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.

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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

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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

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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

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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 = −

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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

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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

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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.

.ε

=

+

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

Mφ

See Findingβ

1

in point 3

d'

T

strain

stress

C

c

0.003

c

b

h

a

ε'

s

~0.0

ε

s

>ε

y

A

s

A'

s

Strunet.com: Concrete Column Design V1.01 - Page 10

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CONCRETE DESIGN AIDS

Point 7: Moment Strength at Zero Axial Force

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