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6. September. 2017 2017 KEPIC-Week Experimental study on design code revision of headed bar Choi, Chang-Sik Hanyang University Chun, Sung-Chul Inchun National University Lee, Byung-Soo KHNP-CRI

Experimental study on design code revision of headed bar bar details for development for standard hooks ... ACI 318-08 12.6 – Development of headed and mechanically anchored deformed

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6. September. 2017

2017 KEPIC-Week

Experimental study on design code revision of headed bar

Choi, Chang-Sik Hanyang University

Chun, Sung-Chul Inchun National University

Lee, Byung-Soo KHNP-CRI

2/31

• Dense and Excessive reinforcement

Extension of the construction period /

Difficulty of reinforcement placing

• Using the Large diameter rebar (#14, #18)

Need the excessive hooked length /

Difficulty to secure the development length

#8 (db = 25mm)

#11 (db = 35mm)

#18 (db = 57mm)

Characteristic of Nuclear Power Plant

Headed Bars

High Strength

Large Diameter

Need the Headed Bars

Lungmen nuclear power plant (Taiwan, 2003)

• To shorten the development length

• To solve the dense reinforcement

• To be easy with reinforcement placing

3/31

Straight bars

Hooked bars

• Bearing (hook) + Bond (deformed bar)

• Development length is shorter than straight anchorage

• Congestion is created in the member joint

Headed Bars

𝒍𝒅𝒉 = 𝟎. 𝟏𝟗𝒇𝒚

𝒇𝒄′𝒅𝒃 ; 𝟗𝟏𝟗𝐦𝐦

𝒍𝒉𝒃 = 𝟎. 𝟐𝟒𝒇𝒚

𝒇𝒄′𝒅𝒃 ; 𝟏𝟏𝟔𝟏𝐦𝐦

• Anchorage capacity is satisfied by bearing force of rib

• Have the longer development length than other anchorage method

• Arrangement of required development length is difficult in the members

• Bearing (Head) + Bond (deformed bar)

• Development length is 80% of hook anchorage (ACI 318-08)

• Resolve the steel congestion

• Simplification of arrangement of bars

#11, 35mm

#14, 43mm

#18, 57mm

Nuclear Structures – Dense arrangement of reinforcement

Large diameter bar : the more mechanical anchorage is required

Hooked bar details for development for standard hooks

Necessity of Headed Bars

𝒍𝒅 = 𝟎. 𝟗𝒇𝒚𝒅𝒃

𝒇𝒄′

𝜶𝜷𝜸

𝒄 + 𝑲𝒕𝒓𝒅𝒃

; 𝟐𝟏𝟕𝟕𝐦𝐦

𝒇𝒚 = 𝟓𝟓𝟎𝑴𝑷𝒂, 𝒇′𝒄 = 𝟒𝟐𝑴𝑷𝒂, 𝒅𝒃 = 𝟓𝟕𝒎𝒎

𝒍𝒂 = 𝟏𝟐𝒅𝒃 ; 𝟔𝟖𝟒𝐦𝐦

4/31

Design codes of Mechanical anchorage

Need to verify for test or to use with design of anchor

- AASHTO LRFD Bridge Design Specifications - Australian Standard - New Zealand Standard - Canadian Standard - Eurocode 2 - fib Model Code 2010 Draft

Other design codes

Current design codes associated with Nuclear power plants

ASME III 2-10 ACI 349-06 ACI 318-08

Status

Problem

Absence of specific design equation

Difficult to determine the development

length

Need the design method of anchor

80% of hooked bar

Conservative design/ Excessive development

length

Limitation of diameter Not applicable design of nuclear

power plant

ACI 318-08

12.6 – Development of headed and mechanically anchored deformed bars in tension 12.6.1 - Development length for headed deformed bars in tension, ldt, shall be determined from 12.6.2. Use of heads to develop deformed bars in tension shall be limited to conditions satisfying (a) through (f):

(a) Bar fy shall not exceed 420 MPa; (b) Bar size shall not exceed 35 mm (f) Clear spacing between bars shall not be less than 4db. fc’ used to calculate ldt shall not exceed 42 MPa

0.19'

ydh b

c

fl d

f

Application with

Mechanical anchorage in nuclear

power plants

Problem 1. Absence of specific design codes and

Limitation of design code

420MPa, 42MPay cf f

35mm, 4b c bd s d

Problem 2. Increase of the development length of mechanical anchorage for large diameter and high strength steel

0.19'

ydh b

c

fl d

f

550MPayf 43mmbd

Need the study • The evaluation of

mechanical anchorage with large diameter

• The development of specific design code of mechanical anchorage

5/31

Research Objective of Headed Bars

· Bar Yield Strength

Gr. 60 (420MPa)

→ Gr. 80 (550MPa)

· Bar diameter

#11 (36mm) → #18 (57mm)

· Effects of transverse reinforcement

No consideration → O

(a) fy ≤ 60,000 psi (420 MPa)

(b) db ≤ #11 (36mm)

(c) fc ’≤ 6000 psi (42 MPa)

(d) Normal-weight concrete

(e) Net bearing area of head Abrg ≥ 4Ab

(f) Clear cover ≥ 2db

(g) Clear spacing ≥ 4db

(h) No consideration on transverse

reinforcement

Objective

Some Limitations of current provisions

6/31

Test Program

• Three tests were planned: Joint test, splice test, and TTC node test

• Joint test: Simulating joints where headed bars are expected to be frequently applied.

• Splice test: Most commonly used test. Expecting very conservative results.

• TTC node test: Simulating a development. (cut-off bars)

P1 P2

• Joint test • TTC node test

• Exterior beam-column Joint test

under cyclic load

• Splice test

7/31

Test setup

Reaction frame

Hydraulic rams

Imaginary

beam

Front view Side view

Joint

8/31

Specimens

• Variables:

- Bars diameter: #14(43mm), #18(57mm)

- Side cover: 1db, 2db

- Embedment length: 7db, 10db, 13db, 16db

- Transverse reinforcement: Ktr = 0.5db, 1.0db

• Longitudinal re-bars of the member were placed between the headed bars to eliminate the confining effects

from the longitudinal re-bars.

• Transverse re-bars parallel to the headed bars were also placed between the headed bars.

Specimens: 27 tests

300

3,032

912

1,0

00

300 912608

41

5

70

0cso = 1db cso = 2db

Unconfined Confined

9/31

• All headed bars anchored in 23 specimens showed side-face blowout failure.

• The first crack initiated at the face of the member due to bond loss. The cracks then propagated toward

the head.

• When the load reached a maximum value, the cover concrete suddenly spalled.

Failure mode

• Even though some diagonal cracks seemed to form a conical-shaped failure, the main failure mode was a

side-face blowout.

10/31

0

100

200

300

400

500

600

0 100 200 300 400 500 600

• The early rise in the bond component shows that the bar force was initially transferred to the concrete

primarily by the bond.

• The bond reached its peak capacity and began to decline and the head bearing component rose rapidly.

• The maximum capacity of the headed bar was provided by peak head bearing plus reduced bond.

Bond and head bearing contributions

Bar

str

ess

from

hea

d b

eari

ng o

r bond (

MP

a)

Total bar stress (MPa)

bond

#18-L16-C1

head bearing

Max. anchorage strength

A

B

C

bond

loss A

B

C

11/31

0

30

60

90

120

0 10 20 30

#14

#18

Bashandy(#8,#11)

ACI318 headed bars

ACI318 hooked bars0

30

60

90

120

0 10 20 30

#18

#14

Bashandy(#8,#11)

ACI318 headed bars

ACI318 hooked bars

• As the side cover, the embedment depth, and the transverse reinforcement index increased, the

anchorage capacities increased. Among the variables, the side cover is the most effect because the

failure mode was a side-face blowout.

ls/db

f s/√

f c’

Anchorage capacity (1/2)

side cover = 2db

0.014 y

dt b

c

fl d

f

Bar yielded

300

600

900

1200

30

60

90

0.17 y

dt b

c

fl d

f

[psi

]

f s/√

f c’

[MP

a]

[US-customary unit] [SI unit]

ls/db

side cover = 1db

0.24 y

dt b

c

fl d

f

f s/√

f c’

300

600

900

1200

30

60

90

[psi

]

f s/√

f c’

[MP

a]

[US-customary unit] [SI unit]

0.020 y

dt b

c

fl d

f

12/31

0

30

60

90

120

0 10 20 30

#18(confined)

#18(unconfined)

#14(confined)

#14(unconfined)

ACI318 headed bars

ACI318 hooked bars

ls/db

Confined headed bars

0.15 y

dt b

c

fl d

f

#18 Headed bar

Transverse

reinforcing

bars

Anchorage capacity (2/2)

33%

f s/√

f c’

0.012 y

dt b

c

fl d

f

300

600

900

1200

30

60

90

[psi

]

f s/√

f c’

[MP

a]

[US-customary unit] [SI unit]

13%

• Transverse reinforcement of a hair-pin type could increase the anchorage strength by 27% on average.

13/31

Test setup

14/31

Specimens

Specimens: 37 tests

• Variables:

- Bars diameter: #8(25mm), #9(29mm), #14(43mm), #18(57mm)

- Clear spacing: 2db, 3db , 4db

- Side cover: 1db, 2db, 3db , 4db

- Splice length: 12db, ~ 30db

- Transverse reinforcement: Ktr = 0.5db ~ 2.5db

200 1,600 2001,600

630 630

2,400

1,140

6,000

6,000

200 1,600 2001,600

630 630

2,400

1,140

D13 stirrup @ 200

D13 stirrup @ 200 D13 confinement @ 140

15/31

Specimens

Specimens: 37 tests

• Variables:

- Bars diameter: #8(25mm), #9(29mm), #14(43mm), #18(57mm)

- Clear spacing: 2db, 3db , 4db

- Side cover: 1db, 2db, 3db , 4db

- Splice length: 12db, ~ 30db

- Transverse reinforcement: Ktr = 0.5db ~ 2.5db

200 1,600 2001,600

630 630

2,400

1,140

6,000

6,000

200 1,600 2001,600

630 630

2,400

1,140

D13 stirrup @ 200

D13 stirrup @ 200 D13 confinement @ 140

16/31

Failure mode

Unconfined Confined

Splitting failures by

• Prying action due to flexural deformation

• Circumferential tensile stresses due to head bearing force

• Circumferential tensile stresses due to bond along lap length

17/31

Bond and head bearing contributions

0

100

200

300

400

500

600

0 100 200 300 400 500 600

• As the transverse reinforcement index increased, the bond and head bearing capacities increased.

• When the bond reached the peak capacity, the bottom cover immediately spalled and the head bearing

lost its capacity, too.

Bar

str

ess

from

hea

d b

eari

ng o

r bond (

MP

a)

Total bar stress (MPa)

bond

#18-L20

#18-L20-Con.

#18-L20-Con.2

head bearing

18/31

Test setup

P1 P2ldt

Inflection

Point

Critical

Section

TTC Node

Moment

Shear

Test Setup Test Concept

19/31

Specimens

Specimens: 16 tests

• Variables:

- Bars diameter: #14(43mm), #18(57mm)

- Clear spacing: 2db, 3db , 4db

- Side cover: 2db, 4db

- Splice length: 12db, ~ 28db

- Transverse reinforcement: Ktr = 1.0db ~ 2.0db

1300280 280

108

270

143

520

143171143

456

855

4460

1300 1300

20/31

Specimens

Specimens: 16 tests

• Variables:

- Bars diameter: #14(43mm), #18(57mm)

- Clear spacing: 2db, 3db , 4db

- Side cover: 2db, 4db

- Splice length: 12db, ~ 28db

- Transverse reinforcement: Ktr = 1.0db ~ 2.0db

143171143

456

855

4460

1300 13001300280 280

108

270

143

520

21/31

Failure mode

Unconfined Confined

• All specimens failed by splitting.

• In unconfined specimen, inclined cracks occurred around the head and splitting failure occurred

immediately.

• In confined specimen, after inclined cracks occurred around the head, splitting failure gradually

occurred with maintaining the load.

① ②

22/31

Splice & TTC node test: Anchorage capcity

ls/db

Unconfined, cmin ≥ 2db

0.4 y

dt b

c

fl d

f

• Clear spacing and transverse reinforcement are effective variables.

• Unconfined headed bars had very low strengths.

• Confined headed bars with Ktr of 1.2db had almost same strength as the hooked bars have.

0

30

60

90

120

0 10 20 30

#8,#9

#14,#18

ACI318 headed bars

ACI318 hooked bars

f s/√

f c’

0.033 y

dt b

c

fl d

f

300

600

900

1200

30

60

90

[psi

]

f s/√

f c’

[MP

a]

[US-customary unit] [SI unit]

ls/db

Confined, Ktr ≥ 1.2db

0

30

60

90

120

0 10 20 30

#8,#9

#14,#18

ACI318 headed bars

ACI318 hooked bars

f s/√

f c’

0.019 y

dt b

c

fl d

f

300

600

900

1200

30

60

90

[psi

]

f s/√

f c’

[MP

a]

[US-customary unit] [SI unit]

0.23 y

dt b

c

fl d

f

23/31

Test setup

24/31

Specimens

25/31

Detail of Specimens

Relation between beam moment versus drift

850

970

Cs=57

685

970

ldt=855

ldt = 15db

Cs = 1db

Failure Mode

Side-face blowout

Plan

Section

Cs=57

685

970

ldt=855

Beam yield

U type transverse re-bars

Failure modes Anchorage capacity

-8 -6 -4 -2 0 2 4 6 8

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

Be

am

Mo

me

nt

[kN

-m]

Drift Ratio [%]

Mn = 1438 kN.m

Displacement [mm]

Mn = -1438 kN.m

M /

Mn

-320 -240 -160 -80 0 80 160 240 320

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

First yield of rebar (1,[email protected]%)

Peak moment (1,[email protected]%)

Brittle failure

Nominal moment (1,438kN.m)

Nominal moment (-1,438kN.m)

Max drift (2.0%)

-8 -6 -4 -2 0 2 4 6 8

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

Be

am

Mo

me

nt

[kN

-m]

Drift Ratio [%]

Mn = 1438 kN.m

Mn = -1438 kN.m

-320 -240 -160 -80 0 80 160 240 320

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

M /

Mn

Displacement [mm]

Ductile failure

First yield of rebar (1,[email protected]%)

Peak moment (1,[email protected]%)

Nominal moment (-1,438kN.m)

Max drift (4.0%)

Nominal moment (1,438kN.m)

0

100

200

300

400

500

600

700

0 1 2 3 4

Bar

te

nsi

le s

tre

ss [

MP

a]

Drift [%]

Bearing

Anchrage

EJ-T1-L15-S1

0

100

200

300

400

500

600

700

0 1 2 3 4

Bar

te

nsi

le s

tre

ss [

MP

a]

Drift [%]

Bearing

Anchrage

EJ-T1-L15-S1-T

26/31

-8 -6 -4 -2 0 2 4 6 8

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

Be

am

Mo

me

nt

[kN

-m]

Drift Ratio [%]

-320 -240 -160 -80 0 80 160 240 320

-1.0

-0.5

0.0

0.5

1.0

Displacement [mm]

M /

Mn

Mn = 2033 kN.m

Mn = -2033 kN.m

-8 -6 -4 -2 0 2 4 6 8

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

Be

am

Mo

me

nt

[kN

-m]

Drift Ratio [%]

Mn = 1438 kN.m

Displacement [mm]

Mn = -1438 kN.m

M /

Mn

-320 -240 -160 -80 0 80 160 240 320

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Detail of Specimens

Relation between beam moment versus drift

850

970

ldt = 15db

Cs = 2db

Failure Mode

Beam yield

Plan

Section Joint shear

First yield of rebar (1,[email protected]%)

Peak moment (1,[email protected]%)

Nominal moment (1,438kN.m)

First yield of rebar (2,[email protected]%)

Peak moment (2,391kN.m @2.0%)

Nominal moment (2,033kN.m)

Nominal moment (-2,033kN.m)

Nominal moment (-1,438kN.m)

Anchorage capacity

Cs=114

ldt=855

800

970

Cs=114

ldt=855

800

970

Max drift (4.0%)

Max drift (3.0%)

0

100

200

300

400

500

600

700

0 1 2 3 4

Bar

te

nsi

le s

tre

ss [

MP

a]

Drift [%]

Bearing

Anchrage

EJ-T1-L15-S2

0

100

200

300

400

500

600

700

0 1 2 3 4

Bar

te

nsi

le s

tre

ss [

MP

a]

Drift [%]

Bearing

Anchrage

EJ-T1-L15-S2-J

Failure modes

27/31

Detail of Specimens

Relation between beam moment versus drift

Anchorage capacity

-8 -6 -4 -2 0 2 4 6 8

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

Be

am

Mo

me

nt

[kN

-m]

Drift Ratio [%]

Mn = 1438 kN.m

Displacement [mm]

Mn = -1438 kN.m

M /

Mn

-280 -210 -140 -70 0 70 140 210 280

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

First yield of rebar (1,[email protected]%)

Peak moment (1,[email protected]%) Nominal moment

(1,438kN.m)

Nominal moment (-1,438kN.m)

Max drift (7.0%)

-8 -6 -4 -2 0 2 4 6 8

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

Be

am

Mo

me

nt

[kN

-m]

Drift Ratio [%]

Mn = 1438 kN.m

Displacement [mm]

Mn = -1438 kN.m

M /

Mn

-280 -210 -140 -70 0 70 140 210 280

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

First yield of rebar (1,[email protected]%)

Peak moment (1,[email protected]%)

Nominal moment (1,438kN.m)

Nominal moment (-1,438kN.m)

Max drift (6.0%)

ldt = 15db

Details

Headed bar Hooked bar

ldh = 20db

1140(ldh=20db)

1255

850850

970

855(ldt=15db)

Plan

0

100

200

300

400

500

600

700

0 1 2 3 4

Bar

te

nsi

le s

tre

ss [

MP

a]

Drift [%]

Bearing

Anchrage

EJ-T2-L15-S2

0

100

200

300

400

500

600

700

0 1 2 3 4

Bar

te

nsi

le s

tre

ss [

MP

a]

Drift [%]

Bearing

Anchrage

EJ-T2-L20-S2-H

Failure modes

28/31

-8 -6 -4 -2 0 2 4 6 8

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

Be

am

Mo

me

nt

[kN

-m]

Drift Ratio [%]

Mn = 1438 kN.m

Displacement [mm]

Mn = -1438 kN.m

M /

Mn

-280 -210 -140 -70 0 70 140 210 280

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

-8 -6 -4 -2 0 2 4 6 8

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

Be

am

Mo

me

nt

[kN

-m]

Drift Ratio [%]

Mn = 1438 kN.m

Displacement [mm]

Mn = -1438 kN.m

M /

Mn

-280 -210 -140 -70 0 70 140 210 280

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Detail of Specimens

Relation between beam moment versus drift

First yield of rebar (1,[email protected]%)

Peak moment (1,[email protected]%)

Nominal moment (1,438kN.m)

First yield of rebar ([email protected]%)

Peak moment (1,[email protected]%)

Nominal moment (1,438kN.m)

Nominal moment (-1,438kN.m)

Nominal moment (-1,438kN.m)

Anchorage capacity

Max drift (7.0%)

Max drift (7.0%)

Details

Headed bar Headed bar

Plan

479

860

850

685(ldt=13db)

ldt = 15db

fck = 42MPa

ldt = 13db

fck = 70MPa

850

970

855(ldt=15db)

0

100

200

300

400

500

600

700

0 1 2 3 4

Bar

te

nsi

le s

tre

ss [

MP

a]

Drift [%]

Bearing

Anchrage

EJ-T2-L15-S2

0

100

200

300

400

500

600

700

0 1 2 3 4

Bar

te

nsi

le s

tre

ss [

MP

a]

Drift [%]

Bearing

Anchrage

EJ-T2-L13-S2-C

Failure modes

29/31

-8 -6 -4 -2 0 2 4 6 8

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

Be

am

Mo

me

nt

[kN

-m]

Drift Ratio [%]

Mn = 1438 kN.m

Mn = -1438 kN.m

-280 -210 -140 -70 0 70 140 210 280

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Displacement [mm]

M /

Mn

-8 -6 -4 -2 0 2 4 6 8

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

Be

am

Mo

me

nt

[kN

-m]

Drift Ratio [%]

Mn = 1438 kN.m

Displacement [mm]

Mn = -1438 kN.m

M /

Mn

-280 -210 -140 -70 0 70 140 210 280

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Detail of Specimens

Relation between beam moment versus drift

First yield of rebar (1,[email protected]%)

Peak moment (1,[email protected]%)

Nominal moment (1,438kN.m)

First yield of rebar (1,[email protected]%)

Peak moment (1,[email protected]%)

Nominal moment (1,438kN.m)

Nominal moment (-1,438kN.m)

Nominal moment (-1,438kN.m)

Failure modes Anchorage capacity

Max drift (7.0%)

Max drift (7.0%)

970

800

855(ldt=15db)

ldt = 15db

Cso1 = 2.0db

Cso2 = 2.0db

Details

Centric Eccentric

Section

ldt = 15db

Cso1 = 2.5db

Cso2 = 1.5db

800

855(ldt=15db)

970

0

100

200

300

400

500

600

700

0 1 2 3 4

Bar

te

nsi

le s

tre

ss [

MP

a]

Drift [%]

Bearing

Anchrage

EJ-T2-L15-S1.5-E

0

100

200

300

400

500

600

700

0 1 2 3 4

Bar

te

nsi

le s

tre

ss [

MP

a]

Drift [%]

Bearing

Anchrage

EJ-T2-L15-S2

30/31

Bond and bearing contributions

0

100

200

300

400

500

600

0 100 200 300 400 500 600

Bar

be

arin

g o

r b

on

d [

MP

a]

Total bar stress [MPa]

Bearing

Bond

EJ-T1-L15-S1

0

100

200

300

400

500

600

0 100 200 300 400 500 600

Bar

be

arin

g o

r b

on

d [

MP

a]

Total bar stress [MPa]

Bearing

Bond

EJ-T1-L15-S1-T

A A’ Section

Plan

850

970

ldt = 15db

Cs = 1db

Failure Mode

Plan

Section

Cs=57

685

970

ldt=855

Beam yield

U type transverse

reinforcement

(B) U type transverse reinforcement of CCT Nodes test. Chun et al (2013).

(A) U type transverse reinforcement of this study

(A) (B)

Peak point of bond

Peak point of bond

(Unconfined)

(Confined) Both of specimens showed that the anchorage

strength approached the yield strength of headed bar.

Confined specimen had higher bond strength than

unconfined specimen.

The reason may be that transverse reinforcement can

suppress the splitting crack generated by the bond

stress and delay the bond stress loss near the yield

strength of headed bar.

31/31

Application TTC nodes – Cut off zone CCT nodes – Ext. B-C Joints

Failure mode

Splitting failure Side-face blowout failure

Main parameter • Development length • Transverse reinforcement

• Side cover thickness • Transverse reinforcement

Resisting components

Bond > Head bearing Bond < Head bearing

Unconfined (Cmin ≥ 2.0db) (Cmin ≥ 1.0db)

Confined (Ktr ≥ 1.2db) (Ktr ≥ 1.0db)

𝑙𝑑𝑡 = 0.40 𝑓𝑦

𝑓𝑐′ 𝑑𝑏

𝑙𝑑𝑡 = 0.23 𝑓𝑦

𝑓𝑐′ 𝑑𝑏

𝑙𝑑𝑡 = 0.20 𝑓𝑦

𝑓𝑐′ 𝑑𝑏

𝑙𝑑𝑡 = 0.17 𝑓𝑦

𝑓𝑐′ 𝑑𝑏

Thank you