# STRUNET

Urban and Civil

Nov 29, 2013 (4 years and 5 months ago)

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The Column Design Section in Strunet contains two mai n parts: Charts to
develop strength interaction diagrams for any given section, and ready -made
Column Interaction Diagrams, for quick design of a given column.

Concrete column is one of the most i nteres ting members in concrete structural
design application. A structural design of a concrete column is quite complicated
procedures. Evaluation, however, of a gi ven column section and reinforcement is
straightforward process. This is due to the fact that pure axial compression is
rarely the case i n column analysis. Some value of moment is always there due to
end restrai nt, or accidental eccentricity due to out of alignment. ACI established
the minimum eccentricity on a concrete column, regardless of the struct ural
analysis proposed for the column, which is defi ned as the maximum axial
compression load that a column can be designed for.

Column Design Charts in Bullets:

One of the demandi ng aspects i n concrete column design is to define the
controlling poi nts on strength i nteraction diagram. The column strength
interaction diagram is a curve plot of points; where each poi nt has two ordi nates.
The first ordi nate is bendi ng moment strength and the second is the
correspondi ng axial force. Both ordi nates are linked with eccentricity. The shape
of the curve, or the strength i nteraction diagram, can be defined by finding the
ordinates of major seven points. Each poi nt has specific requirement, as
established by the code, and thus evaluating the requirement of this poin t will
result of calculating the ordi nates. The points and their respecti ve requirements
are as follows:

Point 1: Pure compression.

Point 2: Maximum compression load permitted by code at zero
eccentricity.

Point 3: Maximum moment strength at the maximum a xial compression
permitted by code.

Point 4: Compression and moment at zero strain in the tension side
reinforcement.

Pont 5: Compression and moment at 50% strai n i n the tension side
reinforcement.

Point 6: Compression and moment at balanced conditions.

Point 7: Pure tension.
STRUNET
CONCRETE DESIGN AIDS
Introduction to Concrete Column Design Flow Charts
Strunet.com: Concrete Column Design V1.01 - Page 1
a
= depth of equi valent rectangular stress block, in.
a
b

= depth of equi valent rectangular stress block at balanced
condition, in.
A
g

= gross area of column, i n
2
.
A
s
= area of reinforcement at tension side, in
2
.
A’
s

= area of reinforcement at compression side, in
2
.
A’
st

= Total area of reinforcement in column cross section, in
2
.
b
= column width dimension, in.
c
= distance from extreme compression fiber to neutral axis, i n.
c
b

= distance from extreme compression fiber to neutral axis at
balanced condition, i n.
C
c

= compression force i n equivalent concrete block.
C
s

= compression force i n tension-side rei nforcement, if any.
C’
s

= compression force i n compression-side rei nforcement.
d
= distance from extreme compression fiber to centroid of tensi on-
side reinforcement
d’
= distance from extreme compression fiber to centroid of
compression-side rei nforcement
e
= eccentricity, in.
e
b

= eccentricity at balanced condition, in.
E
s

= modulus of elasticity of reinforcement, psi.
f’
c

= specified compressive strength of concrete, psi.
f
y

= specified tensile strength of reinforcement, psi.
f
s

= stress i n tension-side rei nforcement at strain
ε
s
, ksi.
f’
s

= stress i n compression-side rei nforcement at strain
ε
'
s
, ksi.
h
= overall column depth, in.
M
b

= nomi nal bendi ng moment at balanced condition.
M
n

= nomi nal bendi ng moment at any poi nt.
P
o

= nomi nal axial load strength at zero eccentricity.
P
b

= nomi nal axial force at balanced condition.
P
lim

= limit of nominal axial load value at which low or high axial
compression can be defined in accordance with ACI 9.3.2.2.
P
n

= nomi nal axial load strength at any point.
T
= tension force i n tension-side reinforcement.
β
?

= factor as defi ned by ACI 10.2.7.3.
ε
s

= strain in tension-side reinforcement at calculated stress
f
s

ε
'
s

= strain in compression-side reinforcement at calculated stress
f’
s

ε
y

= yield strai n of reinforcement.
φ = strength reduction factor

STRUNET
CONCRETE DESIGN AIDS
Strunet.com: Concrete Column Design V1.01 - Page 2
Notations for Concrete Column Design Flow Charts
7
3
4
5
6
increasing φ
consistentφ
comp.
control
tension
control
balanced
pure tension
max. axial comp.
Axial Compression,
φ
Pn
Bending Moment,φM
n
2
1
ε
s
=0.0
ε
s
=0.5ε
y
Strunet.com: Concrete Column Design V1.01 - Page 3
STRUNET
CONCRETE DESIGN AIDS
Main Points of Column Interaction Diagram
Point 1: axial compression at zero moment.
Point 2: maximum permissible axial compression at zero eccentricit.
Point 3: maximum moment strength at maximum permissible axial compression.
Point 4: axial compression and moment strength at zero strain.
Point 5: axial compression and moment strength at 50% strain.
Point 6: axial compression and moment strength at balanced conditions.
Point 7: moment strength at zero axial force.
( )
0 85
o c g st y st
P.f A A f A

= − +
st g c y
A,A,f,f

Spiral?
085
n o
P(max).P=
080
n o
P(max).P=
0 75.φ=
0 70.φ=
064
n o
P(max).Pφ =
056
n o
P(max).Pφ =
Finding Point 1
Finding Point 2
ACI 10.3.5.1
ACI 9.3.2.2ACI 9.3.2.2
Strunet.com: Concrete Column Design V1.01 - Page 4
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CONCRETE DESIGN AIDS
Point 1: Axial Compression at Zero Moment
Point 2: Maximum Permissible Axial Compression at Zero Eccentricity
finding φ
Axial Tension and
Axial Tension with
Flexure
0 90.φ=
Axial Compression
and Axial
Compression with
Flexure
Spiral
0 75.φ=
0 70.φ=
High Values of Axial
Compression
Low Values of Axial
Compression
60
0 70
Symmetric reinf.
y
s
f ksi
h d d.h
• ≤

• − − ≤

0 15
0 9
n
L
.P
.
P
φ = −
0 10
c g
L
.f A
P
φ

=
L n
P P>
Spiral?
0 75.φ=
0 70.φ=
0 133
L c g
P.f A

=
n
P
Spiral?
Spiral?
min(0 133, )
L c g b
P.f A P

=
min(0 143, )
L c g b
P.f A P

=
0 2
0 9
n
L
.P
.
P
φ = −
ACI 9.3.2.2
0 143
L c g
P.f A

=
0 15
0 9
n
L
.P
.
P
φ = −
0 2
0 9
n
L
.P
.
P
φ = −
Strunet.com: Concrete Column Design V1.01 - Page 5
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CONCRETE DESIGN AIDS
Strength Reduction Factor
4000
c
f psi

1
0 85.β=
1
4000
0 85 0 05 0 65
1000
c
f
...β

 
= − ≥
 
 
strain
stress
C
c
C'
s
0.003
c
b
h
a
d'
ε
s
ε'
s
C
s
d
s
A'
s
A
s
d
( )
1
0 85
c c
C.f c bβ

=
( )
0 003
s
c d.
c
ε

=
( )
0 85
s s y c
C A'f.f
′ ′
= −
( )
0 85
s s s c
C A f.f

= −
s s s
f Eε=
( )
0 003
0 85
s s s c
c d.
C A E.f
c

 

= −
 
 
n c s s
P C C C

= + +
( )
( )
( )
1
0 003
0 85 0 85 0 85
n c s y c s s c
c d.
P.f c b A'f.f A E.f
c
β

 
′ ′ ′
= + − + −
 
 
of point 2
n
P
finding distance c
Result:c
( ) ( ) ( )
0 5 0 5 0 5
n c s s s
M.C h a C.h d C.h d
′ ′
= − + − − −
1
a cβ=
Compute:C
c
,C'
s
from above Eqs.
ACI 10.2.7.3
Strunet.com: Concrete Column Design V1.01 - Page 6
STRUNET
CONCRETE DESIGN AIDS
Point 3: Maximum Moment Strength
at Maximum Permissible Compression
s
0 0.ε=
c d=
1
a cβ=
min( )
s s s y
f E,fε
′ ′
=
( )
0 85
s s s c
C A f.f
′ ′ ′ ′
= −
n c s
P C C

= +
n
n
M
e
P
=
2 2 2
n c s
h a h
M C C d
   
′ ′
= − + −
   
   
0 85
c c
C.f ab

=
0 003
s
c d
.
c
ε

 

=
 
 
See finding φ
&
n n
M Pφ φ
Finding Point 4
See Findingβ
1
in point 3
T=0.0
d'
strain
stress
C
c
C'
s
0.003
0.0
c=d
b
h
a
ε'
s
A
s
A'
s
Strunet.com: Concrete Column Design V1.01 - Page 7
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CONCRETE DESIGN AIDS
Point 4: Axial Compression and Moment at Zero Strain
min( )
s s s y
f E,fε
′ ′
=
( )
0 85
s s s c
C A f.f
′ ′ ′ ′
= −
n c s
P C C T

= + −
n
n
M
e
P
=
2 2 2 2
n c s
h a h h
M C C d T d
     
′ ′
= − + − + −
     
     
See finding φ
&
n n
M Pφ φ
Finding Point 5
y
y
s
f
E
ε =
0 5
s y
.ε ε=
0 003
s
c d
.
c
ε

 

=
 
 
1
0 003
s
d
c
.
ε
 
 
=
 
 
+
 
 
1
a cβ=
See Findingβ
1
in point 3
0 85
c c
C.f ab

=
( )
0 5
s y
T A.f=
d'
T
strain
stress
C
c
C'
s
0.003
c
b
h
a
ε'
s
ε
s
=0.5ε
y
A
s
A'
s
Strunet.com: Concrete Column Design V1.01 - Page 8
STRUNET
CONCRETE DESIGN AIDS
Point 5: Axial Compression and
Moment Strength at 50% Strain
Finding Point 6
s
y
y
s
f
E
ε ε= =
0 003
0 003
0 003
b
y
.
c.

 
=
 
 
+
 
1b b
a cβ=
( )
0 85
s s s c
C A f.f
′ ′ ′
= −
y s
T f A=
b c s
P C C T= + −
2 2 2 2
b
b c s
a
h h h
M C C d T d
 
   

= − + − + −
   
 
   
 
b
b
b
M
e
P
=
0 003
b s
s
b
c d
.
c
ε
 

=
 
 
0 85
c c b
C.f a b

=
min( )
s s s y
f E,fε
′ ′
=
See Findingβ
1
in point 3
See finding φ
&
n n
M Pφ φ
d'
T
strain
stress
C
c
C'
s
0.003
c
b
h
a
ε'
s
ε
y
=f
y
/E
s
A
s
A'
s
Strunet.com: Concrete Column Design V1.01 - Page 9
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CONCRETE DESIGN AIDS
Point 6: Axial Compression and Moment
Strength at Balanced Conditions
Finding Point 7
See finding φ
0 85
c c
C.f ab

=
y s
T f A=
0 85
s y
c
A f
a
.f b
=

1
a
c
β
=
0 003
0 003
s y
.
d.
c
ε ε
 
= − >
 
 
0 85
c c b
C.f a b

=
y s
T f A=
2 2 2
n c
h a h
M C T d
   
= − + −
   
   
0 9.φ=
n

See Findingβ
1
in point 3
d'
T
strain
stress
C
c
0.003
c
b
h
a
ε'
s
~0.0
ε
s

y
A
s
A'
s
Strunet.com: Concrete Column Design V1.01 - Page 10
STRUNET
CONCRETE DESIGN AIDS
Point 7: Moment Strength at Zero Axial Force