Chapter 2

1

Introduction to
R
einforced
C
oncrete
M
aterials
About concrete
1.
Concrete is a composite material composed of aggregate bonded by hydrated
Portland cement.
2.
The aggregate generally consists of sand
(fine aggregate) and gravel (coa
rse
aggregate).
A typical ma
ximum gravel size of ¾” will be used through out this class when
this becomes an issue.
Both normal ‘weight’ aggregate and lightweight aggregates exist. Normal
weight aggregate
,
used to produce normal weight concrete, will be used
through this course.
N
ormal weight concrete density is typically 145
pcf
.
Normal weight
reinforced concrete
is assumed to weight
150
pcf
for design
calculations.
3.
Portland cement is produced in five basic types plus some special blends for
special cases. Type I is normal ceme
nt and used in ordinary construction.
Type I cement will be assumed through out this course. A specified
compressive strength (
f
c
') of 4,000
psi
will be assumed through out
this course
except for foundation footings
where 3,000
psi
will be used.
About
reinforced concrete
This course is essentially about
reinforced
conctete. It should be noted however that
plain
concrete can be used economically in
light
frame (typically wood) building foundations
.
In reinforced concrete steel is embedded in the concre
te and located in such a way as to
resist tension forces after the concrete cracks.
Although plain wires and other materials are sometimes used (especially in slabs) in this
course we will assume grade
60
deformed steel bars for all reinforcement, as
is
a
lmost
universal today for cast
–
in
–
place concrete. No prestressed or post
–
tensioned concrete
designs will be considered in this course.
Chapter 2

2

Strength of concrete
1.
Plain concrete has the strength of a moderately strong rock in compression.
Strength in compr
ession is one of concretes major assets.
Note however that a
t
f
c
' = 4,000
psi
concrete is roughly 5% to 10% as strong
as steel in compression and when reinforced has a density of about 30% of
that of steel so the volume of material, and the structural weig
ht will be larger
for a con
crete building than for a steel
b
uilding
. A
light
–
frame wood building
will
be much lighter than a concrete
–
frame
.
S
till concrete is used extensively
and competes with steel for all but very tall building structures.
2.
Plain conc
rete is relatively weak in tension, about 10% (8
–
15%) of
f
c
'. This
explains the need for tensile reinforcement with steel bars
.
S
uch reinforced
concrete has been used since 1850.
Note that the concrete in tension needs to crack before the steel becomes
effective in beams. In columns the steel carries a small
portion of the load unless columns are heavily
re
in
forced.
3.
The strength of concrete in shear (V) is limited by its
strength in tension (see figs). Shear and diagonal tension
exist together. Speci
al shear reinforcement is often
required and will be discussed extensively after pure
compression and
pure flexure (
bending
) have been
discussed
.
Stiffness of concrete
Concrete is less stiff than steel and stiffer than wood. However steel shapes typica
lly
have thin elements (flanges and webs) but concrete shapes are generally solid sections.
C
racking is a major issue that contributes to concrete deflections in beams and slabs, and
buckling is still an issue
if slender columns are used
.
According to th
e ACI code; for normal weight concrete (
1
4
5
pcf
)
'
000
,
57
c
c
f
E
.
Example: For
f
c
' = 4,000
psi
,
ksi
psi
E
c
600
,
3
000
,
600
,
3
000
,
4
000
,
57
.
T
T
V
V
Chapter 2

3

T
est for compressive strength
of
normal weight concrete
The standard acceptance test for measuring
f
c
' uses 6
in
.
x
12
in
. cylinders loaded at
approximate 35
psi
./
second
.
Note that at normal
f
c
' = 4,000
psi
this is
approximately
:
4,000 / 35 = 114
sec
. = 1.9
min
. (1.5
–
2
min
.
short term
test).
The test is carried out 28 days after wet curing.
The value of
f
c
' used to desi
gn the structure must be given on the construction
drawings and the tests must demonstrate that this value is generally
obtained (one
under strength
test
does not
generally
fail the structur
e
).
You will soon see that
many
computations for design use the s
pecified
f
c
' value
.
Factors controlling concrete compressive strength
Some factors affecting concrete strength are:
Water/cement (
W
/
C
) rati
o
: ≈ 0.55
4,000
psi
, ≈0.40
5,700
psi
Type of c
ement (effects rate of cure but generally not final strength
)
.
Aggregate strength and shape (
Angular generally
better)
.
Mixing water: (use potable if possible)
.
Moisture during curing and curing temperature
are important.
Age of concrete: 7 day
strength with ty
pe I cement is 65
–
70% of 28 day
strength
(may determ
ine when forms can be stripped). After one year the concrete is 10%
–
20% stronger and gets stronger with age.
Rate of loading: recall
the
basi
s
for
f
c
' is
a
1
.5
–
2 min. test. For very low rates of
load
ing
strength is reduced up to 33%. For very high ra
te
s
(fail
ure
in 0.1
–
0.15
sec.) increases up to 15% may occur.
Where strain
gradients
are present (beams)
thise
effect
s
mostly
disappears.
Chapter 2

4

Typical uniaxial stress

strain (
σ
c
vs.
ε
c
) for normal weight
f
c
' = 4,000 psi concrete.
Normal weight sand and
stone concrete,
w
c
= 145 #/
ft
3
E
c
=
'
000
,
57
c
f
2
/
#
000
,
600
,
3
000
,
4
000
,
57
in
E
c
Note: Actually expected service loads
are ≈ 45
–
50% of
f
c
'.
Some notes concerning behavior during a
1½
–
2 min. test
Paste (cement) shrinkage while curing with no
load
leads to
micro cracks.
Stress
–
strain curve is linear up to 30
–
40% of
f
c
'.
From
a
bout 30
–
40% of
f
c
'
to 50
–
60% of
f
c
' bond cracks arou
nd aggregate faces occur
.
At 50
–
60% and higher
loads
mortar cracks (cement body
cracks
) between bond cracks
begin to
be produced but
these are
stable under constant load
.
At 75
–
80% of
f
c
' number of mortar cracks increases rapidly and stress vs. strain becomes
more non

linear. About this critical stress level specimen will eventually fail if load level
is held constant
for a long enough time.
T
he system is unstable at the
upper end this
load
level.
0
1000
2000
3000
4000
0
0.001
0.002
0.003
0.004
0.005
ε
c
f
c
(psi)
E
1
1.5  2 min. test
100 day test
Chapter 2

5

Concrete strength under tensile stress
1.
Tensile strength is between 8
–
15% of
f
c
' but depends strongly on type of test used.
The discussion below is for normal weight c
oncrete. The types of tests used for
tension are potentially
the
direct tension test
,
modulus of rupture test
and
split cylinder test
.
2.
The direct tension test is very difficult to actually use and gives
highly variable results due to essential difficulty
of loading eve
nly
and end effects, gives
f
t
' value.
f
t
' typically
'
3
c
f
to
'
5
c
f
(for
reference only
).
3.
The split

cylinder test uses a standard 6" diameter by 12"
long test specimen loaded on edge as shown. This
prod
uces tension (as shown)
perpendicular
to the load.
Give
s
f
ct
value.
d
L
P
f
ct
2
,
typically
'
6
c
f
to
'
8
c
f
.
4.
The modulus of rupture test (beam flexure test) uses a 6"
x
6"
x
30" beam loaded in flexure with
loads
at the 1/3 points. Tension is produced
(maximum between loads) along the bottom
of the beam up to the neutral axis. Gives
f
r
value,
f
r
= modulus of rupture, typically
'
8
c
f
to
'
12
c
f
.
Note
that
tensile strength
increases with
f
c
' but not proportionally, tends to vary with
'
c
f
.
In strength
computations
, ACI code uses
'
6
5
c
r
f
f
and for deflection
computations
ACI code uses
'
5
.
7
c
r
f
f
.
T
T
w
L
=
P
T
T
P
R
=
P
2
6
bh
M
f
r
Chapter 2

6

Biaxial strength of concrete
(conceptual only
, see note at bottom of page
)
1.
Biaxial loadings, nominal
or no stress in 3
rd
direction.
2.
The major point here is that biaxial compression
increases strength slightly to ≈ 1.1
f
c
' for equal
compressive
σ
1
and
σ
2
with
σ
3
=
. If
σ
3
is also
compressive (triaxial compression) strength
increase is very much greater.
3.
Triaxial strength of concrete in compression
σ
1
= major axial compressive stress
σ
3
= confining pressure
For
f
c
' = 3,600
psi
(
from
concrete
uniax
ial loading
,
standard test),
σ
1
at failure ≈
f
c
' + 4
σ
3
.
Example
s
:
σ
3
=
0
,
σ
1
=
f
c
'.
σ
3
= 900
psi
,
σ
1
= 3,600 + 4(900) = 7,200
psi
.
σ
3
= 1,800
psi
,
σ
1
= 3,600 + 4(1,800) = 10,800
psi
.
This page has only been included because in some portions of
foo
tings and 2

way slabs triaxial stresses exist. Some ACI Code
expressions contain modifications which account for this. We will
see this when we study 2

way shear strength of footings.
σ
1
σ
1
σ
3
σ
3
σ
3
(all around)
Chapter 2

7

About
reinforcing steels and steel bars
In reinforced concrete reinf
orcement is primarily used to resist tensile stresses after
the
concrete in tension cracks.
Having stated this
,
note
that
in some cases reinforcement may occur in compression
zones in columns or flexural members. Typically such reinforcement will reduce
long

term deflections due to ‘creep’, or assist in the assembly of reinforcement ‘cages’ (hold’s
bars in place).
Compression reinforcement typically adds very little to the flexural strength and is
usually
ignored in slab, beam and girder strength computa
tions.
Reinforcement must be selected (number and size of bars) based on the type of member
(column, slab, beam, girder)
and the magnitude of the
force
s
to be resisted.
All reinforcement must be extended beyond the point at which
the
computed full area i
s
required in order to develop appropriate bar anchorage (much more later).
Although bars may be straight or bent
,
in this course we will only use straight bars
(typically the most common practice) except for standard ‘hooks’ at bar ends.
Bars may be cut
off where not further required, but ‘rules’ exist concerning where
bars
may be ‘cutoff’ or must be extended into joints. Theses ‘rules’ are sometimes quite
complex (more on this later)! One major reason to cut off bars is to avoid congestion at
beam

gir
der

column connections (not just to avoid use of a little extra steel).
Types of reinforcement include deformed and plain steel bars, welded wire fabric and
even fiber

reinforced ‘polymers’ (FRP). FRP
’
s include glass,
aramid
(Kevlar) and
carbon fibers.
In this course we will use only grade 60 deformed steel bars in sizes #3 to #10.
Chapter 2

8

About grade 60 deformed steel bars and related issues
Grade 60 deformed steel bars are the most common bars used in cast
–
in
–
place building
construction.
Hot

rolled bar
s conforming to ASTM A
–
615 are most common. These bars are available
is standard sizes #3
–
#18.
Bar sizes refer to nominal bar diameter in eighths of inches. Thus a #4 bas has nominal
diameter = ½".
Although bar area is typically obtained from tables
(see appendix ‘A’)
, for bars #3 to #9
area can be computed using
4
2
b
d
A
(for #10 and larger this formula under estimates
actual area).
d
b
is the notation for bar diameter.
Bar grade refers to the minimum specified steel yield stress in ksi (
kips
/
in
2
). Thus a
grade 60 bar has minimum yield stress of 60,000
psi
.
Grade 40 and grade
75
bars are also available under ASTM A
–
615.
The minimum tensile strength of grade 60 bars is
90,000
psi
. Note
also that about 10%
of grade 60 bars yield at ≥ 80,000
psi
.
All steel b
ars have
E
s
= 29,000,000
psi
(29
,000
k
si
).
The figure to the right shows an
i
dealized stress
–
strain curve for ASTM
A
–
615
, grade 60,
deformed steel bars.
For grade 60 bars:
the sharp
ε
y
= 60 /
29,000 ≈ 0.002
Note
the sharp
yield ‘plateau’
for the
grade 60 bar.
G
rade 75 bars do not show
a
sharp yield point.
Note also
the
strain
–
hardening region,
minimum elongation at failure is (fracture not shown) 7
–
9%.
Very Important:
Typically w
e consider bar yield point as defining the
limiting stress in
the bar for
strength computations. However
the
bar has not failed at this point,
this
produces
d
uctile behavior
if steel yields before concrete fractures.
Although strain
–
hardening exists we ‘
model’ the steel stress
–
strain behavior as
elastic
–
plastic
for strength
computations.
0
20
40
60
80
0
0.01
0.02
0.03
0.04
0.05
0.06
ε
s
f
s
(
ksi
)
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