Concrete column Design Flow Charts

STRUNET CONCRETE DESIGN AIDS

Introduction to Concrete Column Design Flow Charts

The Column Design Section in Strunet contains two main parts: Charts to develop develop strength strength inter i nteraction action diagrams diagrams for any given section, and ready -made -made Column Interaction Diagrams, for quick design of a given column. Concret Concrete e column co lumn is one of the most most i nteres teres ting ting members members in concrete concrete structu struct ural design application. A structural design of a concrete column is quite complicated procedures. Evaluation, however, of a given column section and reinforcement is straightfo straightforward rward process. This This is d ue to the the fact that pure axial compressio compression n is rarely the case in column analysis. Some value of moment is always there due to end end restrain restrai nt, or accidental accidental eccentricity due to out of alignment. alignment. AC I establis establish hed the the minimum minimum eccen ecce ntricity on a concrete column, regardle regardless ss of the struct ural analysis 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 One of th t he demanding aspects in con co ncrete column col umn design design is to define define the controllin controlling g poi nts o n strength i nteraction teraction diagram. The The column co lumn strength strength interaction diagram is a curve plot of points; where each point has two ordinates. The first ordinate is bending moment strength and the second is the corresponding a xial force. force. Both ordi ordinat nates es are linked with eccentricity. ecce ntricity. The s hape of the curve, or the strength interaction diagram, can be defined by finding the ordinates of major seven points. Each point has specific requirement, as established established by the code, and thu t hus s evaluating evaluating th t he requirement requirement of this poin t will result of calculating the ordinates. The points and their respective requirements are as follows: • •

•

•

•

• •

Point 1: Pure compression. Point 2: Maximum compression load permitted by code at zero eccentricity. Point 3: Maximum Maximum moment strengt strength h at the maximum a xial compression permitted by code. Point 4: Compression and moment at zero strain in the tension side reinforcement. Pont 5: Compr C ompression ession an a nd moment at 50% strai strain n in the tension side reinforcement. Point 6: Compression and moment at balanced conditions. Point 7: Pure tension.

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


Notations for Concrete Column Design Flow Charts a ab

= =

A g A s A’ s A’ st st b c c b

= = = = = = =

C c c C s C’ s d

= = = =

d’

=

e eb E s f’ c c f y y f s f’ s h M b M n P o P b P lim lim

= = = = = = = = = = = = =

P n T β ? ? ε s 's ε ' ε y y φ

= = = = = = =

depth of equivalent eq uivalent rectangular stress b lock, in. depth of equivalent eq uivalent rectangular stress b lock a t balanced condition, in. gross area of column, i n 2. area of reinforcement at tension side, in 2 . area of reinforcemen reinforcementt at compres sion side, in 2 . Tota Tota l area of reinforcement in column cross section, sec tion, in 2 . column width dimension, dimensio n, in. distance from extreme compression compressio n fiber to to ne ne utral a xis, i n. distance from extreme compression compressio n fiber to to ne ne utral axis at balanced condition, in. compression force i n equiv eq uiva a lent concrete b lock. compression force i n tensio tension n -side reinf rei nforcement, orcement, if a ny. compression force i n compression compressi on-side -side reinf rei nforcement. orcement. distance distance from from extreme extreme compression compression fiber to centroid of tensi onside reinforcement distance from extreme compression compressio n fiber to centroid ce ntroid of compression-side reinforcement eccentricit eccentricity, y, in. eccentrici eccentricity ty at balan ba lanced ced condition, co ndition, in. modulus of elasticity elastic ity of reinforcement, psi. specified specifie d compressive compressi ve strength stre ngth o f concr co ncre e te, psi. specified specifi ed tensile tensile strength stre ngth of reinforcement, psi. stress stress i n tension-side reinforcement reinforcement at strain ε s , ksi. stress stress i n compression-side reinforcement reinforcement at strain ε ' ' s , ksi. overa overa ll column depth, in. nomi nomi nal bending moment at balanced condition. co ndition. nomi nomi nal bending moment a t a ny poi nt. nt. nomi nomi nal axial load strength at zero zero eccentricity. ecce ntricity. nomi nomi nal axial force at balanced condition. co ndition. limit limit of nominal nominal axial load load val valu ue at whic which h low or h igh ig h axial compression can be defined in accordance with ACI 9.3.2.2. nomi nomi nal axial load strength at any point. tensio tension n force i n tension-si tensio n-side de reinforcement. factor as defined defi ned b y ACI AC I 10.2.7.3. 10 .2.7.3. strain in tension-side reinforceme reinforcement nt at calculated ca lculated stress f s strain in compression -side reinforcement at calculated stress f’ s yield strai n of reinforcement. strength reduction factor



Main Points of Column Interaction Diagram

1 3 n

P

, n o i s s e r p m o C l a i x A

max. axial comp.

4

ε s=0.0

2 5

ε s=0.5 ε y

6 balanced

comp. control tension control

consistent φ

increasing φ pure tension Bending Moment

M n

7

Point 1: axial compression at zero moment. Point Point 2: maximum maximum permissible permissible axial axial compression compression at zero eccentricit. eccentr icit. 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.



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

Finding Point 1 ACI 10.3.5.1

Ast ,Ag ,fc′,f y

Po

= 0.85fc′

(A

g

)

− Ast + fy Ast

Finding Point 2

Spiral?

Pn (max) = 0.80Po ACI 9.3.2.2

Pn (max) = 0.85Po ACI 9.3.2.2

φ = 0.70

φ = 0.75

φ Pn(max) = 0.56Po

φ Pn (max) = 0.64Po

Strunet.com: Concrete Column Design V1.01 - Page 4

Strength Reduction Factor

STRUNET

ACI 9.3.2.2

CONCRETE DESIGN AIDS

finding φ Axial Compression and Axial Compression with Flexure

Axial Tension and Axial Tension with Flexure

φ = 0.90 P L

=

0.10fc′Ag φ

Spiral?

φ = 0.75

φ = 0.70 PL

= 0.143fc′Ag

PL

= 0.133fc′Ag

P n PL

> P n

High Values of Axial Compression

Low Values of Axial Compression

Spiral

φ = 0.75

φ = 0.70

• fy ≤

Spiral?

60 ksi 0.70h

•

h − d ′ − ds

•

Symmetric reinf.

≤

Spiral?

PL

= min(0.14 143fc′Ag ,

φ = 0.9 −

0.2P n P L

Pb )

PL

= min(0.13 133fc′Ag ,

φ = 0.9 −

Pb )

0.15P n P L

Strunet.com Strunet.com:: Concrete Concrete Column Design V1.01 - Page 5

φ = 0.9 −

0.2P n P L

φ = 0.9 −

0.15P n P L

Point 3: Maximum Moment Strength at Maximum Permissible Compression

STRUNET

ACI 10.2.7.3


fc ′ ≤ 4000 psi  f c ′ − 4000   ≥ 0.65 1000  

β 1 = 0.85

β 1 = 0.85 − 0.05  finding finding dista distance nce c

Cc = 0.85fc ′ ( β 1c ) b Cs′ = A's (fy − 0.85fc′ )

d'

ε s =

0.003 ε ' 's

( c − d ) 0.003 A' s

c h

fs = ε sE s

 ( c − d ) 0.003 

c

d s

strain

 

Pn = Cc +Cs′ + Cs

P n of point 2

 ( c − d ) 0.003

Pn = 0.85fc′ ( β 1c ) b + A's ( fy − 0.85fc′ ) + As 



c

a = β 1c Compute: C c , C' s from above above Eqs. Eqs.

Mn = 0.5Cc ( h − a) + Cs′ ( 0.5h − d′) − Cs (0.5h − ds ) Strunet.com: Concrete Column Design V1.01 - Page 6



Es − 0 .85 fc′ 

Resul esult: t: c

C s

ε s

b

Es − 0.85fc′ 

C c

a

c

d As

Cs = As ( fs − 0.85fc′ )

Cs = As 

C' s



stress

Point 4: Axial Compression and Moment at Zero Strain


Finding Point 4

ε s = 0.0

c = d a = β 1c

See Finding β 1 in point 3

Cc = 0.85fc ′ab  c − d ′  ε s′ =   0.003  c 

d'

0.003 ε ' 's

A' s

fs′ = min(ε s′Es ,fy )

C' s a

C c

c=d

h As

Cs′ = As′ ( fs′ − 0.85fc′ )

0.0

b

Pn = Cc + C s′ h a h  −  + Cs′  − d ′   2 2 2 

Mn = Cc 

e=

M n P n

φMn & φ P n

T=0.0

See finding φ


strain

stress

Finding Point 5


ε y =

Point 5: Axial Compression and Moment Strength at 50% Strain

f y d'

E s A' s

εs = 0.5ε y

0.003 ε ' 's

C' s a

C c

c

h

    d c =   ε s  1 +  0.003  

a = β 1c

As ε s=0.5 ε ε y

b


Cc = 0.85fc ′ab

 c − d ′   0.003  c 

ε s′ = 

fs′ = min(ε s′Es ,fy ) Cs′ = As′ ( fs′ − 0.85fc′ )

T = As ( 0.5fy )

Pn = Cc + Cs′ − T h h a h   −  + Cs′  − d ′  + T  d −  2  2 2 2  

Mn = Cc 

e=

T

M n P n

φMn & φ P n Strunet.com: Concrete Column Design V1.01 - Page 8

See finding φ

strain

stress

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Point 6: Axial Compression and Moment Strength at Balanced Conditions


Finding Point 6

ε s = ε y =

f y E s

 0.003  cb =  0.003  0.003 + ε y   

ab = β 1c b


Cc = 0.85fc′abb d'

 cb − d s′   0.003 c b  

ε s′ = 

A' s

C c

T ε y =f y /E s

b

Pb = Cc + Cs − T h  h ab  h   −  + Cs  − d ′  + T  d −  2 2   2 2 

Mb = Cc 

M b P b

φMn & φ P n

a

c

As

T = fy As

eb =

C' s

h

fs′ = min(ε s′Es ,fy ) Cs = As′ ( fs′ − 0.85fc′ )

0.003 ε ' 's

See finding φ


strain

stress

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Point 7: Moment Strength at Zero Axial Force


Finding Point 7 d'

Cc = 0.85fc ′ab

A' s

0.003

C c

a

c

ε ' 's ~0.0

h

T = fy As

As

T ε s>ε y

a=

Asf y

b

0.85fc ′b

c =

a β 1


 0.003   d − 0.003 > ε y c  

εs = 

Cc = 0.85fc′abb T = fy As h h a  −  +T d −  2  2 2 

Mn = Cc 

φ = 0.9

See finding φ

φ M n

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

strain

stress

Concrete column Design Flow Charts

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