59 PM
PLEASE ADHERE TO THE HOMEWORK GUIDELINES POSTED ON CANVAS AND IN THE SYLLABUS.
PLEASE REMEMBER TO SHOW ALL WORK FOR EACH PROBLEM. PROVIDE YOUR FINAL ANSWERS IN
THE BOXES PROVIDED
A series of direct shear tests are carried out on Wabash River sand. Two normal (effective vertical) stresses
(10 psi and 20 psi) will be considered. There are one loose and one dense sample for each normal stress (i.e.,
4 test in total).
A square shaped box of 6 cm × 6 cm (2.36 in × 2.36 in) will be used. During the test, the area of the shearing
plane keeps changing and the corrected area Ac can be easily obtained by Ac = Ao
–
b ×
δ
, where Ao is the
original area, b is the width of the box normal to the direction of shear and
δ
is the shear displacement.
The obtained lab test data in Excel spreadsheet (similar to the table shown below) is also posted in the Canvas
website. Please download, fill up the columns with your own calculation to answer the following problems.
Example calculations are shown in red below for your information.
Test No.
1
Sample
Loose Wabash River Sand
Normal Load
55.73
lb
Effective vertical stress:
10
psi
Area
2.36 x 2.36
in
2
Proving Ring Constant (PRC)
0.204
lb/division
Shear Rate
0.015
in/min
①
②
③ = ②
- 897
④
=
③
× PRC
⑤
=
④
/
Ac
⑥
⑦
=
⑥
- 1019
Shear
Proving Ring
Corr.
Shear
Shear
Vertical
Vertical
Remarks
Displ.
Dial
P.R.
Force
Stress
Dial
Deform.
(in)
(Division)
(Division)
(lb)
(psi)
(in)
(in)
x 10
-3
x 10
-4
x 10
-4
0
897
0
0.000
0.000
1019
0
(-) Contraction
3
960
63
12.852
2.310
1004
-15
(+) Dilation
6
976
79
16.116
2.901
997
-22
FLORIDA INTERNATIONAL UNIVERSITY
NAME: ______________
DEPARTMENT OF CIVIL & ENVIRONMENTAL ENGINEERING
DATE: _______________
2
1.
Plot shear stress (
τ
) vs. shear displacement (
δ
), and vertical deformation (
∆
H) vs. shear displacement (
δ
)
for all the 4 tests (i.e., under different densities and normal stresses). An example is shown below.
2.
Plot maximum shear stress (
τ
max
) vs. normal stress (
σ
n
) for all tests in the same
σ
-
τ
space. Plot two
envelops in the
σ
-
τ
space, one for the loose samples and the other one for the dense samples. Measure
ϕ
in degrees for loose and dense specimens. (Note that the shear stress and normal stress must be plotted
in the same scale so that you can graphically determine the
ϕ
from the plots.) Use different symbols, lines
and legend to identify different tests.
3.
Comment on the relative shape of the shear stress (
τ
) vs. shear displacement (
δ
) curves for the loose and
dense samples at the same normal stress.
4.
Similarly as in Problem 3, how does the behavior reflect the volume change tendencies of each sample
during various states of shear?
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1.
2.
9:22 St
Instructions: In preparation for our first completion exam, solve this problem set. Write your solution on
bond paper with a border line and a 1 inch margin on all sides. Follow the format of the sample problem set.
Use engineering lettering and include FBD with a complete and proper label. Our first exam will be held on
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STATICS OF RIGID BODIES
PROBLEM SET NO. 1
300 lb
K
Three chains act on the bracket such that they create a resultant force having a magnitude of 500 lb. If
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measured clockwise from the positive x axis, so that the magnitude of the force F in this chain is a
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148
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Actual
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Mode
Task Name
Duration
4
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NS
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149
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