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D.9 — Installation of anchors

D.9 — Installation of anchors

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APPENDIX E



439



APPENDIX E — STEEL REINFORCEMENT INFORMATION

As an aid to users of the ACI Building Code, information on sizes, areas, and weights of various steel

reinforcement is presented.



CODE



COMMENTARY



ASTM STANDARD REINFORCING BARS

Bar size, no.*



Nominal

diameter, mm



Nominal area,

mm2



Nominal mass,

kg/m



10



9.5



71



0.560



13



12.7



129



0.994



16



15.9



199



1.552



19



19.1



284



2.235



22



22.2



387



3.042



25



25.4



510



3.973



29



28.7



645



5.060



32



32.3



819



6.404



36



35.8



1006



7.907



43



43.0



1452



11.38



57



57.3



2581



20.24



*Bar numbers approximate the number of millimeters of the nominal diameter of the bar.



ASTM STANDARD PRESTRESSING TENDONS

Type*



Seven-wire strand

(Grade 1725)



Seven-wire strand

(Grade 1860)



Prestressing wire



Prestressing bars

(plain)



Prestressing bars

(deformed)



Nominal

diameter, mm



Nominal area,

mm2



Nominal mass,

kg/m



6.4



23.2



0.182



7.9



37.4



0.294



9.5



51.6



0.405



11.1



69.7



0.548



12.7



92.9



0.730



15.2



139.4



1.094



9.53



54.8



0.432



11.1



74.2



0.582



12.70



98.7



0.775



15.24



140.0



1.102



4.88



18.7



0.146



4.98



19.5



0.149



6.35



31.7



0.253



7.01



38.6



0.298



19



284



2.23



22



387



3.04



25



503



3.97



29



639



5.03



32



794



6.21



35



955



7.52



15



181



1.46



20



271



2.22



26



548



4.48



32



806



6.54



36



1019



8.28



*



Availability of some tendon sizes should be investigated in advance.



E



ACI 318 Building Code and Commentary



440



APPENDIX E



CODE



COMMENTARY



WRI STANDARD WIRE REINFORCEMENT*

Area, mm2/m of width for various spacings

Plain



Deformed



Nominal

diameter,

mm



150



200



250



300



MW290



MD290



19.22



2.27



5800



3900



2900



1900



1450



1160



970



MW200



MD200



15.95



1.5700



4000



2700



2000



1300



1000



800



670



MW130



MD130



12.90



1.0204



2600



1700



1300



870



650



520



430



MW120



MD120



12.40



0.9419



2400



1600



1200



800



600



480



400



MW100



MD100



11.30



0.7849



2000



1300



1000



670



500



400



330



MW90



MD90



10.70



0.7064



1800



1200



900



600



450



360



300



MW80



MD80



10.10



0.6279



1600



1100



800



530



400



320



270



MW70



MD70



9.40



0.5494



1400



930



700



470



350



280



230



MW65



MD65



9.10



0.5102



1300



870



650



430



325



260



220



MW60



MD60



8.70



0.4709



1200



800



600



400



300



240



200



MW55



MD55



8.40



0.4317



1100



730



550



370



275



220



180



MW50



MD50



8.00



0.3925



1000



670



500



330



250



200



170



MW45



MD45



7.60



0.3532



900



600



450



300



225



180



150



MW40



MD40



7.10



0.3140



800



530



400



270



200



160



130



MW35



MD35



6.70



0.2747



700



470



350



230



175



140



120



MW30



MD30



6.20



0.2355



600



400



300



200



150



120



100



MW25



MD25



5.60



0.1962



500



330



250



170



125



100



83



MW20



5.00



0.1570



400



270



200



130



100



80



67



MW15



4.40



0.1177



300



200



150



100



75



60



50



MW10



3.60



0.0785



200



130



100



70



50



40



33



MW5



2.50



0.0392



100



67



50



33



25



20



17



MW & MD size



Center-to-center spacing, mm



Nominal

mass, kg/m



50



75



100



E



ACI 318 Building Code and Commentary



APPENDIX F



441



APPENDIX F — EQUIVALENCE BETWEEN SI-METRIC,

MKS-METRIC, AND U.S. CUSTOMARY UNITS OF

NONHOMOGENOUS

CODE EQUATIONS IN THE CODE

COMMENTARY

SI-metric stress

in MPa



mks-metric stress

in kgf/cm2



U.S. Customary units stress in

pounds per square inch (psi)



1 MPa



10 kgf/cm2



142.2 psi



f ′c = 21 MPa



f ′c = 210 kgf/ cm2



f ′c = 3000 psi



f ′c = 28 MPa



f ′c = 280 kgf/ cm2



f ′c = 4000 psi



f ′c = 35 MPa



f ′c = 350 kgf/ cm2



f ′c = 5000 psi



f ′c = 40 MPa



2



f ′c = 420 kgf/ cm



f ′c = 6000 psi



fy = 280 MPa



fy = 2800 kgf/ cm2



fy = 40,000 psi



fy = 420 MPa



fy = 4200 kgf/ cm2



fy = 60,000 psi



fpu = 1725 MPa

fpu = 1860 MPa



fpu = 17,600



kgf/ cm2



fpu = 250,000 psi



fpu = 19,000



kgf/ cm2



fpu = 270,000 psi



√f ′c in MPa



3.18√f c′ in kgf/ cm2



12√f ′c in psi



0.313√f ′c in MPa



√f ′c in kgf/ cm2



3.77√f ′c in psi



0.083√f ′c in MPa

0.17√f ′c in MPa



0.27√f′c in



kgf/ cm2



√f ′c in psi



0.53√f ′c in



kgf/ cm2



2√f ′c in psi



(5-2)



f ′cr = f ′c + 2.33ss – 3.5

f ′cr = f ′c + 7.0



f ′cr = f ′c + 2.33ss – 35

f ′cr = f ′c + 70



f ′cr = f ′c + 2.33ss – 500

f ′cr = f ′c + 1000



Table

5.3.2.2



f ′cr = f ′c + 8.3

f ′cr = 1.10f ′c + 5.0



f ′cr = f ′c + 84

f ′cr = 1.10f ′c + 50



f ′cr = f ′c + 1200

f ′cr = 1.10f ′c + 700



Section

7.12.2.1(c)



0.0018 × 420

---------------------------------fy



0.0018 × 4200

-------------------------------------fy



0.0018 × 60, 000

---------------------------------------------fy



Ec = w1.5

c 0.043√f ′c



Ec = w1.5

c 0.14√f ′c



Ec = w1.5

c 33√f ′c



Ec = 4700√f ′c



Ec = 15,100√f ′c



Ec = 57,000√f ′c



Section

8.6.1



λ = fct /(0.56√f c′ ) ≤ 1.0



λ = fct /(1.78√f ′c ) ≤ 1.0



λ = fct /(6.7√f c′ ) ≤ 1.0



Table

9.5(a)



(1.65 – 0.0003wc) ≥ 1.09

fy ⎞

⎛ 0.4 + --------⎝

700⎠



(1.65 – 0.0003wc) ≥ 1.09

fy ⎞

⎛ 0.4 + -----------⎝

7000⎠



(1.65 – 0.005wc) ≥ 1.09

fy

⎛ 0.4 + ----------------------⎞



100,000 ⎠



(9-10)



fr = 0.62λ √f ′c



fr = 2λ √f ′c



fr = 7.5λ √f ′c



(9-12)



fy ⎞

l n ⎛ 0.8 + -----------⎝

1400⎠

h = ------------------------------------------------- ≥ 125 mm

36 + 5β ( α fm – 0.2 )



fy ⎞

l n ⎛ 0.8 + ------------------⎝

14 ,000⎠

h = ------------------------------------------------- ≥ 12.5 cm

36 + 5β ( α fm – 0.2 )



fy

-⎞

l n ⎛ 0.8 + ---------------------⎝

200 ,000 ⎠

h = ------------------------------------------------- ≥ 5 in.

36 + 5β ( α fm – 0.2 )



(9-13)



fy ⎞

l n ⎛ 0.8 + -----------⎝

1400⎠

h = --------------------------------------- ≥ 90 mm

36 + 9β



fy ⎞

l n ⎛ 0.8 + ------------------⎝

14 ,000⎠

h = ---------------------------------------------- ≥ 9 cm

36 + 9β



fy

-⎞

l n ⎛ 0.8 + ---------------------⎝

200 ,000⎠

h = ------------------------------------------------- ≥ 3.5 in.

36 + 9β



(10-3)



0.25 fc′

1.4

bwd ≥ -------- bwd

As,min = ---------------------fy

fy



0.8 fc′

14

bwd ≥ ------ bwd

As,min = -----------------fy

fy



3 fc′

200

As,min = ------------- bwd ≥ ---------- bwd

fy

fy



(10-4)



280

s = 380 ⎛ 280

-⎞ – 2.5cc ≤ 300⎛⎝ ----------⎞⎠

⎝ --------f ⎠

f



2800

s = 38 ⎛ 2800

-⎞ – 2.5cc ≤ 30⎛⎝ -------------⎞⎠

⎝ -----------f ⎠

f



40 ,000 ⎞ – 2.5c ≤ 12 ⎛ 40 ,000 ⎞

s = 15 ⎛ -------------------⎠

c

⎝ f -⎠

⎝ ------------------f



Section

8.5.1



s



s



s



s



ACI 318 Building Code and Commentary



s



s



F



442



APPENDIX F



CODE



(10-17)

Section

11.1.2



COMMENTARY



SI-metric stress

in MPa



mks-metric stress

in kgf/cm2



U.S. Customary units stress in

pounds per square inch (psi)



M2,min = Pu(15 + 0.03h)



M2,min = Pu(1.5 + 0.03h)



M2,min = Pu(0.6 + 0.03h)



f c′ ≤ 8.3 MPa



f c′ ≤ 27 kgf/cm



2



f c′ ≤ 100 psi



(11-3)



V c = 0.17λ f c′ b w d



V c = 0.53λ f c′ b w d



V c = 2λ f c′ b w d



(11-4)



Nu ⎞

Vc = 0.17 ⎛ 1 + ------------- λ f c′ b w d



14A g⎠



Nu ⎞

- λ f c′ b w d

Vc = 0.53 ⎛ 1 + ---------------⎝

140A g⎠



Nu ⎞

Vc = 2 ⎛ 1 + -------------------- λ f c′ b w d



2000A g⎠



V u d⎞

Vc = ⎛ 0.16λ fc′ + 17ρ w ---------- b d



M ⎠ w



V u d⎞

Vc = ⎛ 0.5λ fc′ + 176ρ w --------- b d



M ⎠ w



V u d⎞

Vc = ⎛ 1.9λ fc′ + 2500ρ w ---------- b d



M ⎠ w



(11-5)



u



≤ 0.29λ f c′ b w d



u



≤ 0.93λ f c′ b w d



u



≤ 3.5λ f c′ b w d



(11-7)



0.29N

Vc = 0.29λ f c′ b w d 1 + ------------------uAg



Nu

Vc = 0.93λ f c′ b w d 1 + ------------35A g



Nu

Vc = 3.5λ f c′ b w d 1 + ---------------500A g



(11-8)



0.29N

Vc = 0.17 ⎛ 1 + ------------------u-⎞ λ f c′ b w d ≥ 0





A



Nu ⎞

λ f c′ b w d ≥ 0

Vc = 0.53 ⎛ 1 + ------------⎝

35A ⎠



Nu ⎞

λ f c′ b w d ≥ 0

Vc = 2 ⎛ 1 + ----------------⎝

500A ⎠



V u d p⎞

V c = ⎛ 0.05λ f c′ + 4.8 ------------- b d



M ⎠ w



V u d p⎞

V c = ⎛ 0.16λ f c′ + 49 ------------ b d



M ⎠ w



V u d p⎞

V c = ⎛ 0.6λ f c′ + 700 ------------- b d



M ⎠ w



0.17λ f c′ b w d ≤ V c ≤ 0.42λ f c′ b w d



0.53λ f c′ b w d ≤ V c ≤ 1.33λ f c′ b w d



2λ f c′ b w d ≤ V c ≤ 5λ f c′ b w d



V i M cre

Vci = 0.05λ f c′ bwdp + Vd +-----------------M max



V i M cre

Vci = 0.16λ f c′ bwdp + Vd + ----------------M max



V i M cre

Vci = 0.6λ f c′ bwdp + Vd +-----------------M max



≥ 0.14λ f c′ bwd



≥ 0.45λ f c′ bwd



≥ 1.7λ f c′ bwd



I ⎞ (0.5λ f ′ + f – f )

Mcre = ⎛ ---pe

d

c

⎝ y-⎠

t



Mcre = ⎛ ---I-⎞ (1.6λ f c′ + fpe – fd)

⎝y ⎠

t



I ⎞ (6λ f ′ + f – f )

Mcre = ⎛ ---pe

d

c

⎝ y-⎠

t



g



(11-9)



(11-10)



(11-11)



u



g



u



g



u



V cw = ( 0.29λ f c′ + 0.3f pc )b w d p + V p V cw = ( 0.93λ f c′ + 0.3f pc )b w d p + V p V cw = ( 3.5λ f c′ + 0.3f pc )b w d p + V p

(11-12)

Section

11.4.5.3

Section

11.4.6.1(f)



0.33λ f c′



1.1λ f c′



4λ f c′



0.33 f c′ bwd



1.1 f c′ bwd



4 f c′ bwd



φ0.17 f c′ bwd



φ0.53 f c′ bwd



φ2 f c′ bwd



bw s

Av,min = 0.062 f c′ ---------f yt



bw s

Av,min = 0.2 f c′ --------f yt



bw s

Av,min = 0.75 f c′ ---------f yt



(11-13)

bw s

≥ 3.5 --------f yt



bw s

≥ 0.35 ---------f yt

(11-17)



Vs = Av fy sinα ≤ 0.25 f c′ bwd



Vs = Av fy sinα ≤ 0.8 f c′ bwd



Vs = Av fy sinα ≤ 3 f c′ bwd



Section

11.4.7.9



0.66 f c′ bwd



2.2 f c′ bwd



8 f c′ bwd



Section

11.5.1(a)



⎛ A cp⎞

Tu < φ0.083λ f c′ ⎜ ---------⎟

⎝ p cp ⎠



2



2



F



50b w s

≥ ----------------f yt



f pc

⎛ A cp⎞

Section

-⎟ 1 + ------------------------11.5.1(b) Tu < φ0.083λ f c′ ⎜ --------p

⎝ cp ⎠

0.33λ f c′



2



⎛ A cp⎞

Tu < φ0.27λ f c′ ⎜ --------⎟

⎝ p cp ⎠

2



f pc

⎛ A cp⎞

Tu < φ0.27λ f c′ ⎜ --------⎟ 1 + ------------p

⎝ cp ⎠

λ f c′



ACI 318 Building Code and Commentary



2



⎛ A cp⎞

Tu < φλ f c′ ⎜ ---------⎟

⎝ p cp ⎠

2



f pc

⎛ A cp⎞

Tu < φλ f c′ ⎜ ---------⎟ 1 + ----------------p

⎝ cp ⎠

4λ f c′



APPENDIX F



443



SI-metric stress

in MPa



mks-metric stress

in kgf/cm2



CODE

Tu <



Tu <



2



U.S. Customary units stress in

pounds per square inch (psi)



COMMENTARY

Tu <



2



Section

11.5.1(c)



Nu

⎛ A cp⎞

φ0.083λ f c′ ⎜ ---------⎟ 1 + --------------------------------p

⎝ cp ⎠

0.33A g λ f c′



Section

11.5.2.2(a)



⎛ A cp⎞

Tu = φ0.33λ f c′ ⎜ ---------⎟

⎝ p cp ⎠



⎛ A cp⎞

Tu = φλ f c′ ⎜ --------⎟

⎝ p cp ⎠



2



f pc

⎛ A cp⎞

Tu = φλ f c′ ⎜ --------⎟ 1 + ------------⎝ p cp ⎠

λ f c′



2



2



f pc

⎛ A cp⎞

Section

-⎟ 1 + ------------------------11.5.2.2(b) Tu = φ0.33λ f c′ ⎜ --------⎝ p cp ⎠

0.33λ f ′

c



(11-18)



2



Tu =



Tu =

Section

11.5.2.2(c)



Nu

⎛ A cp⎞

φ0.27λ f c′ ⎜ --------⎟ 1 + -------------------p

⎝ cp ⎠

A g λ f c′



2

⎛ A cp⎞



Nu

φ0.33λ f c′ ⎜ ----------⎟ 1 + --------------------------------⎝ p cp ⎠

0.33A g λ f c′



2

⎛ A cp⎞



Nu

φλ f c′ ⎜ ---------⎟ 1 + -------------------⎝ p cp ⎠

A g λ f c′



2



Nu

⎛ A cp⎞

φλ f c′ ⎜ ---------⎟ 1 + ------------------------p

⎝ cp ⎠

4A g λ f c′

2



⎛ A cp⎞

Tu = φ4λ f c′ ⎜ ---------⎟

⎝ p cp ⎠

2



f pc

⎛ A cp⎞

Tu = φ4λ f c′ ⎜ ---------⎟ 1 + ----------------⎝ p cp ⎠

4λ f c′

Tu =

2

⎛ A cp⎞



Nu

φ4λ f c′ ⎜ ----------⎟ 1 + ------------------------⎝ p cp ⎠

4A g λ f c′



V u ⎞ 2 ⎛ T u ph ⎞ 2

⎛ ---------+ ⎜ -------------------⎟

⎝ b d-⎠

⎝ 1.7A 2 ⎠

w

oh



V u ⎞ 2 ⎛ T u ph ⎞ 2

⎛ --------+ ⎜ ------------------⎟

⎝ b d-⎠

⎝ 1.7A 2 ⎠

w

oh



V u ⎞ 2 ⎛ T u ph ⎞ 2

⎛ ---------+ ⎜ -------------------⎟

⎝ b d-⎠

⎝ 1.7A 2 ⎠

w

oh



Vc

≤ φ ⎛ ---------- + 0.66 f c′ ⎞

⎝b d



w



Vc

≤ φ ⎛ --------- + 2 f c′ ⎞

⎝b d



w



Vc

≤ φ ⎛ ---------- + 8 f c′ ⎞

⎝b d



w



V u ⎞ ⎛ T u ph ⎞

⎛ --------+

-⎟

⎝ b d-⎠ ⎜⎝ ----------------2

w

1.7A oh⎠



V u ⎞ ⎛ T u ph ⎞

⎛ ---------+

-⎟

⎝ b d-⎠ ⎜⎝ -----------------2

w

1.7A oh⎠



Vc

≤ φ ⎛ --------- + 2 f c′ ⎞

⎝b d



w



Vc

≤ φ ⎛ ---------- + 8 f c′ ⎞

⎝b d



w



V u ⎞ ⎛ T u ph ⎞

⎛ ---------+

-⎟

⎝ b d-⎠ ⎜⎝ -----------------2

w

1.7A oh⎠

(11-19)

Vc

≤ φ ⎛ ---------- + 0.66 f c′ ⎞

⎝b d



w

bw s

(Av + 2At) = 0.062 f c′ ---------f yt



bw s

(Av + 2At) = 0.2 f c′ --------f yt



bw s

(Av + 2At) = 0.75 f c′ ---------f yt



(11-23)

0.35b w s

≥ ---------------------f yt



3.5b w s

≥ -----------------f yt



50b w s

≥ ----------------f yt



0.42 f c′ A cp ⎛ A t⎞ f yt

Al,min = -------------------------------- – ------ p h -----⎝ s⎠

fy

fy



1.33 f c′ A cp ⎛ A t⎞ f yt

- – ----- p h ----Al,min = ------------------------------⎝ s⎠ f

fy

y



5 f c′ A cp ⎛ A t⎞ f yt

Al,min = ------------------------ – ------ p h -----⎝ s⎠

fy

fy



A t 0.175b w

------ ≥ ---------------------s

f yt



A t 1.75b w

----- ≥ -----------------s

f yt



A t 25b w

------ ≥ -------------s

f yt



Section

11.6.5



(3.3 + 0.08fc′)Ac

11Ac

5.5Ac



(34 + 0.08fc′)Ac

110Ac

55Ac



(480 + 0.08fc′)Ac

1600Ac

800Ac



Section

11.7.3



0.83 f c′ bwd



2.65 f c′ bwd



10 f c′ bwd



Section

11.8.3.2.1



(3.3 + 0.08fc′)bwd

11bwd



(34 + 0.08fc′)bwd

110bwd



(480 + 0.08fc′)bwd

1600bwd



Section

11.8.3.2.2



a v⎞

⎛ 5.5 – 1.9 ----- b d



d⎠ w



⎛ 55 – 20 a

-----v⎞ b w d



d⎠



a v⎞

⎛ 800 – 280 ----- b d



d⎠ w



Section

11.9.3

Section

11.9.5



0.83 f c′ hd



2.65 f c′ hd



10 f c′ hd



0.17λ f c′ hd



0.53λ f c′ hd



2λ f c′ hd



(11-24)



ACI 318 Building Code and Commentary



F



444



APPENDIX F



CODE

SI-metric stress

in MPa



U.S. Customary units stress in

pounds per square inch (psi)



(11-27)



Nu d

Vc = 0.27λ f c′ hd + ---------4l w



Nu d

Vc = 0.88λ f c′ hd + ---------4l w



Nu d

Vc = 3.3λ f c′ hd + ---------4l w



(11-28)



0.2N ⎞



u

l ⎜ 0.1λ f ′ + -----------------⎟

w⎝

c

l h ⎠

w

0.05λ f c′ + ------------------------------------------------------------ hd

Mu l

w

-------- – -----V

u 2



0.2N ⎞



u

l ⎜ 0.33λ f ′ + ----------------⎟

w⎝

c

l h ⎠

w

0.16λ f c′ + -------------------------------------------------------------- hd

Mu l

w

-------- – -----V

u 2



0.2N ⎞



u

l ⎜ 1.25λ f ′ + -----------------⎟

w⎝

c

l h ⎠

w

0.6λ f c′ + ---------------------------------------------------------------- hd

Mu l

w

-------- – -----V

u 2



Vc =



Vc =



Vc =



(11-31)



2

Vc = 0.17 ⎛ 1 + ---⎞ λ f c′ b o d



β⎠



2

Vc = 0.53 ⎛ 1 + ---⎞ λ f ′c b o d



β⎠



4

Vc = ⎛ 2 + ---⎞ λ f c′ b o d



β⎠



(11-32)



αs d

Vc = 0.083 ⎛ --------- + 2⎞ λ f c′ b o d

⎝ b



o



αs d

- + 2⎞ λ f c′ b o d

Vc = 0.27 ⎛ --------⎝ b



o



αs d

Vc = ⎛ --------- + 2⎞ λ f c′ b o d

⎝ b





(11-33)



Vc = 0.33λ f c′ b o d



Vc = λ f c′ b o d



Vc = 4λ f c′ b o d



(11-34)



Vc = (βpλ f c′ + 0.3fpc)bod + Vp

Note: β has units



Vc = (3.16βpλ f c′ + 0.3fpc)bod + Vp

Note: βp has the same units as the

SI-metric version



Vc = (βpλ f c′ + 0.3fpc)bod + Vp

Note: βp has units



p



Section

11.11.2.2

Section

11.11.3.1

Section

11.11.3.2

Section

11.11.4.8



Section

11.11.5.1

Section

11.11.5.2

Section

11.11.5.4

Section

11.11.7.2

Section

11.11.7.3

Section

12.1.2



F



COMMENTARY

mks-metric stress

in kgf/cm2



o



f c′ ≤ 5 kgf/cm2



f c′ ≤ 70 psi



0.17λ f c′ bod



0.53λ f c′ bod



2λ f c′ bod



0.5 f c′ bod



1.6 f c′ bod



6 f c′ bod



0.33 f c′ bod



1.1 f c′ bod



4 f c′ bod



0.58 f c′ bod



1.9 f c′ bod



7 f c′ bod



0.25λ f c′ bod



0.8λ f c′ bod



3λ f c′ bod



0.66 f c′ bod



2.1 f c′ bod



8 f c′ bod



0.17 f c′



0.53 f c′



2 f c′



0.5φ f c′



1.6φ f c′



6φ f c′



0.17φλ f c′



0.53φλ f c′



2φλ f c′



0.17φλ f c′



0.53φλ f c′



2φλ f c′



0.33φλ f c′



1.1φλ f c′



4φλ f c′



f c′ ≤ 0.5 MPa



f c′ ≤ 8.3 MPa



f c′ ≤ 26.5 kgf/cm2



f c′ ≤ 100 psi



Section

12.2.2



⎛ fy ψt ψe ⎞

ld = ⎜ ----------------------⎟ d b

⎝ 2.1λ f c′ ⎠



⎛ fy ψt ψe ⎞

ld = ⎜ ---------------------⎟ d b

⎝ 6.6λ f c′ ⎠



⎛ fy ψt ψe ⎞

ld = ⎜ --------------------⎟ d b

⎝ 25λ f c′ ⎠



Section

12.2.2



⎛ fy ψt ψe ⎞

ld = ⎜ ----------------------⎟ d b

⎝ 1.7λ f c′ ⎠



⎛ fy ψt ψe ⎞

ld = ⎜ ---------------------⎟ d b

⎝ 5.3λ f c′ ⎠



⎛ fy ψt ψe ⎞

ld = ⎜ --------------------⎟ d b

⎝ 20λ f c′ ⎠



Section

12.2.2



⎛ fy ψt ψe ⎞

ld = ⎜ ----------------------⎟ d b

⎝ 1.4λ f c′ ⎠



⎛ fy ψt ψe ⎞

ld = ⎜ ---------------------⎟ d b

⎝ 4.4λ f c′ ⎠



⎛ 3f y ψ t ψ e⎞

ld = ⎜ ---------------------⎟ d b

⎝ 50λ f c′ ⎠



Section

12.2.2



⎛ fy ψt ψe ⎞

ld = ⎜ ----------------------⎟ d b

⎝ 1.1λ f c′ ⎠



⎛ fy ψt ψe ⎞

ld = ⎜ ---------------------⎟ d b

⎝ 3.5λ f c′ ⎠



⎛ 3f y ψ t ψ e⎞

ld = ⎜ ---------------------⎟ d b

⎝ 40λ f c′ ⎠



ACI 318 Building Code and Commentary



APPENDIX F



445



mks-metric stress

in kgf/cm2



SI-metric stress

in MPa



CODE



U.S. Customary units stress in

pounds per square inch (psi)



COMMENTARY

3f

ψψ



fy

ψt ψe ψs

ld = ---------------------- --------------------------d

b

1.1λ f c′ ⎛ c b + K tr⎞

-------------------⎝ d





fy

ψt ψe ψs

- db

ld = --------------------- -----------------------3.5λ f c′ ⎛ c b + K tr⎞

-⎠

⎝ -----------------d



Section

12.3.2



⎛ 0.24f y⎞

⎜ ----------------⎟ d b ≥ ( 0.043f y )d b

⎝ λ f c′ ⎠



⎛ 0.075f y⎞

⎜ -------------------⎟ d b ≥ ( 0.0044f y )d b

⎝ λ f c′ ⎠



⎛ 0.02f y⎞

⎜ ----------------⎟ d b ≥ ( 0.0003f y )d b

⎝ λ f c′ ⎠



Section

12.5.2



⎛ 0.24ψ e f y⎞

l dh = ⎜ -----------------------⎟ d b

⎝ λ f c′ ⎠



⎛ 0.075ψ e f y⎞

l dh = ⎜ -------------------------⎟ db

⎝ λ f c′ ⎠



⎛ 0.02ψ e f y⎞

l dh = ⎜ -----------------------⎟ d b

⎝ λ f c′ ⎠



Section

12.6.2



⎛ 0.19ψ e f y⎞

l dh = ⎜ -----------------------⎟ d b



f c′ ⎠



⎛ 0.06ψ e f y⎞

l dh = ⎜ ----------------------⎟ d b



f c′ ⎠



⎛ 0.016ψ e f y⎞

l dh = ⎜ -------------------------⎟ db





f c′



Section

12.7.2



y – 240⎞

⎛ f-------------------⎝ f





y – 2460⎞

⎛ f----------------------⎠



f

y



f y – 35, 000 ⎞

⎛ -------------------------------⎠



f



(12-3)



A ⎛ fy ⎞

l d = 3.3 ⎛ ------b-⎞ ⎜ ------------⎝ s ⎠ ⎝ λ f ′-⎟⎠



A ⎛ fy ⎞

l d = ⎛ ------b⎞ ⎜ ------------⎝ s ⎠ ⎝ λ f ′ ⎟⎠



A ⎛ fy ⎞

l d = 0.27 ⎛ ------b-⎞ ⎜ ------------⎝ s ⎠ ⎝ λ f ′-⎟⎠



(12-4)



f se⎞

f –f

d + ⎛ ps se⎞ d b

l d = ⎛ -----⎝ 21-⎠ b ⎝ --------------------⎠

7



f se ⎞

f –f

d + ⎛ ps se-⎞ d b

l d = ⎛ --------⎝ 210-⎠ b ⎝ ------------------70 ⎠



f se ⎞

f –f

d + ⎛ ps se⎞ d b

l d = ⎛ -----------⎝ 3000-⎠ b ⎝ --------------------1000 ⎠



Section

12.10.5.2



bw s

0.41 ---------f yt



bw s

4.2 --------f yt



bw s

60 ---------f yt



Section

12.13.2.2



d b fyt

0.17 ------------λ f c′



d b fyt

0.053------------λ f c′



d b fyt

0.014 ------------λ f c′



Section

12.16.1



0.071fydb

(0.13fy – 24)db



0.0073fydb

(0.013fy – 24)db



0.0005fydb

(0.0009fy – 24)db



0.55bvd



5.6bvd



80bvd



(1.8 + 0.6ρv fy )λ bvd ≤ 3.5bv d



(18 + 0.6ρv fy )λ bvd ≤ 35bv d



(260 + 0.6ρv fy )λ bvd ≤ 500bv d



(12-1)



b



y



c



Section

17.5.3.1

and

17.5.3.2

Section

17.5.3.3



Section

18.3.3



b



y

t e ψs

ld = -------------------- --------------------------d

b

40λ f c′ ⎛ c b + K tr⎞

-------------------⎝ d



b



y



c



c



(a) Class U : ft ≤ 0.62 f c′



(a) Class U : ft ≤ 2 f c′



(a) Class U : ft ≤ 7.5 f c′



(b) Class T : 0.62 f c′ < ft ≤ 1.0 f c′



(b) Class T : 2 f c′ < ft ≤ 3.2 f c′



(b) Class T : 7.5 f c′ < ft ≤ 12 f c′



(c) Class C : ft > 1.0 f c′



(c) Class C : ft > 3.2 f c′



(c) Class C : ft > 12 f c′



ft ≤ 0.50 f ci





ft ≤ 1.6 f ci′



0.50 f ci





1.6 f ci′



6 f ci







0.25 f ci



0.8 f ci′





3 f ci



(18-4)



f c′

fps = fse + 70 + --------------100ρ p



f c′

fps = fse + 700 + --------------100ρ p



f c′

fps = fse + 10,000 + --------------100ρ p



(18-5)



f c′

fps = fse + 70 + --------------300ρ p



f c′

fps = fse + 700 + --------------300ρ p



f c′

fps = fse + 10,000 + --------------300ρ p



Section

18.9.3.1

and

18.9.3.2



0.17 f c′



0.53 f c′



2 f c′



Section

18.4.1(c)



ft ≤ 6 f ci





F



ACI 318 Building Code and Commentary



446



APPENDIX F



CODE

SI-metric stress

in MPa



mks-metric stress

in kgf/cm2



U.S. Customary units stress in

pounds per square inch (psi)



Section

18.12.7



2.1b w d

-------------------fy



21b w d

----------------fy



300b w d

--------------------fy



Section

18.13.4.1

Section

19.4.10



fps = fse + 70



fps = fse + 700



fps = fse + 10,000



0.33φλ f c′



1.1φλ f c′



4φλ f c′



Section

21.5.2.1



1.4b w d

-------------------fy



14b w d

----------------fy



200b w d

--------------------fy



(21-2)



350 – h

so = 100 ⎛ ---------------------x-⎞





3



35 – h

so = 10 ⎛ -----------------x-⎞

⎝ 3 ⎠



14 – h

so = 4 ⎛ ------------------x-⎞

⎝ 3 ⎠



100 mm ≤ so ≤ 150 mm



10 cm ≤ so ≤ 15 cm



4 in. ≤ so ≤ 6 in.



1.7 f c′ Aj



5.3 f c′ Aj



20 f c′ Aj



1.2 f c′ Aj



4 f c′ Aj



15 f c′ Aj



1.0 f c′ Aj



3.2 f c′ Aj



12 f c′ Aj



fy db

ldh = -----------------5.4 f c′



fy db

ldh = --------------------17.2 f c′



fy db

ldh = ----------------65 f c′



0.083Acvλ f c′



0.27Acvλ f c′



Acvλ f c′



0.17Acvλ f c′



0.53Acvλ f c′



2Acvλ f c′



Section

21.7.4.1



(21-6)

Section

21.9.2.1

Section

21.9.2.2



(21-7)



Section

21.9.4.4

Section

21.9.4.5

Section

21.9.6.5(a)

Section

21.9.6.5(b)

Section

21.9.7.2



F



COMMENTARY



Vn = Acv(αcλ f c′ + ρt fy)



Vn = Acv(αcλ f c′ + ρ t fy)



Vn = Acv(αcλ f c′ + ρt fy)



hw

αc = 0.25 for ------ ≤ 1.5

lw



hw

αc = 0.80 for -----≤ 1.5

lw



hw

αc = 3.0 for ------ ≤ 1.5

lw



hw

αc = 0.17 for ------ ≥ 2.0

lw



hw

αc = 0.53 for -----≥ 2.0

lw



hw

αc = 2.0 for ------ ≥ 2.0

lw



0.66 Acv f c′



2.12 Acv f c′



8 Acv f c′



0.83 Acw f c′



2.65 Acw f c′



10 Acw f c′



0.83 Acw f c′



2.65 Acw f c′



10 Acw f c′



28/f y



2.8/f y



400/f y



0.083 Acvλ f c′



0.27 Acvλ f c′



Acvλ f c′



0.33 λ f c′ Acw



λ f c′ Acw



4 λ f c′ Acw



(21-9)



Vn = 2Avd fy sinα ≤ 0.83 f c′ Acw



Vn = 2Avd fy sinα ≤ 2.65 f c′ Acw



Vn = 2Avd fy sinα ≤ 10 f c′ Acw



(21-10)



Vn = Acv ( 0.17λ f c′ + ρt fy )



Vn = Acv ( 0.53λ f c′ + ρ t fy )



Vn = Acv ( 2λ f c′ + ρt fy )



Section

21.11.9.2

Section

21.13.6



0.66Acv f c′



2.12Acv f c′



8Acv f c′



0.29 f c′ bo d



0.93 f c′ bo d



3.5 f c′ bo d



(22-2)



Mn = 0.42λ f c′ Sm



Mn = 1.33λ f c′ Sm



Mn = 5λ f c′ Sm



ACI 318 Building Code and Commentary



APPENDIX F



447



CODE



COMMENTARY



SI-metric stress

in MPa



mks-metric stress

in kgf/cm2



U.S. Customary units stress in

pounds per square inch (psi)



(22-7)



M

P

-------u- – ------u- ≤ φ0.42λ f c′

Sm Ag



P

M

-------u- – ------u ≤ φ1.33λ f c′

Sm Ag



M

P

-------u- – ------u- ≤ φ5λ f c′

Sm Ag



(22-9)



Vn = 0.11λ f c′ bw h



Vn = 0.35λ f c′ bw h



4λ f c′

Vn = ----------------- bw h

3



2

V n = 0.11 1 + --- λ f c′ b o h

β



V n = 0.35 1 + 2

--- λ f c′ b o h

β



(22-10)



≤ 0.22 λ f c′ b o h

(B-1)



≤ 0.71 λ f c′ b o h



0.85β 1 fc′ ⎛ 600 ⎞

ρ b = ------------------------ --------------------⎝ 600 + f ⎠

fy

y

1.5



(D-7)



1.5



Nb = kcλ f c′ hef



Nb = kcλ f c′ hef



kc = 10 or 7

(D-8)



Nb = 3.9λ



0.85β 1 fc′ ⎛ 6120 ⎞

ρ b = ----------------------- -----------------------⎝ 6120 + f ⎠

fy

y



kc = 10 or 7



5/3

fc′ hef



Nb = 5.8λ



5/3

fc′ hef



4 8

--- + ------ λ f c′ b o h

3 3β



Vn =



≤ 2.66 λ f c′ b o h

0.85β 1 fc′ ⎛ 87, 000 ⎞

ρ b = ------------------------ ------------------------------⎝ 87, 000 + f ⎠

fy

y

1.5



Nb = kcλ f c′ hef

kc = 24 or 17



5/3



Nb = 16λ fc′ hef



(D-17)



Nsb = 13ca1 A brg λ fc′



Nsb = 42.5ca1 A brg λ fc′



Nsb = 160ca1 A brg λ fc′



(D-24)



l 0.2

1.5

d a λ fc′ ( c a1 )

Vb = 0.6 ⎛ -----e-⎞

⎝d ⎠



l e ⎞ 0.2

1.5

Vb = 1.9 ⎛ ----d a λ fc′ ( c a1 )

⎝d ⎠



l 0.2

1.5

Vb = 7 ⎛ -----e-⎞

d a λ fc′ ( c a1 )

⎝d ⎠



l 0.2

1.5

Vb = 0.66 ⎛ -----e-⎞

d a λ fc′ ( c a1 )

⎝d ⎠



l e ⎞ 0.2

1.5

Vb = 2.1 ⎛ ----d a λ fc′ ( c a1 )

⎝d ⎠



l 0.2

1.5

Vb = 8 ⎛ -----e-⎞

d a λ fc′ ( c a1 )

⎝d ⎠



a



(D-25)



a



a



a



a



a



F



ACI 318 Building Code and Commentary



448



APPENDIX F



CODE



COMMENTARY



F



ACI 318 Building Code and Commentary



REFERENCES



449



COMMENTARY REFERENCES

References, Chapter 1



1.16. “Building Construction and Safety Code—NFPA 5000,”

National Fire Protection Association, Quincy, MA, 2006.



1.1. ACI Committee 332, “Requirements for Residential Concrete

Construction (ACI 332-04) and Commentary,” American Concrete

Institute, Farmington Hills, MI, 2004, 26 pp.

1.2. ACI Committee 307, “Design and Construction of Reinforced

Concrete Chimneys (ACI 307-98),” American Concrete Institute,

Farmington Hills, MI, 1998, 18 pp.

1.3. ACI Committee 313, “Standard Practice for Design and

Construction of Concrete Silos and Stacking Tubes for Storing

Granular Materials (ACI 313-97),” American Concrete Institute,

Farmington Hills, MI, 1997, 19 pp.



1.17. “The BOCA National Building Code, 13th Edition,”

Building Officials and Code Administration International, Inc.,

Country Club Hills, IL, 1996, 357 pp.

1.18. “Standard Building Code,” Southern Building Code

Congress International, Inc., Birmingham, AL, 1996, 656 pp.

1.19. Uniform Building Code, V. 2, Structural Engineering Design

Provisions, 1997 Edition, International Conference of Building

Officials, Whittier, CA, 1997, 492 pp.



1.4. ACI Committee 349, “Code Requirements for Nuclear SafetyRelated Concrete Structures (ACI 349-06) and Commentary,”

American Concrete Institute, Farmington Hills, MI, 2006, 153 pp.



1.20. “NEHRP Recommended Provisions for Seismic Regulations

for New Buildings and Other Structures,” Part 1: Provisions, and

Part 2: Commentary (FEMA 450), Building Seismic Safety

Council, Washington D.C., 2004.



1.5. Joint ACI-ASME Committee 359, “Code for Concrete

Containments (ACI 359-01),” American Concrete Institute, Farmington Hills, MI, 2001.



1.21. ACI Committee 350, “Code Requirements for Environmental

Engineering Concrete Structures (ACI 350-06) and Commentary,”

American Concrete Institute, Farmington Hills, MI, 2006, 486 pp.



1.6. ACI Committee 543, “Design, Manufacture, and Installation

of Concrete Piles (ACI 543R-00) (Reapproved 2005),” American

Concrete Institute, Farmington Hills, MI, 2000, 49 pp.



1.22. ACI Committee 311, “Guide for Concrete Inspection (ACI

311.4R-05),” American Concrete Institute, Farmington Hills, MI,

2005, 13 pp.



1.7. ACI Committee 336, “Design and Construction of Drilled

Piers (ACI 336.3R-93) (Reapproved 1998),” American Concrete

Institute, Farmington Hills, MI, 1993, 30 pp.



1.23. ACI Committee 311, ACI Manual of Concrete Inspection,

SP-2, 9th Edition, American Concrete Institute, Farmington Hills,

MI, 1999, 209 pp.



1.8. “Recommended Practice for Design, Manufacture, and Installation of Prestressed Concrete Piling,” PCI Journal, V. 38, No. 2,

Mar.-Apr. 1993, pp. 14-41.



References, Chapter 3



1.9. ACI Committee 360, “Design of Slabs-on Ground (ACI 360R06),” American Concrete Institute, Farmington Hills, MI, 2006, 74 pp.

1.10. PTI, “Design of Post-Tensioned Slabs-on-Ground,” 3rd

Edition, Post-Tensioning Institute, Phoenix, AZ, 2004, 106 pp.

1.11. ANSI/ASCE 3-91, “Standard for the Structural Design of

Composite Slabs,” ASCE, Reston, VA, 1994.

1.12. ANSI/ASCE 9-91, “Standard Practice for the Construction

and Inspection of Composite Slabs,” American Society of Civil

Engineers, Reston, VA, 1994.

1.13. “Design Manual for Composite Decks, Form Decks and Roof

Decks,” Publication No. 30, Steel Deck Institute, Fox River Grove,

IL, 2000, 48 pp.

1.14. “Minimum Design Loads for Buildings and Other Structures

(ASCE/SEI 7-05),” ASCE, Reston, VA, 2005.

1.15. “International Building Code,” International Code Council,

Falls Church, VA, 2006.



3.1. ACI Committee 214, “Evaluation of Strength Test Results of

Concrete (ACI 214R-02),” American Concrete Institute, Farmington Hills, MI, 2002, 20 pp.

3.2 ACI Committee 440, “Guide for the Design and Construction

of Structural Concrete Reinforced with FRP Bars (ACI 440.1R-06),”

American Concrete Institute, Farmington Hills, MI, 44 pp.

3.3 ACI Committee 440, “Guide for the Design and Construction

of Externally Bonded FRP Systems for Strengthening of Concrete

Structures (ACI 440.2R-02),” American Concrete Institute, Farmington Hills, MI, 45 pp.

3.4. Gustafson, D. P., and Felder, A. L., “Questions and Answers

on ASTM A 706 Reinforcing Bars,” Concrete International, V. 13,

No. 7, July 1991, pp. 54-57.

3.5. Rutledge, S., and DeVries, R. A., “Development of D45

Wire in Concrete,” Report, School of Civil and Environmental

Engineering, Oklahoma State University, Stillwater, OK, Jan.

2002, 28 pp.

3.6. Parra-Montesinos, G. J., “Shear Strength of Beams with

Deformed Steel Fibers,” Concrete International, V. 28, No. 11,

Nov. 2006, pp. 57-66.



ACI 318 Building Code and Commentary



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