Chapter 1
1. d
2. a
3. d
4. d
5. c
6. b
7. c
8. In elastic-plastic model (Figure 1.4c), the stress-strain plot consists of two separate segments
with the first segment being perfectly elastic and the second being perfectly plastic. In
elasto-plastic model, the elastic and plastic strains occur simultaneously at all strain levels.
9.
a b
This can be written as
b
a
1
When , = u = 1/b
2 2
( ) ( )
( )1
a b
a
a b
a b b
d
d
At = 0,
d a
d 1
10. From Figure 1.16, the yield stress is about 145 MPa.
Young’s modulus E = 155/0.005 = 31,000 MPa or 31.0 GPa.
At 3% strain (i.e., = 0.03), the stress is 280 MPa.
Unloading takes place along the line BC shown in the figure. The elastic strain is given by
0.009
31000
280
e
or 0.9%
Therefore, the plastic strain is given by
2
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0.03 0.009 0.021 p e
or 2.1%
Figure 1.16
11. The element is shown in the figure here.
Axial strain, Axial stress, (MPa)
0.00 0.01 0.02 0.03
0
50
100
150
200
250
300
0.04
x
z
y
15
40
25
40
20
20
10
10
15
15
15
25
25
25
5
5
5
5
B
C
3
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12.
{
?
?
?
??
??
??}
=
1
?
[
1 − − 0 0 0
− 1 − 0 0 0
− − 1 0 0 0
0 0 0 2(1 + ) 0 0
0 0 0 0 2(1 + ) 0
0 0 0 0 0 2(1 + )]
{
?
?
?
??
??
??}
(1.15)
For principal stresses (and no shear stresses),
{
1
2
3
??
??
??}
=
1
?
[
1 − − 0 0 0
− 1 − 0 0 0
− − 1 0 0 0
0 0 0 2(1 + ) 0 0
0 0 0 0 2(1 + ) 0
0 0 0 0 0 2(1 + )]
{
1
2
3
0
0
0 }
This can be simplified as
(
1
2
3
) =
1
?
(
1 − −
− 1 −
− − 1
) (
1
2
3
)
{
?
?
?
??
??
??}
=
?
(1 +)(1 −2 )
[
1 − 0 0 0
1 − 0 0 0
1− 0 0 0
0 0 0
(1 − 2 )
2
0 0
0 0 0 0
(1 − 2 )
2
0
0 0 0 0 0
(1 −2 )
2 ]
{
?
?
?
??
??
??}
(1.16)
For principal strains (and no shear strains),
{
1
2
3
??
??
??}
=
?
(1 + )(1 − 2 )
[
1 − 0 0 0
1 − 0 0 0
1 − 0 0 0
0 0 0
(1 −2 )
2
0 0
0 0 0 0
(1 −2 )
2
0
0 0 0 0 0
(1 − 2 )
2 ]
{
1
2
3
0
0
0}
4
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(
1
2
3
) =
?
(1 + )(1 − 2 )
(
1 −
1 −
1 −
) (
1
2
3
)
13. Some of the systems of units include:
SI
English
US Customary Units (derived from English units)
MKS (meter, kilogram and second) system of units
Metric
See https://en.wikipedia.org and other sites for details.
Some of the advantages of SI units are as follows.
Only one unit for each physical quantity.
No fractions and only decimals.
Short and unambiguous prefixes.
Power of 10. Nothing to memorise (e.g. mile = 5280 ft).
World-wide use
14. Non-destructive testing
Often we take samples from steel, concrete, timber, soils and rocks for testing in the
laboratory. Sometimes, it is required to test the structure without causing even the slightest
damage. That is, we cannot always obtained specimens from the structure for testing. Such
non-destructive testing methods apply to all branches of civil engineering. Look for the
following points for the 500-word essay.
Acoustic emission
Hardness testing
Optical or scanning electron microscopy
NDT applications in concrete, steel, timber, rocks and soils
Schmidt rebound hammer
Digital imaging
Electromagnetic methods
Leak testing
Nuclear density meter
Geophysical methods
Structural health monitoring
15. Impact echo tester is used for measuring thicknesses of concrete elements and detect cracks,
honeycombing or other damages in concrete.
Half-cell potential meter (ASTM C876) is used for measuring the surface potential
differences induced by any corrosion process and hence any likelihood of future corrosion
in the reinforcements.
5
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Acoustic emission is a technique where elastic waves are sent through the material to detect
the properties.
Scanning electron microscope is used to obtained images of the microstructure of most
materials.
16. Look for ABAQUS, ANSYS, ELFEN, RocScience, Plaxis, FLAC, UDEC, Matlab, ETABS,
STAAD Pro, SAP2000, etc.
17.
a. Angstrom = 10-10 m
b. kip = 4.448103 N
c. psi = 6.895103 Pa
d. bar = 105 Pa
18.
a. 3
b. 2
c. 5
d. 5
e. 3
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Sophia Finance Milestone Final_Complete Questions and Answers 2021...
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