Civil Engineering Materials

11
Civil Engineering Materials – CIVE 2110Civil Engineering Materials – CIVE 2110
Concrete MaterialConcrete Material
Stress vs. Strain CurvesStress vs. Strain Curves
Steel ReinforcementSteel Reinforcement

22
Stress-Strain Curve for CompressionStress-Strain Curve for Compression
 Slightly ductile shape of Stress-Strain curve
 A descending branch exists after is reached
 Due to redistribution of load to un-cracked regions with less stress,
'
cf
(MacGregor, 5(MacGregor, 5thth
ed., Fig. 3-26)ed., Fig. 3-26)

33
 Strength of Reinforced Concrete structures controlled by,
 Size of members,
 Shape of members,
 Stress-Strain curves of; - concrete,
- reinforcement.
Five properties of Stress-Strain curves;
(1) - Initial slope, Ec
(2) - Ascending parabola
(3) - Strain at max stress,
(4) - Descending parabola
(5) - Strain at failure
'
cf
(Fig. 3-18, MacGregor, 5(Fig. 3-18, MacGregor, 5thth
ed.)ed.)

44
 (1) - Initial Slope, Ec ;
 ACI 318, Sect. 8.5, 8.6
 sensitive to Eaggregate , Ecement .
 For normal weight concrete;
 For other weight concrete;
 Defined as the slope
of a line drawn from
As water increases, Ec decreases,
because cement paste becomes
'
45.00 cfto == σσ (MacGregor, 5(MacGregor, 5thth
ed., Fig. 3.17)ed., Fig. 3.17)
( ) ( )
( ) '5.1
33
33
16090
ccc
c
fwpsiE
FtLbwFtLb
=
≤≤
( )
( ) '
3
000,57
145
cc
c
fpsiE
FtLbw
=
≈

55
 Lightweight Concrete ;
 ACI 318, Sect. 8.5, 8.6
 sensitive to Eaggregate .
 For all parameters involving
 Each parameter shall be multiplied by a modification factor
for sand-lightweight conc.
for all-lightweight concrete
 If splitting tensile strength, fct , is specified, then
 This accounts for the reduced
capacity of lightweight concrete
due to aggregate failure;
Such as:
 Shear strength
 Splitting resistance
 Concrete-rebar bond
For normal weight concrete the averageFor normal weight concrete the average
splitting tensile strength is;splitting tensile strength is;
( )[ ] 0.17.6/ '
≤= cct ffλ
'
cf
( )'
7.6 cct ff ≈
ed., Fig. 3.26)ed., Fig. 3.26)
( ) ( )
( ) '5.1
33
33
12090
ccc
c
fwpsiE
FtLbwFtLb
=
≤≤
75.0
85.0
=
=
λ
λ
λ

66
 (2) – Ascending Parabola;
 Curve becomes steeper
as increases.'
cf
(Fig. 3.18(Fig. 3.18, MacGregor, 5MacGregor, 5thth
ed.,)ed.,)
 (3) – Strain ( ) at ;
 Strain at max stress increases
as increases.
'
cf
'
cf
 (4) – Slope of descending branch;
 Less steep than ascending branch,
 Slope increases as increases.
'
cf
 (5) – Strain ( ) at failure;
 Decreases with increases in '
cf
0ε
cuε
 (4 and 5) – depend on;
 Specimen size; Load, type, rate
ksifc 6'
≤

77
Stress-Strain Curve forStress-Strain Curve for TensionTension
 Tensile strength of concrete:
 Determined by one of 2 tests:
 (1) Flexure (Modulus of Rupture) test,
 (2) Split Cylinder test, fct

( )
2
3
6
12
2
BH
M
f
BH
HM
f
I
My
f
r
r
Flexurer
=
=
== σ
 (1) Flexure (Modulus of Rupture) test;
 Load until failure due to cracking on tension side,
 ASTM C78 or ASTM C293,
 H = 6”, B = 6” L = 30”
3
PL
H
B
P P
3” 3”
8” 8” 8”
P
-P
V
M
0
0

88
Stress-Strain Curve for TensionStress-Strain Curve for Tension
( )
ld
P
f
ld
P
f
asistingAre
P
f
ldasistingAre
ct
ct
ct
π
π
σ
π
2
2
Re
2
Re
=
=
==
=
 (2) Split Cylinder test, fct ;
 Load in compression along long side,
 ASTM C496,
 a standard 6”x12” cylinder is placed on side,
 Outside surface area,
 Load is resisted by only half of surface area,
dlrlArea ππ == 2
ed., Fig. 3.9)ed., Fig. 3.9)

99
1max σσ =Tension
ApCσσ =2
2
max
ApCσ
τ =
σ
τ
2x90˚
Compression
Tension
Concrete always cracks
on plane of MaxTensionσ
Split Cylinder Test
Bi-Axial Stress

1010
 Determined by one of 2 tests:
 (1) Flexure (Modulus of Rupture) test,
 (2) Split Cylinder test,
rf
 Tensile strength from
Split Cylinder test
is less than that from
Flexure (modulus of Rupture) test
because;
 In Flexure test, only bottom of beam reaches
 In Split Cylinder test, majority of cylinder reaches
ctf
MaxTensionσ
MaxTensionσ
ctr ff 5.1≈
H
B
P P

1111
 Results from various Split Cylinder
tests vs. are plotted in Fig. 3.10
 The mean Split Cylinder strength is:
 ACI 318, Sect. R8.6.1 states;
 The mean Modulus of Rupture
strength is:
 ACI 318, Sects. 8.6.1 & 9.5.2.3 state,
for deflection calculations:
'
3.8 cr ff =
'
4.6 cct ff =
ed., Fig. 3.10)ed., Fig. 3.10)
'
cf
'
7.6 cct ff ≈
0.1
7.6
5.7
'
'
≤=
=
c
ct
cr
f
f
ff
λ
λ
concretetlightweighallfor
concretetlightweighsandfor
concreteweightnormalfor
−=
−=
=
75.0
85.0
0.1
λ
λ
λ

1212
( ) ''
15.008.0 ct ff →=
 Concrete tensile failure is BRITTLE.
 Same factors affect as ;
 Water/Cement ratio,
 Type of Cement,
 Type of Aggregate,
 Curing Moisture conditions,
 Curing Temperature,
 Age,
 Maturity,
 Loading rate.
(MacGregor,(MacGregor,
55thth
ed., Fig. 3-21)ed., Fig. 3-21)
'
tf '
cf
''
'
'
4.6
8.1
cctt
c
t
t
fff
where
E
f
==
=ε
E
tinitial=linear
flexurefor
tensionpurefor
MAX
MAX
t
t
0002.000014.0
0001.0
'
'
→=
=
ε
ε
'
5.0 tfFrom: 0 →
c
t
t E
f '
'
=ε
''
5.0 tt ff →From:
''
5.0 tt ff →
'
5.0 tf

1313
Steel Reinforcement in ConcreteSteel Reinforcement in Concrete
 In any beam (concrete, steel, masonry, wood):
 Applied loads produce
Internal resisting Couple,
Tension and Compression
forces form couple.
MacGregor, 5th
ed.
Fig. 1-4
In a concrete beam:In a concrete beam:
-- Cracks occur in areas ofoccur in areas of Tension,,
-- Beam will have suddenBeam will have sudden Brittle failurefailure
unless Steel reinforcementreinforcement
is present to takeis present to take Tension.

1414
Mohr’s Circle Method – Failure ModesMohr’s Circle Method – Failure Modes
ionslightTens=maxσ
Brittle concrete fails on plane of max normal (tension) Stress.
Failure stress located at: 2x90˚=180˚on Mohr Circle
ApCσσ =min
2
max
ApCσ
τ =
σ
τ
2x45˚
2x90˚
tensionσ
Shear Stress Normal Stress Principal
Stress
Neutral Axis
90˚
tensionσ
Plane of
max
Tension
Concrete
Brittle

1515
 Steel Reinforcement:
Hot-Rolled deformed bars (rebars)
Welded wire fabric
Reinforcement Bars (Rebars):
ASTM specs specify;ASTM specs specify;
- diameter, cross-sectional area- diameter, cross-sectional area
- sizes in terms of 1/8 inch- sizes in terms of 1/8 inch
- #4 rebar, diameter = 4/8 in.- #4 rebar, diameter = 4/8 in.
- metallurgical properties- metallurgical properties
- mechanical properties- mechanical properties
- Grade- Grade →→ min. Tensile Yield Strengthmin. Tensile Yield Strength
- Grade 60, Yield Strength = f- Grade 60, Yield Strength = fyy = 60 ksi= 60 ksi
ASTM A 615:ASTM A 615:
- made from steel billets- made from steel billets
- most commonly used- most commonly used
ASTM A 706:ASTM A 706:
- made from steel billets- made from steel billets
- for seismic applications- for seismic applications
- better - ductility- better - ductility
- bendability- bendability
- weldability- weldability

1616
Upper Limit on
( )dStrengthactualYielygthnsileStrenUltimateTe f σσ =≤ 25.1
ed., Table 3-4)ed., Table 3-4)

1717
Rebars in US customary units:
- Grade 60, →
- # 11 →
Rebars in metric units:Rebars in metric units:
- just numerical conversions- just numerical conversions
of US customary sizes.of US customary sizes.
- #36- #36 →
- Grade 420,- Grade 420, → MPafy 420=
ksify 60=
ed., Fig. 3-30)ed., Fig. 3-30)
"41.1"375.1
8
"11
≈==d "409.1
"14.25
8.35
==
mm
mm
d

1818
Reinforcement Bars (Rebars): (MacGregor, 5(MacGregor, 5thth
ed., Table A-1)ed., Table A-1)

1919
Reinforcement Bars (Rebars): (MacGregor, 5(MacGregor, 5thth
ed., Table A-1M)ed., Table A-1M)

2020
- modulus of Elasticity,
ES = 29,000,000 psi
ACI 318, Sect. 8.5.2
- for rebars with
fy > 60,000 psi
must use
fy = ES x ( )
ACI 318, Sect. 3.5.3.2
0035.0=Sε
ed., Fig. 3-31)ed., Fig. 3-31)

2121
- at temperatures > 850at temperatures > 850˚F˚F
ffyy and fand fultimateultimate
drop significantlydrop significantly
- concrete cover- concrete cover
over the rebarsover the rebars
helps to delay losshelps to delay loss
loss during firesloss during fires
ed., Fig. 3-34)ed., Fig. 3-34)

2222
Fatigue Strength of rebars:
- Bridge decks subjected to large number of load cycles
- Stress Range, Sr =
ed., Fig. 3-33)ed., Fig. 3-33)
- Fatigue failure may
occur if at least one
stress is tensile
and Sr > 20 ksi
- Fatigue failure will not
occur if;
cyclesany
cyclesiniteksi
Max
Max
000,20
inf20
=
<
σ
σ
- Fatigue strength
reduced at: Bends, Welds
( ) ( ) cyclesameinMinStresscycleainStressMaxTensile σσ −

2323
Example: Fatigue Failure not possible;
Fatigue Strength of rebars:
- Stress Range, Sr = ( ) ( ) cyclesameinMinStresscycleainStressMaxTensile σσ −
( ) ( )
ksiS
ksiksiS
r
cyclesameincycleainr
21
165
=
−−=
( ) ( )
ksiS
ksiksiS
r
cyclesameincycleainr
21
265
=
−−−=
Example: Fatigue Failure possible;

2424
Welded-Wire Reinforcement:
- used in: Walls, Slabs, Pavements.
- due to cold-working process used in drawing the wire
strain-hardening occurs, so wire is BRITTLE.
- Plain wire; ASTM A82; A185;
ACI 318, Sect. R3.5.3.6 → fy = 60,000 psi
- mechanical anchorage in concrete provided by
- cross-wires
- Deformed wire; ASTM A496; A497;
ACI 318, Sect. R3.5.3.7
→ fy = 60,000 psi
- mechanical anchorage
in concrete provided by
- cross-wires

2525
- Wire diameter = 0.125” → 0.625”
- Wire area → increments of 0.01 in2
.
- Plain wire; W
- Deformed wire: D
- ACI 318, Sect. 3.5.3.5
D-4 ≤ wire size ≤ D-31
area = 0.04 in2
area = 0.031 in2
.
-
ed., Table A-2a)ed., Table A-2a)

2626
- Wire area → increments of 0.01 in2
.
- Wire center-center spacing → a x b , inches
- Plain wire; W
-
ed., Table A-2b)ed., Table A-2b)

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