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Evo Design - structural engineering
Calculation No.
001-RC COLUMN
INTERACTIVE ONLINE CALCULATION SHEET
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SAMPLE CALCULATION
Project Title:
Reinforced concrete column - interactive design spreadsheet
Calc. By
Date
Rev.
MN
16.04.2014
0
Subject
RC Column Capacity - Axial Force Bending Moment
Checked By
Date
Interaction (ACI318)
CN
16.04.2014
Input
Â
Output
Column dimensions
Moment capacity
Reinforcement
Column interaction diagram
Materials (steel, concrete, bolts)
RC Column Capacity - Axial Force - Bending Moment Interaction (ACI 318)
Axial force - bending moment interaction -
Â
ultimate limit state
Column dimensions
h =
15
in
b =
15
in
(parameters that can not be modified in the demo version)
A
g
= h * b =
in
2
RC Element Area
Reinforcement
cover
in
cover to the center of the bars
d =
in
depth of bottom reinforcement (h- cover)
d
c
=
in
depth of top reinforcement (h- cover)
Tension side reinforcement
#
3
4
5
6
7
8
9
10
11
14
18
bar size
n =
no of bars
A
s
=
in
2
area of tension reinforcement
r
tens.reinf
=
%
percentage of tension reinforcement
Compression side reinforcement
#
3
4
5
6
7
8
9
10
11
14
18
bar size
n =
no of bars
A
s.b
=
in
2
area of compression reinforcement
r
comp.reinf
=
%
percentage of compression reinforcement
A
s.t
= A
s
+ A
s.b
=
in
2
total area of reinforcement
r
=
%
element total percentage of reinforcement
per ACI 318
Section 10.9.1
Reinf percentage should be between 0.01Ag and 0.08Ag
Confinement reinforcement (tied or spiral)
tied
spiral
Materials
Concrete
f
c
'
=
2.5
3
3.5
4
5
6
7
8
9
10
ksi
concrete characteristic
Â
cylinder strength
Reinforcement type
see reinforcement types here
Grade
40
50
60
75
f
y
=
ksi
reinforcement yield strength
References:
ACI318-05 - Building code requirements for structural concrete
""
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Reinforcement modulus of elasticity
per ACI 318
E
s
=
ksi
Section 8.5.2
Modulus of elasticity of reinforcement
Yield reinforcement strain:
f
y
/ E
s
=
The relationship between concrete compressive stress and concrete strain is satisfied
per ACI 318-05
by an equivalent rectangular concrete stress distribution defined by a 0.85*f
c
' uniform
Sections 10.2.6 and 10.2.7
stress over an equivalent compression zone bounded by edges of the cross section and
a straight line located parallel to the neutral axis at a distance
Â
a =
b
1
*c
Â
from the fiber of
Â
maximum compressive strain.
Section strength reduction factor
f
=
Â
0.90
For tension controlled sections
per ACI 318-05
0.70
Compression controlled section with spiral reinforcement
Section 9.3
0.65
Compression controlled section other reinforced members
Â
Values of
f
strength reduction factor
Maximum usable strain at extreme concrete compression fiber
is
0.003
per ACI 318-05
Section 10.2.3
Maximum usable strain at extreme concrete
compression fiber shall be assumed equal to 0.003;
The relation between concrete compressive stress and
Â
concrete strain is assumed rectangular
Section 10.2.7.1
0.85f
c
' value uniformly distributed over an equivalent
compression zone bounded by edges of the cross section
and a straigth line located parale to the neutral axis at a
distance a =
b
1
*c from the fiber of max. compression strain
b
1
=
factor relating depth of equivalent
per ACI 318-05
rectangular compressive stress block
Section 10.2.7.3
to neutral axis depth
between 2500 and 4000 psi b1 = 0.85, above 4000
b
1
will
be reduced lineary at a rate of 0.05 per 1000 psi but not
lower than 0.65
a =
b
1
* c
depth of equivalent rectangular
Section 10.2.7.1
stress block
Section 10.2.3
stress in reinforcement below f
y
shall be taken as E
s
times
steel strain. For strains greater than that corresponding
Â
to fy, stress in reinforcement shall be considered
independent of strain and equal to f
y
.
""
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Point 1 - Pure compression
f
=
Â
compression controlled section
Section strength reduction factor
f
P
n,max
=
Â
f
[0.85f
c
'(A
g
-A
st
)+f
y
A
st
]
per ACI 318
eq. 10-1 and 10-2
f
P
n,max
=
Â
kips
Maximum allowable value of the nominal axial strength
of cross section multiplied
Â
by the strength reduction factor
Point 2 - f
s
= 0
Concrete strain:
Concrete has reached ultimate concrete design
The neutral axis is located in the center of the bottom reinforcement
compressive shortening strain and
Â
f
s
= 0
c =
d
Â
=
in
Neutral axis location - in this case in the center of
the bottom reinforcement
Top reinforcement strain (compression):
*(c-d
c
)/c=
Yield reinforcement strain:
=>
f
=
Â
compression controlled section
Section strength reduction factor
a =
b
1
* c =
in
depth of equivalent rectangular
stress block
f
P
n
=
Â
f
*
Â
[ 0.85* f
c
' * a * b +
A
s.b
]
f
P
n
=
Â
kips
f
M
n
=
Â
f
*
Â
[(0.85* f
c
' * a * b) * (h/2 - a/2) +
A
s.b
) * (h/2 - d
c
)]
f
M
n
=
Â
ft -kips
Point 3 - f
s
= 0.5 * f
y
Concrete strain:
Concrete has reached ultimate concrete design
Â
compressive shortening strain and
Â
f
s
= 0.5 * f
y
Bottom reinforcement strain (tension):
e
t
= ( 0.5 * f
y
) / E
s
=
c =
in
From the relation [c / (d - c)] = 0.003 /
e
t
Top reinforcement strain (compression):
*(c-d
c
)/c =
Yield reinforcement strain:
=>
f
=
Â
compression controlled section
Section strength reduction factor
a =
b
1
* c =
in
depth of equivalent rectangular
stress block
f
P
n
=
Â
f
*
Â
[ 0.85* f
c
' * a * b +
A
s.b
-
Â
e
t
* E
s
* A
s
]
f
P
n
=
Â
kips
f
M
n
=
Â
f
*
Â
[(0.85* f
c
' * a * b) * (h/2 - a/2) +
A
s.b
) * (h/2 - d
c
) +
e
t
* E
s
* A
s
* (d - h/2)]
f
M
n
=
Â
ft -kips
""
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Point 4 - f
s
=
Â
f
y
(Balanced point)
per ACI 318-05
Concrete strain:
Section 10.3.2
Concrete has reached ultimate concrete design
Bottom reinforcement strain (tension):
e
t
= f
y
/ E
s
=
Â
compressive shortening strain and
Â
tension reinforcement
reaches the strain corresponding to f
y
Â
(f
s
= f
y
)
c =
in
From the relation [c / (d - c)] = 0.003 /
e
t
Top reinforcement strain (compression):
*(c-d
c
)/c =
Yield reinforcement strain:
=>
f
=
Â
compression controlled section
Section strength reduction factor
a =
b
1
* c =
in
depth of equivalent rectangular
stress block
f
P
n
=
Â
f
*
Â
[ 0.85* f
c
' * a * b +
A
s.b
-
Â
f
y
* A
s
]
f
P
n
=
Â
kips
f
M
n
=
Â
f
*
Â
[(0.85* f
c
' * a * b) * (h/2 - a/2) +
A
s.b
) * (h/2 - d
c
) + f
y
* A
s
* (d - h/2)]
f
M
n
=
Â
ft -kips
Point 4b - f
s
=
Â
f
y
Transition from Compression controlled section to Tension Controlled
per ACI 318-05
Concrete strain:
Section 9.3.2.2
For sections in which the net tensile strain at nominal
Bottom reinforcement strain (tension):
e
t
= f
y
/ E
s
=
strength
e
t
is between the limits for compression
controlled ans tension controlled sections f will be
linearly increased from that for compression controlled to 0.9
c =
in
From the relation [c / (d - c)] = 0.003 /
e
t
Top reinforcement strain (compression):
*(c-d
c
)/c =
Yield reinforcement strain:
=>
f
=
Â
transition from compression controlled
Â
to tension controlled section
Section strength reduction factor
a =
b
1
* c =
in
depth of equivalent rectangular
stress block
f
P
n
=
Â
f
*
Â
[ 0.85* f
c
' * a * b +
A
s.b
-
Â
f
y
* A
s
]
f
P
n
=
Â
kips
f
M
n
=
Â
f
*
Â
[(0.85* f
c
' * a * b) * (h/2 - a/2) +
A
s.b
) * (h/2 - d
c
) + f
y
* A
s
* (d - h/2)]
f
M
n
=
Â
ft -kips
""
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Point 4c - f
s
=
Â
f
y
Transition from Compression controlled section to Tension Controlled
per ACI 318-05
Concrete strain:
Section 9.3.2.2
Concrete has reached ultimate concrete design
Bottom reinforcement strain (tension):
e
t
= f
y
/ E
s
=
compressive shortening strain and
Â
tension reinforcement
is in transition from tension controlled to tensin controlled
c =
in
From the relation [c / (d - c)] = 0.003 /
e
t
Top reinforcement strain (compression):
*(c-d
c
)/c =
Yield reinforcement strain:
=>
f
=
Â
transition from compression controlled
Â
to tension controlled section
Section strength reduction factor
a =
b
1
* c =
in
depth of equivalent rectangular
stress block
f
P
n
=
Â
f
*
Â
[ 0.85* f
c
' * a * b +
A
s.b
-
Â
f
y
* A
s
]
f
P
n
=
Â
kips
f
M
n
=
Â
f
*
Â
[(0.85* f
c
' * a * b) * (h/2 - a/2) +
A
s.b
) * (h/2 - d
c
) + f
y
* A
s
* (d - h/2)]
f
M
n
=
Â
ft -kips
Point 5 -
e
t
=
Â
0.005 - tension controlled section
Concrete strain:
Concrete has reached ultimate concrete design
compressive shortening strain and
Â
et has reached 0.005
Bottom reinforcement strain (tension):
e
t
=
0.0050
corresponding to
f
= 0.9 (tension controlled section)
c =
in
From the relation [c / (d - c)] = 0.003 /
e
t
Top reinforcement strain (compression):
*(c-d
c
)/c =
Yield reinforcement strain:
=>
f
=
Â
tension controlled section
Section strength reduction factor
a =
b
1
* c =
in
depth of equivalent rectangular
stress block
f
P
n
=
Â
f
*
Â
[ 0.85* f
c
' * a * b +
A
s.b
-
Â
f
y
* A
s
]
f
P
n
=
Â
kips
f
M
n
=
Â
f
*
Â
[(0.85* f
c
' * a * b) * (h/2 - a/2) +
A
s.b
) * (h/2 - d
c
) + f
y
* A
s
* (d - h/2)]
f
M
n
=
Â
ft -kips
""
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Point 6 - Pure Bending
Concrete strain:
Concrete has reached ultimate concrete design
compressive shortening strain and
Â
et has reached 0.005
Bottom reinforcement strain (tension):
e
t
=
corresponding to
f
= 0.9 (tension controlled section)
c =
in
From the relation [c / (d - c)] = 0.003 /
e
t
Top reinforcement strain (compression):
*(c-d
c
)/c =
Yield reinforcement strain:
=>
f
=
Â
tension controlled section
Section strength reduction factor
a =
b
1
* c =
in
depth of equivalent rectangular
stress block
f
P
n
=
Â
f
*
Â
[ 0.85* f
c
' * a * b +
A
s.b
-
Â
f
y
* A
s
]
f
P
n
=
Â
kips
f
M
n
=
Â
f
*
Â
[(0.85* f
c
' * a * b) * (h/2 - a/2) +
A
s.b
) * (h/2 - d
c
) + f
y
* A
s
* (d - h/2)]
f
M
n
=
Â
ft -kips
Point 7 - Maximum tension
f
=
Â
tension controlled section
Section strength reduction factor
f
P
n
=
Â
Â
= -
f
* f
y
* [A
s.b
+ A
s
]
f
P
n
=
Â
kips
f
M
n
=
Â
0.00
ft -kips
Data for the M-N interaction graph:
N
cap
M
cap
Point 1
0.00
Point 2
Point 3
Point 4
Point 4b
Point 4c
Point 5
Point 6
Point 7
0.00
N
eff
M
eff
CO1
CO2
CO3
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