aci design aids

27
DESIGN AID J.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

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American Concrete Institute design aids

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Page 1: ACI Design Aids

DESIGN AID J.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

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PositiveMoment

NegativeMoment

Shear

n n n n

Prismatic members

n

nuw nuw nuw

nuw avgnuw avgnuw nuw nuwSpandrelSupport

ColumnSupport

nuw

nuw nuwnuw nuwnuw nuw

nuw

nnavgn

Note A nuw avgnuw avgnuw nuw nuw

Two or more spans

Uniformly distributed load wu (L/D 3)

nuw

DESIGN AID J.1-2

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DESIGN AID J.1-3

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DESIGN AID J.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

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.

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DESIGN AID J.1-51

Assumptions:

yf

cc

sf

Bar Size

Beam Width (in.)

Minimum number of bars, nmim:

1)5.0(2

sdcb

n bcwmin

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.

db

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DESIGN AID J.1-61

Assumptions:

yf

sc

Bar Size

Beam Width (in.)

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.

db

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1 2 3

5.18/1h 21/2h 8/3h

1 2 3

24/1h 28/2h 10/3hSolid 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 ( 145cw 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 J.1-7h

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DESIGN AID J.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.

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DESIGN AID J.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)

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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 J.1-10 T-beam Construction

8.12

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DESIGN AID J.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).

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DESIGN AID J.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).

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DESIGN AID J.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).

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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 J.1-14

Moment of Inertia of Cracked Section Transformed to Concrete, crI

h

h

nAs

kd

d (n – 1)A′s

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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 J.1-14

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

h

h yt

d (n – 1)A′s

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DESIGN AID J.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)

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DESIGN AID J.2-1

f

f

scs

bcbf IE

IE

cE

cc fw cw

sb II

Page 1 of 11

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DESIGN AID J.2-2

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

Page 2 of 11

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DESIGN AID J.2-3

n

n

Page 3 of 11

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DESIGN AID J.2-4

Flat Plate or Flat Slab

Flat Plate or Flat Slab with Spandrel Beams

t

Page 4 of 11

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DESIGN AID J.2-4

Flat Plate or Flat Slab with End Span Integral with Wall

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

Page 5 of 11

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DESIGN AID J.2-4

Two-Way Beam-Supported Slab

f t

Page 6 of 11

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DESIGN AID J.2-5

f

CC2

ha

b

beff = b + 2(a – h) b + 8h

Beam, Ib

Slab, Is

2

ha

b

Beam, Ib

Slab, Is

CL

beff = b + (a – h) b + 4h

Interior Beam Edge Beam

scs

bcbf IE

IE

cE

cc fw cw

hIs

beffeffbb yhahbhbhayhabhabI

habhb

habhahby

eff

eff

b

Page 7 of 11

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DESIGN AID J.2-6

t

CC2

ha

b

beff = b + 2(a – h) b + 8h

Interior Beam

Case A

yxyx

yxyxCA

Case B

yxyx

yxyxCB

C AC BC

scs

cbt IE

CE

hIs cc fwE cw

x2x1

y1

y2y2

x2

x1

y1

y2

Page 8 of 11

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2

ha

b

CL

beff = b + (a – h) b + 4h

DESIGN AID J.2-6

t

Edge Beam

Case A

yxyx

yxyxCA

Case B

yxyx

yxyxCB

C AC BC

scs

cbt IE

CE

hIs cc fwE cw

x2x1

y1

y2

x2

x1

y1

y2

Page 9 of 11

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DESIGN AID J.2-7

Nc NcNFk NFC NFm

sbcsNFsb IEkK

uFN qmFEM

FN cc FN cc uqPCA Notes on ACI 318-11

Nc

Nc

Fc

Fc

Page 10 of 11

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DESIGN AID J.2-8

cHABk ABC

ccccBABAc

ccccABABc

IEkK

IEkK

PCA Notes on ACI 318-11

H c

Page 11 of 11

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