314 Design Aids

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Members of ACI Committee 314, Simplified Design of Concrete Buildings, created and reviewed 

a series of helpful design aids for reinforced concrete.   

Design Aid 1‐1  Areas of Reinforcing Bars Design Aid 1‐2  Approximate Bending Moments and Shear Forces for Continuous Beams and One‐

way Slabs  Design Aid 1‐3  Variation of φ with Net Tensile Strain in Extreme Tension Steel  εt and c/dt – Grade 

60 Reinforcement and Prestressing Steel  Design Aid 1‐4  Simplified Calculation of As Assuming Tension‐Controlled Section and Grade 60 

Reinforcement Design Aid 1‐5  Minimum Number of Reinforcing Bars Required in a Single Layer  Design Aid 1‐6  Maximum Number of Reinforcing Bars Permitted in a Single Layer  Design Aid 1‐7  Minimum Thickness h for Beams and One‐Way Slabs Unless Deflections are 

Calculated  Design Aid 1‐8  Reinforcement Ratio ρt for Tension‐Controlled Sections Assuming Grade 60 

Reinforcement Design Aid 1‐9  Simplified Calculation of bw Assuming Grade 60 Reinforcement and ρ = 0.5ρmax Design Aid 1‐10  T‐beam Construction Design Aid 1‐11  Values of φVs = Vu ‐ φVc (kips) as a Function of the Spacing, s Design Aid 1‐12  Minimum Shear Reinforcement Av,min /s Design Aid 1‐13  Torsional Section Properties Design Aid 1‐14  Moment of Inertia of Cracked Section Transformed to Concrete, Icr Design Aid 1‐15  Approximate Equation to Determine Immediate Deflection, Δi, for Members 

Subjected to Uniformly Distributed Loads   Two Way Slabs – Direct Design Method, includes Design Aid 2.1 through D.8. Design Aid 2‐1  Conditions for Analysis by the Direct Design Method Design Aid 2‐2  Definitions of Column Strip and Middle Strip Design Aid 2‐3  Definition of Clear Span, ℓn Design Aid 2‐4  Design Moment Coefficients used with the Direct Design Method Design Aid 2‐5  Effective Beam and Slab Sections for Computation of Stiffness Ratio, αf Design Aid 2‐6  Computation of Torsional Stiffness Factor, βt, for T‐ and L‐Sections Design Aid 2‐7  Moment Distribution Constants for Slab‐Beam Members without Drop Panels Design Aid 2‐8  Stiffness and Carry‐Over Factors for Columns 

 

1

DESIGN AID 1-1 Areas of Reinforcing Bars

Total Areas of Bars (in.2)

Bar Size

Number of Bars 1 2 3 4 5 6 7 8 9 10

No. 3 0.11 0.22 0.33 0.44 0.55 0.66 0.77 0.88 0.99 1.10 No. 4 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 No. 5 0.31 0.62 0.93 1.24 1.55 1.86 2.17 2.48 2.79 3.10 No. 6 0.44 0.88 1.32 1.76 2.20 2.64 3.08 3.52 3.96 4.40 No. 7 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00 No. 8 0.79 1.58 2.37 3.16 3.95 4.74 5.53 6.32 7.11 7.90 No. 9 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 No. 10 1.27 2.54 3.81 5.08 6.35 7.62 8.89 10.16 11.43 12.70 No. 11 1.56 3.12 4.68 6.24 7.80 9.36 10.92 12.48 14.04 15.60

Areas of Bars per Foot Width of Slab (in.2/ft)

Bar Size

Bar Spacing (in.) 6 7 8 9 10 11 12 13 14 15 16 17 18

No. 3 0.22 0.19 0.17 0.15 0.13 0.12 0.11 0.10 0.09 0.09 0.08 0.08 0.07 No. 4 0.40 0.34 0.30 0.27 0.24 0.22 0.20 0.18 0.17 0.16 0.15 0.14 0.13 No. 5 0.62 0.53 0.46 0.41 0.37 0.34 0.31 0.29 0.27 0.25 0.23 0.22 0.21 No. 6 0.88 0.75 0.66 0.59 0.53 0.48 0.44 0.41 0.38 0.35 0.33 0.31 0.29 No. 7 1.20 1.03 0.90 0.80 0.72 0.65 0.60 0.55 0.51 0.48 0.45 0.42 0.40 No. 8 1.58 1.35 1.18 1.05 0.95 0.86 0.79 0.73 0.68 0.63 0.59 0.56 0.53 No. 9 2.00 1.71 1.50 1.33 1.20 1.09 1.00 0.92 0.86 0.80 0.75 0.71 0.67 No. 10 2.54 2.18 1.91 1.69 1.52 1.39 1.27 1.17 1.09 1.02 0.95 0.90 0.85 No. 11 3.12 2.67 2.34 2.08 1.87 1.70 1.56 1.44 1.34 1.25 1.17 1.10 1.04

2

Positive Moment

Negative Moment

Shear

n,2 < n,1 ≤ 1.2n,2 n,2

Prismatic members

n,2

Integral with Support

Simple Support

14

21,nuw

16

22,nuw

11

22,nuw

24

21,nuw

10

*2,avgnuw

11

2,avgnuw

11

22,nuw

10

*22,nuw

0

Spandrel Support

Column Support 16

21,nuw

21,nuw

22,nuw

22,nuw

22,nuw

215.1 1,nuw

215.1 2,nuw

9

2nuw

22,1,

,nn

avgn

+

=

(2 spans)

(8.3.3)

Note A 12

21,nuw

12

2,avgnuw

12

2,avgnuw

12

22,nuw

12

**22,nuw

0

Note A: Applicable to slabs with spans ≤ 10 ft and beams where the ratio of the sum of column stiffness to beam stiffness > 8 at each end of the span.

Two or more spans

Uniformly distributed load wu (L/D ≤ 3)

10

22,nuw

(for beams)

*

**

DESIGN AID 1-2 Approximate Bending Moments and Shear Forces for Continuous Beams

and One-way Slabs 8.3.3

3

DESIGN AID 1-3

Variation of φ with Net Tensile Strain in Extreme Tension Steel tε and td c / – Grade 60 Reinforcement and Prestressing Steel

9.3.2

0.65

0.75 Spiral

Other

Compression-controlled

0.002=εt

φ

Transition Tension-controlled

0.002)(50)(0.75 −ε+=φ t

0.90

Spiral: (5/3)])/0.15[(1/0.75 −+=φ tdc

Other: (5/3)])/0.25[(1/0.65 −+=φ tdc

/3)0.002)(250(0.65 −ε+=φ t

c = 0.6dt

εt = 0.002

0.003

dt

0.005=εt

c = 0.375dt

εt = 0.005

0.003

dt

4

DESIGN AID 1-4

Simplified Calculation of sA Assuming Tension-Controlled Section and Grade 60 Reinforcement

cf ′ (psi) sA (in.2)

3,000 d

M u

84.3

4,000 d

M u

00.4

5,000 d

M u

10.4

uM is in ft-kips and d is in inches

In all cases, d

MA us 4

= can be used.

Notes:

• d

ff

f

MA

c

yy

us

×

−

=

'85.05.0

1ρ

φ

• For all values of ρ < 0.0125, the simplified As equation is slightly conservative. • It is recommended to avoid ρ > 0.0125 when using the simplified As equation.

5

DESIGN AID 1-51

Minimum Number of Reinforcing Bars Required in a Single Layer 10.6.4

Assumptions:

• Grade 60 reinforcement ( yf = 60,000 psi)

• Clear cover to the tension reinforcement cc = 2 in. • Calculated stress sf in reinforcement closest to the tension face at

service load = 40,000 psi

Bar Size

Beam Width (in.) 12 14 16 18 20 22 24 26 28 30 36 42 48

No. 4 2 2 3 3 3 3 3 4 4 4 5 5 6 No. 5 2 2 3 3 3 3 3 4 4 4 5 5 6 No. 6 2 2 3 3 3 3 3 4 4 4 5 5 6 No. 7 2 2 3 3 3 3 3 4 4 4 5 5 6 No. 8 2 2 3 3 3 3 3 4 4 4 5 5 6 No. 9 2 2 3 3 3 3 3 4 4 4 5 5 6 No. 10 2 2 3 3 3 3 3 4 4 4 5 5 6 No. 11 2 2 3 3 3 3 3 4 4 4 5 5 6 Minimum number of bars, nmim:

1)5.0(2

++−

=s

dcbn bcw

min

where

≤

−

=

s

cs

f

cf

s

000,4012

5.2000,4015

1 Alsamsam, I.M. and Kamara, M. E. (2004). Simplified Design Reinforced Concrete Buildings of Moderate Size and Heights, EB104, Portland Cement Association, Skokie, IL.

cccc bbww

11--11//22″″ cclleeaarr

cccc

db

CClleeaarr ssppaaccee ≥≥

ddss

ccss

rr == ¾¾″″ ffoorr NNoo.. 33 ssttiirrrruuppss

11″″ ffoorr NNoo.. 44 ssttiirrrruuppss

11″″

ddbb

11..3333((mmaaxx.. aaggggrreeggaattee ssiizzee))

6

DESIGN AID 1-61 Maximum Number of Reinforcing Bars Permitted in a Single Layer

7.6

Assumptions:

• Grade 60 reinforcement ( yf = 60 ksi)

• Clear cover to the stirrups sc = 1.5 in. • ¾-in. aggregate

• No. 3 stirrups are used for No. 5 and No. 6 longitudinal bars, and No. 4 stirrups are used for No. 7 and larger bars

Bar Size

Beam Width (in.) 12 14 16 18 20 22 24 26 28 30 36 42 48

No. 4 5 6 8 9 10 12 13 14 16 17 21 25 29 No. 5 5 6 7 8 10 11 12 13 15 16 19 23 27 No. 6 4 6 7 8 9 10 11 12 14 15 18 22 25 No. 7 4 5 6 7 8 9 10 11 12 13 17 20 23 No. 8 4 5 6 7 8 9 10 11 12 13 16 19 22 No. 9 3 4 5 6 7 8 8 9 10 11 14 17 19 No. 10 3 4 4 5 6 7 8 8 9 10 12 15 17 No. 11 3 3 4 5 5 6 7 8 8 9 11 13 15 Maximum number of bars, nmax:

1space)(Clear

)(2+

+++−

=b

sswdrdcb

nmax

1 Alsamsam, I.M. and Kamara, M. E. (2004). Simplified Design Reinforced Concrete Buildings of Moderate Size and Heights, EB104, Portland Cement Association, Skokie, IL.

cccc bbww

11--11//22″″ cclleeaarr

cccc

db

CClleeaarr ssppaaccee ≥≥

ddss

ccss

rr == ¾¾″″ ffoorr NNoo.. 33 ssttiirrrruuppss

11″″ ffoorr NNoo.. 44 ssttiirrrruuppss

11″″

ddbb

11..3333((mmaaxx.. aaggggrreeggaattee ssiizzee))

7

1 2 3

One end continuous

5.18/1≥h 21/2≥h

Both ends continuous

8/3≥h

Cantilever

1 2 3

One end continuous

24/1≥h

28/2≥h

Both ends continuous

10/3≥h

Cantilever

Solid One-way Slabs

• Applicable to one-way construction not supporting or attached to partitions or other construction likely to be damaged by large deflections.

• Values shown are applicable to members with normal weight concrete ( 145=cw lbs/ft3) and Grade 60 reinforcement. For other conditions, modify the values as follows:

For structural lightweight having cw in the range 90-120 lbs/ft3, multiply the values by ( ) .09.1005.065.1 ≥− cw

For yf other than 60,000 psi, multiply the values by ( ).000,100/4.0 yf+

• For simply-supported members, minimum

=slabsway -one ribbedor beamsfor 16/

slabsway -one solidfor 20/

h

Beams or Ribbed One-way Slabs

DESIGN AID 1-7 Minimum Thickness h for Beams and One-Way Slabs Unless Deflections are

Calculated 9.5.2

8

DESIGN AID 1-8

Reinforcement Ratio tρ for Tension-Controlled Sections Assuming Grade 60 Reinforcement

cf ′ (psi) tρ when εt = 0.005 tρ when εt = 0.004

3,000 0.01355 0.01548

4,000 0.01806 0.02064

5,000 0.02125 0.02429 Notes:

1. ( )bcfC c 1'85.0 β=

ys fAT = ( ) ysc fAbcfTC =⇒= 1'85.0 β

a. When εt = 0.005, c/dt = 3/8.

( ) ystc fAbdf =83'85.0 1β

y

c

t

st f

f

bdA )8

3(85.0 1 ′==

βρ

b. When εt = 0.004, c/dt = 3/7.

( ) ystc fAbdf =73'85.0 1β

y

c

t

st f

f

bdA )7

3(85.0 1 ′==

βρ

2. β1 is determined according to 10.2.7.3.

9

DESIGN AID 1-9

Simplified Calculation of wb Assuming Grade 60 Reinforcement and maxρ=ρ 5.0

cf ′ (psi) wb (in.)*

3,000 26.31

d

M u

4,000 27.23

d

M u

5,000 20.20

d

M u

* uM is in ft-kips and d is in inches

In general:

( ) 211 2143.01

600,36

df

Mb

c

uw

βρ−′βρ=

where maxρρ=ρ / , cf ′ is in psi, d is in inches and uM is in ft-kips and

003.0004.0003.085.0 1+

′β=ρ

y

cmax f

f (10.3.5)

10

1s

fhh =

+−

+

+

≤

2443

612lengthSpan

121

1

1

1sbb

hb

b

b

ww

w

w

e

1eb

2s 1wb 2wb

2eb

++

+−

+≤

242

164lengthSpan

21312

22ssbbb

hbb

www

we

3wb

2w

fbhh ≥=

wb

we bb 4≤

Isolated T-beam

DESIGN AID 1-10 T-beam Construction

8.12

11

DESIGN AID 1-11

Values of cus VVV φ−=φ (kips) as a Function of the Spacing, s*

s No. 3 U-stirrups No. 4 U-stirrups No. 5 U-stirrups d/2 19.8 36.0 55.8

d/3 29.7 54.0 83.7

d/4 39.6 72.0 111.6 * Valid for Grade 60 ( 60=ytf ksi) stirrups with 2 legs (double the tabulated values for

4 legs, etc.).

In general:

sdfA

V ytvs

φ=φ (11.4.7.2)

where ytf used in design is limited to 60,000 psi, except for welded deformed wire reinforcement, which is limited to 80,000 psi (11.4.2).

12

DESIGN AID 1-12

Minimum Shear Reinforcement */, sA minv

cf ′ (psi) s

A minv,

in.in.2

500,4≤ wb00083.0

5,000 wb00088.0

* Valid for Grade 60 ( 60=ytf ksi) shear reinforcement.

In general:

yt

w

yt

wc

minv

fb

fb

fs

A 5075.0, ≥′= Eq. (11-13)

where ytf used in design is limited to 60,000 psi, except for welded deformed wire reinforcement, which is limited to 80,000 psi (11.4.2).

13

DESIGN AID 1-13 Torsional Section Properties

Section* Acp pcp Aoh ph

Edge

bwh + behf 2(h + bw + be) x1y1 2(x1 + y1)

x1 = bw - 2c - ds

y1 = h - 2c - ds

Interior

bw(h - hf) + behf 2(h + be) x1y1 2(x1 + y1)

x1 = bw - 2c - ds

y1 = h - 2c - ds

L-shaped

b1h1 + b2h2 2(h1 + h2 + b2) x1y1 + x2y2 2(x1 + x2 + y1)x1 = b1 - 2c - dsy1 = h1 + h2 - 2c - dsx2 = b2 - b1y2 = h2 - 2c - ds

Inverted tee

b1h1 + b2h2 2(h1 + h2 + b2) x1y1 + 2x2y2 2(x1 + 2x2 + y1)x1 = b1 - 2c - dsy1 = h1 + h2 - 2c - ds

x2 = (b2 - b1)/2y2 = h2 - 2c - ds

* Notation: xi, yi = center-to-center dimension of closed rectangular stirrup c = clear cover to closed rectangular stirrup(s) ds = diameter of closed rectangular stirrup(s)

hf

h

hf

yo

yo

xo

h

bw

hf

be = bw + 2(h - hf) ≤ bw + 8hf

h

bw

hf

be = h - hf ≤ 4hf

x1

y1

y1

x1

b1

y1

b1

h1

h2

b2

y1

y2

x1

x2

h1

h2

b2

y2

b1

x1

x2

y1

Note: Neglect overhanging flanges in cases where cpcp pA /2 calculated for a beam with flanges is less than that computed for the same beam ignoring the flanges (11.5.1.1).

14

Gross Section Cracked Transformed Section

Cracked Moment of Inertia, crI

23

)(3

)( kddnAkdbI scr −+=

where

BdBkd 112 −+

=

2

23

)()1(

)(3

)(

dkdAn

kddnAkdbI

s

scr

′−′−+

−+=

where

( ) ( )

B

rrddrdB

kd+−++

′

++=

1112 2

---continued next page--- 12/3bhI g =

cs EEn /= )/( snAbB =

)/()1( ss nAAnr ′−=

b

As

A′s

b d′

n.a.

nAs

kd

d

b

n.a.

b

As

DESIGN AID 1-14

Moment of Inertia of Cracked Section Transformed to Concrete, crI

h

h

nAs

kd

d (n – 1)A′s

15

Gross Section Cracked

Transformed Section

Cracked Moment of Inertia, crI

2

2

33

)(

2)(

3)(

12

)(

kddnA

hkdhbb

kdbhbbI

s

ffw

wfwcr

−+

−−+

+−

=

where

C

fffhdCkd

f )1()1()2( 2 +−+++=

22

2

33

)()1()(

2)(

3)(

12

)(

dkdAnkddnA

hkdhbb

kdbhbbI

ss

ffw

wfwcr

′−′−+−+

−−+

+−

=

where

C

frfrdrfhdCkd

f )1()1()22( 2 ++−+++′++=

]})/[(])[(5.0{ 22 hbhbbhbhbbhy wfwwfwt +−+−−=

2233 )5.0()5.0()(12/12/)( hyhbyhhhbbhbhbbI twtffwwfwg −+−−−++−=

cs EEn /= )/( sw nAbC =

)/()( swf nAbbhf −=

)/()1( ss nAAnr ′−=

nAs

kd

b

n.a.

d′ b

As

hf

bw

A′s

nAs

kd d

b

n.a.

b

As

hf

bw

DESIGN AID 1-14

Moment of Inertia of Cracked Section Transformed to Concrete, crI (continued)

h

h yt

d (n – 1)A′s

16

DESIGN AID 1-15

Approximate Equation to Determine Immediate Deflection, i∆ , for Members Subjected to Uniformly Distributed Loads

ec

ai IE

KM48

5 2=∆

where =aM net midspan moment or cantilever moment

= span length (8.9)

=cE modulus of elasticity of concrete (8.5.1)

= cc fw ′335.1 for values of cw between 90 and 155 pcf

=cw unit weight of concrete

=eI effective moment of inertia (see Flowchart A.1-5.1)

=K constant that depends on the span condition

Span Condition K

Cantilever* 2.0

Simple 1.0

Continuous **)/(2.02.1 ao MM−

* Deflection due to rotation at supports not included

** 8/2wM o = (simple span moment at midspan)

17

DESIGN AID 2-1 Conditions for Analysis by the Direct Design Method

13.6.1

For a panel with beams between supports on all sides, Eq. (13-2) must also be satisfied:

0.52.0 212

221 ≤

α

α≤

f

f

where scs

bcbf IE

IE=α Eq. (13-3)

=cE modulus of elasticity of concrete (8.5.1)

= cc fw ′335.1 for values of cw between 90 and 155 pcf

=sb II , moment of inertia of beam and slab, respectively (see Design Aid J.2-5)

18

DESIGN AID 2-2 Definitions of Column Strip and Middle Strip

13.2

½-Middle strip

½-Middle strip

1

Column strip

Minimum of 1/4 or (2)A/4

Minimum of 1/4 or (2)B/4 (2)A

(2)B

19

DESIGN AID 2-3

Definition of Clear Span, n

13.6.2.5

1

165.0 ≥n

0.89h

h

0.93h

h

h

h

h

h

20

DESIGN AID 2-4 Design Moment Coefficients used with the Direct Design Method

13.6.3 – 13.6.6

Flat Plate or Flat Slab

Flat Plate or Flat Slab with Spandrel Beams

See Design Aid J 2-6 for determination of tβ

21

DESIGN AID 2-4 Design Moment Coefficients used with the Direct Design Method

13.6.3 – 13.6.6 (continued)

Flat Plate or Flat Slab with End Span Integral with Wall

Flat Plate or Flat Slab with End Span Simply Supported on Wall

22

DESIGN AID 2-4 Design Moment Coefficients used with the Direct Design Method

13.6.3 – 13.6.6 (continued)

Two-Way Beam-Supported Slab

Notes:

• Mo is defined per 13.6.2

See Design Aids J 2-5 and J 2-6 for determination of fα and tβ respectively

23

DESIGN AID 2-5

Effective Beam and Slab Sections for Computation of Stiffness Ratio fα

C

C 2

h a

b

beff = b + 2(a – h) ≤ b + 8h

Beam, Ib

Slab, Is

2

h a

b

Beam, Ib

Slab, Is

CL

beff = b + (a – h) ≤ b + 4h

Interior Beam Edge Beam

scs

bcbf IE

IE=α Eq. (13-3)

=cE modulus of elasticity of concrete (8.5.1)

= cc fw ′335.1 for values of cw between 90 and 155 pcf

3212

1 hI s =

2

32

3212

12

)()(121

−−++

−

−−+−= beffeffbb yhahbhbhayhabhabI

where

( )

)(22

2

habhb

habhahby

eff

eff

b −+

−+

−

=

24

DESIGN AID 2-6

Computation of Torsional Stiffness Factor, tβ , for T- and L-Sections

C

C 2

h a

b

beff = b + 2(a – h) ≤ b + 8h

Interior Beam Case A

363.012

363.01

232

2

2

131

1

1

yxyx

yxyxCA

−+

−=

Case B

363.01

363.01

232

2

2

131

1

1

yxyx

yxyxCB

−+

−=

=C maximum of AC and BC

scs

cbt IE

CE2

=β Eq. (13-5)

where 12/32hI s = and cc fwE ′= 335.1 for values of cw between 90 and 155 pcf (8.5.1)

x2 x1

y1

y2 y2

x2

x1

y1

y2

25

2

h a

b

CL

beff = b + (a – h) ≤ b + 4h

DESIGN AID 2-6

Computation of Torsional Stiffness Factor, tβ , for T- and L-Sections (continued)

Edge Beam Case A

363.01

363.01

232

2

2

131

1

1

yxyx

yxyxCA

−+

−=

Case B

363.01

363.01

232

2

2

131

1

1

yxyx

yxyxCB

−+

−=

=C maximum of AC and BC

scs

cbt IE

CE2

=β Eq. (13-5)

where 12/32hI s = and cc fwE ′= 335.1 for values of cw between 90 and 155 pcf (8.5.1)

x2 x1

y1

y2

x2

x1

y1

y2

26

DESIGN AID 2-7 Moment Distribution Constants for Slab-Beam Members without Drop Panels*

11 / Nc 22 / Nc Stiffness Factor,

NFk Carry-over Factor,

NFC Fixed-end Moment Coefficient, NFm

0.10

0.10 4.18 0.51 0.0847 0.20 4.36 0.52 0.0860 0.30 4.53 0.54 0.0872 0.40 4.70 0.55 0.0882

0.20

0.10 4.35 0.52 0.0857 0.20 4.72 0.54 0.0880 0.30 5.11 0.56 0.0901 0.40 5.51 0.58 0.0921

0.30

0.10 4.49 0.53 0.0863 0.20 5.05 0.56 0.0893 0.30 5.69 0.59 0.0923 0.40 6.41 0.61 0.0951

0.40

0.10 4.61 0.53 0.0866 0.20 5.35 0.56 0.0901 0.30 6.25 0.60 0.0936 0.40 7.37 0.64 0.0971

Slab-beam stiffness 1/ sbcsNFsb IEkK =

Fixed-end moment 212uFN qmFEM =

* Applicable where (1) 11 FN cc = and 22 FN cc = and (2) a uniformly distributed load uq

acts over the entire span length. See PCA Notes on ACI 318-11 for other cases, including constants for members with drop panels.

1

2 2Nc

1Nc

2Fc

1Fc

27

DESIGN AID 2-8 Stiffness and Carry-Over Factors for Columns*

cH / Stiffness Factor, ABk

Carry-over Factor, ABC

1.05 4.52 0.54 1.10 5.09 0.57 1.15 5.71 0.60 1.20 6.38 0.62 1.25 7.11 0.65 1.30 7.89 0.67 1.35 8.73 0.69 1.40 9.63 0.71 1.45 10.60 0.73 1.50 11.62 0.74

Column stiffness: ( )

( )

=

=

ccccBABAc

ccccABABc

IEkK

IEkK

/

/

* See PCA Notes on ACI 318-11 for other cases, including factors for members with drop

panels and column capitals.

H

A

B

c

28