strunet

8/10/2019 strunet

1/10

The Column Design Section in Strunet contains two main parts: Charts todevelop 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 interes ting members in concrete structuraldesign application. A structural design of a concrete column is quite complicatedprocedures. Evaluation, however, of a given column section and reinforcement is

straightforward process. This is due to the fact that pure axial compression is

rarely the case in column analysis. Some value of moment is always there due toend restraint, or accidental eccentricity due to out of a lignment. ACI establishedthe minimum eccentricity on a concrete column, regardless of the struct uralanalysis proposed for the column, which is defined as the maximum axial

compression load that a column can be designed for.

Column Design Charts in Bullets:

One of the demanding aspects in concrete column design is to define the

controlling points on strength interaction diagram. The column strengthinteraction diagram is a curve plot of points; where each point has two ordinates.

The first ordinate is bending moment strength and the second is thecorresponding axial force. Both ordinates are linked with eccentricity. The shapeof the curve, or the strength interaction diagram, can be defined by finding the

ordinates of major seven points. Each point has specific requirement, asestablished by the code, and thus evaluating the requirement of this poin t will

result of calculating the ordinates. The points and their respective requirementsare 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 compressionpermitted by code.

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

Pont 5: Compression and moment at 50% strain in the tension sidereinforcement.

Point 6: Compression and moment at balanced conditions.

Point 7: Pure tension.

STRUNETCONCRETE DESIGN AIDS

Introduction to Concrete Column Design Flow Charts

Strunet.com: Concrete Column Design V1.01 - Page 1

8/10/2019 strunet

2/10

a = depth of equivalent rectangular stress block, in.

ab = depth of equivalent rectangular stress block at balanced

condition, in.Ag = gross area of column, in

2.

As = area of reinforcement at tension side, in2.

As = area of reinforcement at compression side, in2.

Ast = Total area of reinforcement in column cross section, in2.

b = column width dimension, in.

c = distance from extreme compression fiber to neutral axis, in.

cb = distance from extreme compression fiber to neutral axis atbalanced condition, in.

Cc = compression force in equivalent concrete block.

Cs = compression force in tension-side reinforcement, if any.Cs = compression force in compression-side reinforcement.

d = distance from extreme compression fiber to centroid of tensi on-side reinforcement

d = distance from extreme compression fiber to centroid of

compression-side reinforcement

e = eccentricity, in.

eb = eccentricity at balanced condition, in.

Es = modulus of elasticity of reinforcement, psi.

fc = specified compressive strength of concrete, psi.

fy = specified tensile strength of reinforcement, psi.fs = stress in tension-side reinforcement at strain s, ksi.

fs = stress in compression-side reinforcement at strain 's, ksi.

h = overall column depth, in.

Mb = nominal bending moment at balanced condition.

Mn = nominal bending moment at any point.

Po = nominal axial load strength at zero eccentricity.

Pb = nominal axial force at balanced condition.

Plim = limit of nominal axial load value at which low or h igh axial

compression can be defined in accordance with ACI 9.3.2.2.

Pn = nominal axial load strength at any point.T = tension force in tension-side reinforcement.

? = factor as defined by ACI 10.2.7.3.

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

's = strain in compression-side reinforcement at calculated stress fs

y = yield strain of reinforcement.

= strength reduction factor



Notations for Concrete Column Design Flow Charts

8/10/2019 strunet

3/10

7

3

4

5

6

increasing

consistent

comp.control

tensioncontrol

balanced

pure tension

max. axial comp.

AxialCompression

,

Pn

Bending Moment Mn

2

1

s=0.0

s=0.5y



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.

8/10/2019 strunet

4/10

( )0 85o c g st y st P . f A A f A= +st g c y A ,A ,f ,f

Spiral?

0 85n oP (max) . P =

0 80n oP (max) . P =

0 75. =0 70.=

0 64n oP (max) . P =0 56n oP (max) . P =

Finding Point 1

Finding Point 2

ACI 10.3.5.1

ACI 9.3.2.2ACI 9.3.2.2



Point 1: Axial Compression at Zero MomentPoint 2: Maximum Permissible Axial Compression at Zero Eccentricity

8/10/2019 strunet

5/10

finding

Axial Tension andAxial Tension with

Flexure

0 90.=

Axial Compressionand Axial

Compression with

Flexure

Spiral

0 75.=0 70. =

High Values of AxialCompression Low Values of Axial

Compression

60

0 70

Symmetric reinf.

y

s

f ksi

h d d . h

0 150 9 n

L

. P.

P =

0 10 c gL

. f AP

=

L nP P>

Spiral?

0 75.=0 70. =

0 133L c gP . f A=

nP

Spiral?

Spiral?

min(0 133 , )L c g bP . f A P =min(0 143 , )L c g bP . f A P =0 2

0 9 n

L

. P.

P =

ACI 9.3.2.2

0 143L c gP . f A=

0 150 9 n

L

. P.

P =

0 20 9 n

L

. P.

P =



Strength Reduction Factor

8/10/2019 strunet

6/10

8/10/2019 strunet

7/10

s 0 0. =

c d=

1a c=

min( )s s s y f E ,f =

( )0 85s s s c C A f . f =

n c sP C C= +

n

n

Me

P=

2 2 2n c s

h a hM C C d

= +

0 85c cC . f ab=

0 003sc d

.c

=

See finding &n nM P

Finding Point 4

See Finding 1 in point 3

T=0.0

d'

strain stress

Cc

C's

0.003

0.0

c=d

b

h

a

's

As

A's



Point 4: Axial Compression and Moment at Zero Strain

8/10/2019 strunet

8/10


( )0 85

s s s c

C A f . f =

n c sP C C T = +

n

n

Me

P=

2 2 2 2

n c s

h a h hM C C d T d

= + +

See finding &n nM P

Finding Point 5

y

y

s

f

E =

0 5s y. =

0 003sc d

.c

=

10 003

s

dc

.

= +

1a c= See Finding 1 in point 3

0 85c cC . f ab=

( )0 5s yT A . f =

d'

T

strain stress

Cc

C's

0.003

c

b

h

a

's

s=0.5y

As

A's



Point 5: Axial Compression andMoment Strength at 50% Strain

8/10/2019 strunet

9/10

Finding Point 6

s

y

y

s

f

E = =

0 0030 003

0 003b

y

.c .

.

= +

1b ba c=

( )0 85s s s c C A f . f =

y sT f A=

b c sP C C T = +

2 2 2 2b

b c s

ah h hM C C d T d

= + +

bb

b

Me

P=

0 003b ssb

c d.

c

=

0 85c c bC . f a b=



See finding &n nM P

d'

T

strain stress

Cc

C's

0.003

c

b

h

a

's

y=fy/Es

As

A's



Point 6: Axial Compression and MomentStrength at Balanced Conditions

8/10/2019 strunet

10/10

Finding Point 7

See finding

0 85c cC . f ab=

y sT f A=

0 85

s y

c

A fa

. f b=

1

ac

=

0 0030 003s y

.d .

c

= >

0 85c c bC . f a b=

y sT f A=

2 2 2n c

h a hM C T d

= +

0 9.=

nM


d'

T

strain stress

Cc0.003c

b

h

a

's~0.0

s>y

As

A's



Point 7: Moment Strength at Zero Axial Force

strunet

Documents

Transcript of strunet