Two-Way Post-Tensioned Slab Design

(Example: Hand Calculations)

2016

សចត ីលែ លែងំ ងំណគុ ណគុណ រោោញចោ ោ ់  ិកកំ កកំ ិ  ិថ ថ ក់   ិ ិា រ រកុម ម ើ្ ្ ំ   មលំ ំណ ណ ណ ំ  ករូ ករូ ករូ  ង ង ់រៀ រៀ ផត់ ជ ់  ំ ំន ន អៗ  ិ ិ ក៏ផត ផត់ ់ ជំ ិ ិ ឺ  ឺ ង ង ផ    ើ ើៅន ៅន ់រកុម ម ិក ក ើ្ ្ ំ  ទំ ទំ់ ់ ។  ើ្ ្ ំ   មឲយករូ  ករូ ករូ   ិ ិរកុ រកុមរួស ស កត កត ី  ។

អភថ ខរោមជឯកស ោវ ើឧទហណ៍ ឧទហណ៍  កវិគ គ ិងគណន ងគណន មា ខណឌឌ សេុងសមេុ ខណ ងសមេុងមរំ ងមរំង ករ់  ី ី  ិ ិកេ កេ់ ់រកុម  ើ្ ្ ំ   រ់កអ កអ   ិ ិត ត ិក ក (ផកំ កំណ់)  ើ ើមប ម ីបកៅរសរជែ កៅរសរជែម ឲយ ំណ ណ ំ ំនោ់ នោ់រ រ ើ ។ "

"

 ើ ើ ិជកំ ជកំហ ហឆគ រកុម ម ើ្ ្ ំ   មរ័ ហ ើក៏ ក៏ មឲយអ  ផត់ ់ ជម ិ ិ  ឺ ឺ ់ ់  ើ ើមប ម ីបឲយជរ៍ ឲយជរ៍់ ់ក ក ិក ក កមព  ជទំ ជទំ់ ់ ។ ំឯកស ឯកស  ើ្ ្ ំ  រ រ ើ ើរ់ រ់ រ់ឧទហណ៍ ឧទហណ៍ ខរោម  ើ ើអ អ  រូោកៅរ ោកៅរ ើ ើរ់ រ់ ទក់មក្ មក្ ំ  ម ីម៉ ម៉ ខរោម [email protected]

ណ

ាិក ជំពូពកទី កូ ទី ១ ១ រវភគ និងគណោងបង្  ងគណោងបង្ ដែលៅលើ ំដែលៅលើ ី ែ ី ១.១ កព័ កព័នធនធោងង្   ោងង្  ........................... ......................................... ............................ ............................ ............................ ............................ ............................ ............................ ............................ .................... ...... 3 ១.១.១ ទដា នគណ ........................... ......................................... ............................ ............................ ............................ ............................ ............................ ............................ ............................ ................ 3 ១.១.២ ជហនក   ហនកងសិ ងសិកគណោងង្ កគណោងង្  អោ អ  ោ ........................... ......................................... ............................ ............................ ............................ ............................ ................ 3 ១.១.៣ ទិននយស់ យ័ ស់សិសិកគណ កគណ(Data Load Design) ........................................................................................... 4 ១.២ គណកលខណឌ តុងកុ ងកុងរង ........................... ......................................... ............................ ............................ ............................ ............................ ........................... .............8 ១. ២ ២.១ បតស់គណកលខណឌ គណកលខណឌ ........................... ......................................... ............................ ............................ ............................ ............................ ...................... ........ 8 ១. ២ ២.១.១ ជសើ សើស strip លកក កក សិ សិក ក .......................... ......................................... ............................. ........................... ........................... .................. .... 8 ១. ២ ២.១.២ កណត់ ណត់កស់ កស់កលខណឌ កលខណឌ ............................ .......................................... ............................ ............................ ............................ ............................ ...................... ........ 9 ១. ២ ២.១.៣ ស ៈស់ បស់ បស់គណ គណ ............................ .......................................... ............................ ............................ ............................ ........................... .............10 ១. ២ ២.១.៤ ន  ន កែលនអពពលកលខណឌ កលខណឌ ........................... .......................................... ............................. ........................... ........................... ....................... ......... 11 ១.២.២ គណកកហតង់ ហតង់ស់ ស់ខ ខ (Prestressing Losses) .................................................................... 12 ១.២.២.១ Instantaneous Instantaneous loss ............................ .......................................... ............................ ............................ ............................ ............................ ............................ .................. .... 12 ១.២.២.១.១ Elastic shortening of the concrete ........................................................................... 13 ១.២.២.១.២ Anchorage seating loss .............................. .................... .................... ..................... ..................... ..................... ...................... ................... ........ 15 ១.២.២.១.៣ Friction Friction loss ............................ .......................................... ............................ ............................ ............................ ............................ ......................... ...........15 ១.២.២.២ Time-dependent loss..................... .......... ..................... .................... ..................... ..................... ..................... ..................... ..................... ...................... ................... ........ 16 ១.២.២.២.១ Creep loss ............................ .......................................... ............................ ............................ ............................ ............................ ........................... .............17 ១.២.២.២.២ Shrinkage loss ......................................................................................................... 17 ១.២.២.២.៣ Steel relaxation ....................................................................................................... 18 ១.២.៣ គណកលខណឌ ........................... ......................................... ............................ ............................ ............................ ............................ ............................ ........................... .............20 ១. ២ ២.៣.១ សិកកក កកក ង ស់ខ ខ ........................... ......................................... ............................ ............................ ............................ ............................ .................... ...... 20

១. ២ ២.៣.២ សិកកក កកក ង Moments [Equivalent Frame Method] ................................................................ 23 ១. ២ ២.៣.៣ Check stress at jacking និង at service load...................................... .................................................... ............................ ........................... .............32 ១. ២ ២.៣.៤ សិកភពដស់ កភពដស់កលខណឌ កលខណឌ (Deflection Evaluation) ..................... .......... ..................... ..................... ..................... ................. ....... 36 ១ ២. ២.៣.៤.១ សិករទិ ករទិសៅ Long ........................... .......................................... ............................. ........................... ........................... ....................... ......... 37 ១ ២. ២.៣.៤.២ សិករទិ ករទិសៅ Short .......................... ......................................... ............................. ........................... ........................... ....................... ......... 40 ១ ២. ២.៣.៤.៣ សិកភពដយៈពលខ កភពដយៈពលខីសុ សុ (Total Immediate Central Deflection) Deflect ion) ...................... .............. ........ 42 ១ ២. ២.៣.៤.៤ សិកភពដគិ កភពដគិតញ តញ ូលឥទធ ឥទ ិលពល លធ ពល long-term cambers ............................................ 43 ១. ២ ២.៣.៥ សិក ក Ultimate Ultimate Strength Strength........................................ ...................................................... ............................ ............................ ............................ ........................... .............45 ១ ២. ២.៣.៥.១ សិក ក Secondary Post-Tensioning Moment ............................................................. 45 ១ ២. ២.៣.៥.២ សិក ក Load Combination for Ultimate Strength ....................................................... 46 ១ ២. ២.៣.៥.៣ សិកត កតន់ ន់ ៉ ង់ងអវ អ់ វជនគល់  នគល់ត តងសងង ងសងងកងល ............................ ................................ ....46 ១ ២. ២.៣.៥.៤ សិកត កតន់ ន់ ៉ ង់វជនក  នក  លល លល ង ងកង កង ........................... ......................................... .................. 47 ១ ២. ២.៣.៥.៥  ៀងផ ៀងផ ត់ែក ែក Minimum for Ultimate Strength .......................................................... 48 ១. ២ ២.៣.៦ សិក ក Shear Strength .......................... ......................................... ............................. ............................ ............................ ........................... ........................... .................. 52 ១ ២. ២.៣.៦.១ Nominal One-Way Shear Strength .......................................................................... 52 ១ ២. ២.៣.៦.២ Nominal Two-Way Shear Strength .......................................................................... 55 ១ ២. ២.៣.៦.៣ Flexure transfer moment ......................................................................................... 59 ១. ២ ២.៣.៧ សិក កបស់ បស់ែកក   ែកកង Slab Band............................ .......................................... ............................ ............................ ............................ .................. .... 60 ១. ២ ២.៣.៨ សិក ក End Blocks at Support Anchorage Zones .................................................................. 61 ១. ២ ២.៣.៩ សិកវងល៉ កវងល៉តស់ តស់ខ ខ (Elongation) (Elongation) ........................... ......................................... ............................ ............................ .................... ...... 67

Two-Way Post-Tensioned Slab Design

Example (Hand Calculations)

ជំពូពូកទី កទី ១ ១ វភគ និងគណោងបង្   ងគណោងបង្ ំដែលៅលើ ដែលៅលើ ី ែ ី ១ ១ ដកបព័នធនធោងបង្   ោងបង្ ំ .

១.១.១ ដ ដ គ ដយដេសកម ុ ដយដេសកម ុជដយងព ទន់ ទន់ននូ ននូវេ េ នផ នផ ល់ ខខន ដេដក ុ ដក ុងគណដោងង្  ដត ដុ ុ តងសស ងសស ែកដន ក ុ ុមដយ មដយងខ ងខ  នដរ ុ ុ នដរសដើសយកនូ សយកនូវេ វេ ន ACI Code និង ASSHTO មកដ គណ គណ និង ASCE_7-M10 (Minimum Design Loads for Buildings and Other Structures) មកដ ន នន ុ ន ុក ។

១.១.២ ំ  ំ ហន ហន ុ ុងក ងក ិគរោងង្ គរោងង្ ំ ុ ុោ ោ

ក ុ ុកងគណសិ ងគណសិកដោងង្ កដោងង្  ដែ ុ ុ ដែមបីមបីឲែ ឲែដណ ដណដលឿន ដលឿន ដយលល ដយ ដយងគួ ងគួតនរ តនរហនសិកែូ កែូចងដមៈ ចងដមៈ

តង ី ី ១.១ ១.១ : ំ  ំ ហន ហន ុ ុងកគរោងង្ ងកគរោងង្ ំ ុ ុោ ោ

BUT Borith

1



១.១.៣  ិ ិ ័នយន រ់ ិគ គ(Data Load Design) តង ី ី ១.២ ១.២ :  ិ ិ ័នយ យន  ៈ ិ  ិងទ ងទ ុ ុរូ រូវករើ វករើរ់ រ់រ់ រ់គរោងង្ គរោងង្ ំ ុ ុ ល.

ពិពណ៌ ពណ៌

1.1

Concrete

1.1.1

Compressive strength design cylinder

និមិមតតិ 

PT slabs (35 ~ 70MPa)

Proposed

Reference /(page)

35 MPa

Prestressed Concrete Analysis

35 MPa

and Design_2.3.3

 28 MPa

(ACI 318M-14_25.9.4.5.4 /

f ' f 'c columns, walls, beams, stairs Compressive strength of concrete at

f ' f 'ci

stressing (for multistrand tendons)

(test of cylinder) page 452)

1.1.2

Poisson's ratio: (0.15 ~ 0.20)

.

0.18

Structural Concrete /23

1.1.3

coefficient of thermal expansion

t.

0.000012

Structural Concrete /26

1.1.3

Modulus of elasticity Ec

27800 MPa

(ACI 318M-14_19.2.2.1)

Eci

24870 MPa

f y

390 MPa

after 28 days

[= 4700 f 'c]

at stressing,10 days [= 4700 f 'ci] 1.2

Nonprestressed reinforcing

1.2.1

Deformed bars (DB)

specify from manufacturer 1.2.2

Round bars (RB)

f v

235 MPa

1.2.3

Modulus of elasticity

Es

200000 MPa

1.3

Prestressing: (Bonded System)

1.3.1

Stress relieved and low relaxation

1.3.2

7-wire strand (ASTM A416) grade 270k

(ACI 318M-14_20.2.2.2) /327

Post-Tension

f pu

1860 MPa

(ACI 318M-14_20.3.2.2) /330

1.3.3

yield strength

f py py

0.9 f pu pu

(AASHTO_Table 5.4.4.1-1)

1.3.4

diameter

Dp

12.54 mm

Prestressed Concrete Analysis

1.3.5

strand area

Aps

98.71 mm2

and Design Table 2.4

1.3.6

curvature coefficient (0.15 ~ 0.25)

.

0.2 /radian

(ACI 318M-08_Commentary

1.3.7

wobble coefficient (0.0016 ~ 0.0066)

k

0.004 rad/m

Table R18.6.2 /288

BUT Borith

2


1.3.8


Anchor set: assumed in practice when specify information from the manufacturer set

Prestressed Concrete Analysis 6 mm and Design_8.17 /498

is not available, vary between(4 to10mm) 1.3.9

Ratio of jacking stress to strand's ultimate strength

2.1

Dead loads

2.1.1

Self-weights

2.1.2

0.80f pu pu

(ACI 318M-14_20.3.2.4.1)

unit weight of concrete

c

23.6 kN/m3

-

reinforcement & stand

s

78.5 kN/m3

-

parking (passenger vehicles only)

SDL

1.10 kN/m2

(Ceramic tile and mortar:1.1 +

lobbies and first-floor corridors

SDL

1.77 kN/m2

Suspended metal and gypsum

bed room (residential)

SDL

1.77 kN/m2

plaster: 0.48 + Mechanical

gymnasiums

SDL

1.77 kN/m2

duct allowance: 0.19 =1.77 )

roofs (used for roof gardens)

SDL

1.77 kN/m2

(ASCE 7-10_Table 4.1) /401

stairs and exit ways

SDL

1.10 kN/m2

SDL

2.35 kN/m2

SDL

4.26

kN/m2

SDL

0.38 kN/m2

Super impose dead loads

brick wall100 (1.87kN/m2) including plastering both sides (0.24kN/m2  2) brick wall200 (3.78kN/m2) including plastering both sides

(0.24kN/m2

 2)

skylight, metal frame, 10mm wire glass 2.2

(ASCE 7-10Table C3-1) /403

Live loads parking (passenger vehicles only),

LL 1.92 kN/m2

impact factor increase 33% (ASSTHO- 33% (ASSTHO-

 (1.33)

(ASCE 7-10_Table 4.1) /17

LRFD 2012_TABLE 3.6.2.1-1) = 2.60 kN/m2

BUT Borith

3


lobbies and first-floor corridors


LL

4.79 kN/m2

LL

1.92 kN/m2

gymnasiums

LL

4.79

kN/m2

terrace (used for roof gardens)

LL

4.79 kN/m2

stairs and exit ways

LL

4.79 kN/m2

private room and corridor saving them (residential)

(ASCE 7-10_Table 4.1) /17

Elevator: 900 kg/lot, (impact factor, specify from manufacturer increase 100%), (ASCE 7-10_C4.6/410)

LL

18.0 kN

Elevator: weight of actual equipment (fixed service equipment is treated as a

specify from manufacturer of

Dead Load instead of Live Load.

Elevators

 force of buffer on hoist way pit, car

Note: All Reaction Loads F9 to

side (F9)

 force of buffer on hoist way pit,

89.9 kN LL

with live load and ready

counterweight side (F10)

 force of guide rail, car side (F11, F12)

72.3 kN

include impact factor 100%

48.4 kN

For: Planning Data Reaction

 force of guide rail, counterweight side

Loads see in Appendix A

(F13, F14) 2.3

F14 are combined equipment

26.9 kN

គណ wind load គឺដ ដ ស់ក ុ ុកង Software ETABS 2015 ដេយក យក Result (Auto Lateral Load to Stories) ពី Software មកដ ងផ ងផ ត់ជមួ ជមួយ គណដយែ ។

Wind load

See in Appendix B 2.3.1

Lowest level of storm wind basic wind speed (30 ~ 50 m/s)

BUT Borith

V

120 km/h

Adopted

4


exposure (building in city) " B "


=>

zg

365.76 m

(ASCE 7-10_Table 26.9-1)

=>

.

7

/256

wind directionality factor

Kd

0.85

(ASCE 7-10_26.6) /246

topographic factor

Kzt

1.00

(ASCE 7-10_26.8.2) /254

gust-effect factor

G

0.937

See in Appendix C

2.4

Other loads (for basement wall)

2.4.1

Earth pressure (back fill soil 3.2m down)

set

20 kN/m3

Adopted

2.4.2

Fluid pressure

water

10 kN/m3

Adopted

ា ក់ៈ ល់ន ុ ន ុកដងៗដេៀតែលអត់នដក ុ ុ នដកងងេី ងងេី ១.២ ១.២ ងដលដន ដន គឺនល នលអិអិតដក ុ តដក ុង សិកគណ កគណ ដោងង្ ុ ុ ដោងង្ និនិមួមយៗងដម យួ ៗងដម ។

BUT Borith

5



១.២ គណកាលខណឌ គណកាលខណឌ បតុងបកុ ងបកុងរំ ងរំង

១.២.១ ៉ ៉ ររ់ ររ់គរឌ គរឌ ១.២.១.១ ជរសជើ សជើស strip ជកមកជ កមកជ្វ  សិ សិក ក

ក ុ ុកងគណកក ងគណកក ងក ុ ុ ង កងស់ ងស់មមខត់ ខត់ ដោងង្ ុ ុ ដោងង្ កលខណ កលខណ ដន ក ុ ុមស់ មស់ដយ ដយងខ ងខ  នដរ ុ ុ នដរសដើ សដើសយក សយក Equivalent Frame Method ។ ក ុ ុមស់ មស់ដយ ដយងដរសដើ សដើសយកត សយកត 1 Strip ដ Grid 3 ែូច ចញក ុ ុកង ងងែលនក់ ់ ែលនក់ hacth ងដមយកមកគណញ ។ ា ក់ ដគតវដ វដ គណគ់ Strip ដម Grid ទងេិ ង េិសខ ស ីខ និងវងទ ងវងទងអស់ ងអស់ ។ ។

  ី ី ១.១ ១.១ : លង ់  Layout plan BUT Borith

6



១.២.១.២ កំណត់កស់ កស់កខណឌ កខណឌ [Naaman - PRESTRESSED CONCRETE ANALYSIS AND DESIGN] លដៀ L/h from 35 to 50 កណត់ ណត់យក យក L/h = 45 (លដៀវង ដលកស់ កស់កលខណ កលខណ ) យកមកសិកកកស់ កកកស់កលខណ កលខណ កលបង s

s

  ី ី ១.២ ១.២ : លង ំុ់ ុុ ុក់ ក់ Section Grid 3 L = 11.5 m វង Span វង h = 11.5 m/45 = 0.255 m ឲដយ ឲដយងទញន ងទញន ដស់ ស់កស់ កស់កលខណ កលខណ h = 260 mm (preliminary slab thickness) ដយវង Span ដយងវង ងវង ែូចដន ចដន profile ខតវេ វេក់ ក់ឲដង ឬ ែក់ ង ដែមបីមបីដយដល ដយដលក (balance) កលខណ កលខណ មិនឲ នឲ និ និង ន tension stress  ងដ ង ដកតកលខណ កតកលខណ តង់ mid span ។ ែូដច ដច តវ កស់កលខណ កលខណ ស់ដែដែមបីមបីេេក់   ក់ profile ខ ។ ដែមបីមបីចចដណញ ដ ណញ ណដត ណដតងដគោន់ ងដគោន់តដង តដង នកស់ នកស់ កលខណ កលខណ តកនងែលត់ខជក ខជក ុ ុម ជេូដដកបជ់ ដដកបជ់សស សស ែលក៏ចរ ចរនួនួសជ សជ Drop panel ងែ ។ េួេី េីដ ដ ែូ ែូច Slab ែោន់តនកស់ តនកស់ស់ ស់ជងន ជងនិច ដយដគដដ  ''Slab band" ែូច ចញក ុ ុកង ូូងដមដន ងដមដន ។ ដងមឯក " ADAPT Technical Note " Slab band h Æ 2(h ) កស់ Slab h = 410 mm មកកលបង កណត់ ណត់យកកស់ យកកស់ េេឹងស់ ងស់ Slab band b > 3(h ) b = 1500 mm មកកលបង កណត់ ណត់យកេេឹ យកេេឹង s

s

sb

s

sb

sb

sb

sb

BUT Borith

7



ចដគណកសសែក ដគណកសសែក កស់កលខណ កលខណ គួតដ តដដម ដម equivalent uniform slab thickness (h ) e

  ី ី ១.៣ ១.៣ : Slab Band Equivalent for Minimum Bars   hs  L 2  bs  (h b  L2 )   he =  L2

260 260  5550 5550  1500 1500 (410 (410  260) 260)  = 5550

= 300 mm



គណ Section Properties Ac = bh = [(1.9 m + 2.15 m) (0.26 m)] + [1.5 m  0.41 m] = 1.668 m2 2

S =

=

bh



(1.9m 2.1 2.155m) (0.2 (0.26m)

6

2



1.5m .5m  (0.4 (0.411m)

6

2

6

(1.9m 1.9m  2.15 2.15m) m)  (0.2 (0.26m 6m))

2



1.5m 1.5m (0.41m (0.41m))

6

2

6

= 0.0876 m3 3

Is

=

=

bh



(5.5 (5.550 50m) m)(0 (0.2 .26m 6m))

12

3



1.5m 1.5m (0.4 (0.41m 1m))

12

(5.550 (5.550m) m)(0.2 (0.26m 6m)) 12

3

12

3



1.5m 1.5m  (0.41m (0.41m))

3

12

= 0.0167 m4

១.២.១.៣ ស ស ៈសប់ជប ជបាស់ ាស់គណ គណ 

អពីពដត ដី តង Normal weight c

= 23.6 kN/m3

f ' f 'c

= 35.0 MPa

Ec

= 27805 MPa

BUT Borith

េងន់ ងន់ឌដត ឌដតង) (ភពន់ស់ ស់ដតង 28ៃ ស សកស ីឡង)ង) ( ូ មលឌ លឌលដអឡស លដអឡសចស់ ិចស់ដត ដតងក ក ង f' = 35 MPa)

(

c

8






f ' f 'ci

= 28.0 MPa

Eci

= 24870 MPa


ភពន់ស់ ស់ដតង 10ៃ ជភពន់ដៃ ដៃទញខ) ( ូ មលឌ លឌលដអឡស លដអឡសចស់ ិចស់ដត ដតងក ក ង f' = 28 MPa) (

ci

អពីពែក ី ែក Cold formed steel f y

= 390 MPa

Es

= 200000 MPa

ភពន់ស់ ស់ែក ែក ងអ ង អដ) ដ) ( ូ មលឌ លឌលដអឡស លដអឡសចស់ ិចស់ែក ែក ងអ ង អដ) ដ) (

អពីពខ ី ខ Bonded tendons system 1/2'', 7-wire strands

ដេមខត់ ខត់ស់ ស់ខែលយកមកដ ខែលយកមកដ) (អងត់ ត ិ់តស់ តស់ខ ១ ខ) (កឡម មខត់ ខ ត់ស់ ស់ខ ខ ១ ខ) (ភពន់ ultimate ស់ខ) ខ) (ភពន់ yield ស់ខ ខ) (ភពន់អន អន តឲដស់ ស់ខ ខ ែលមិនទន់ នទន់ែកក ែកកហតង់ ហតង់) (ភពន់អន អន តឲដស់ ស់ខ) ខ)

(

Dp

= 12.54 mm

A

= 0.143 in2 = 98.71 mm2

f pu pu

= 1860 MPa

f py py

= 0.9 f pu pu

f pipi

= 0.7 f pu pu

f pe pe

= 0.7 f pu pu - Total loss

១.២.១.៤ បនទ ុ ុ បនទកែនអំ កែនអំជ ជជ ជកខណឌ កខណឌ

ន ុ ន ុកងដមនលអិអិតក ុ ុ តកងងេី ងងេី ១.២ ១.២ ងដល Framing Dead Load, SW

= 0.30 m x 23.6 kN/m3

(េងន់ ងន់ផ ល់ ខខន ស់កលខណ កលខណ ) = 4.17 kN/m (moving wall100, M/E, tile with mortar ) moving wall100 នមកពី មូលន ុ លន ុករា ងងក ុ ង ងក ុងែលសិ ថ តដ តដ Strip ទ Strip (2.4 kN/m ) ដល  Strip ទងអស់ ង អស់ មកចកនឹ មកចកនឹងក ងកស់ ស់ Strip និង M/E, tile with mortar (1.77 kN/m ) ដមលក ុ លក ុងងេី ១.២ ១.២ ងដល = 1.92 kN/m អោ អោ ក់ដ ដ (condo) = 7.08 kN/m2

Superrimposed Dead Load , SDL

2

2

2

Live Load, LL 

2

No pattern loading required, if service of:

(ACI 318M-14_ 6.4/ page 69)

LL / DL = 1.92 kN/m2 / 4.17 kN/m2

មិនច់ នច់នឆ នឆ ស់ន ុ ន ុក Live load ា ក់ កណីដ ដលដៀ លដៀ LL / DL > 0.75 ដកតម ូមមម ង់ង ែលដក ់ ែលដកតពី តពីន ុ ន ុក Live load តវតកែូ វតកែូចម ច ូមមមង់ង ដដល ដ់ ដល  នែ គឺក់ ក់ន ុ ន ុកចល័ត (Influence Line) ដយនគ់លក លកខណ ខណ ដែមបីមបីកតម moment envelop មកដ ។ ។ = 0.46 < 0.75

BUT Borith



9



១.២.២ កគំហង់ ហង់់ ក ់ ក (Prestressing Losses) កហតង់ ហតង់ស់ ស់ខត ខតវនដគងចកជ វនដគងចកជ ពីែែក់ ក់លគឺ លគឺ ដយឥេធ ិពលយៈដពលភ ពលយៈដពលភ ម (Instantaneous) និងដយឥេធ ងដយឥេធ ិពលស័យដល យដលយៈដពលយូ យៈដពលយូ (Time dependent) ។ កហតង់ ហតង់ដនដក ដនដកតដចញពី តដចញពី ឥេធ ឥេធ ិពលស់ ពលស់ ដត ដតង (Due to concrete) និងែក ងែក (Due to steel) ែូច ចញក ុ ុកងូ ងូងដម ងដម ។ សិកក កកហតង់ ហតង់ដនគឺ ដនគឺ អនដមមដសៀវដ ដមមដសៀវដ '' PRESTRESSED CONCRETE A FUNDAMENTAL APPROACH_[EDWARD G. G. NAWY] ''

។

  ី ី ១.៤ ១.៤ : Interrelationships of causes and effects between prestress losses ១.២.២.១ Instantaneous loss   

កហតង់ ហតង់ស់ ស់ខដយឥេធ ខដយឥេធ ិពលយៈដពលភ ពលយៈដពលភ មៗ (Instantaneous) នីគឺគឺៈ Elastic shortening of the concrete (ួមច់ មច់ដត ដតង ដយទញមិនសដពលជមួ នសដពលជមួយោ យោ ) Anchorage Seating loss (អិលក់ ឬ ឬ កលកិ ) Friction loss (កកិតងជមួ តងជមួយ យពង់ ពង់)

BUT Borith

10



កហតង់ ហតង់ស់ ស់ខដក ខដកង ងងដមឥេធ ងដមឥេធ ិពលន ពលន Elastic shortening តវនដក វនដកតដ តដងដដពលែលខ ងដដពលែលខ តវនដគទញមិ វនដគទញមិនសដពលជមួ នសដពលជមួយោោ ដលគឺត តវនដគទញម វនដគទញមងមួយៗ យៗ ។ ដយងនូមន មនស់  ់គណ គណ f pES =

Eps Ec

f

cs

 nf cs

Eps

n =

(3.2b)

ែល E ជម ូឌឌលដអឡស លដអឡសចស់ ចិ ស់ដត ដតងដៃទញខ ទញខ f 'f ' = 28 MPa ci

Eci

ci

Eci = 4700 700  28M 28MPa  2487 24870M 0MPa Pa

Eps = 200000 MPa 200000MPa  8.04 24870MPa P  e2  M e f cs =  i  1  2   SW A c  Ic r  n =

(3.4)

Ac = 1.668 m2 f pipi = 0.70 f pu pu = 0.701860MPa = 1302 MPa

  ី ី ១.៥ ១.៥ : Relationships of Elastic shortening សនត់កកហតង់ ហតង់កលបងដយ elastic shortening 10% of f = 130.2 MPa ដ net-steel stress pi pi

f pipi

 Pi

= 1302 MPa 130.2 MPa = 1171.8 MPa

ំំពឹពឹងេ ងេកខែលត កខែលតវគឺ វគឺ 20 Strands

= Aps  f pipi

= (20 Strands  98.71 mm2)  1171.8 MPa = 2313.4 kN

គឺជច ជចយងអ័ យងអ័កស់ កស់ខដអ័ ខដអ័កស់ កស់កលខណ កលខណ (ដមលក ុ លក ុងូេី េី ១.៧ ១.៧ ងដម)

e

=

= 230 mm Ic

r

2

(

Ic 0.0167m4 = 0.01 m2  = 2 A c 1.668m

MSW = MSW =

BUT Borith

ូមមមង់ង និន់ ចលភពស់ ិចលភពស់មមខត់ ខ ត់កលខណ កលខណ ) (ដននិ នចលភព ចិ លភព)

= 0.0167 m4

w SW L2

ែល W

SW =

8

7.08 kN/m

ជេន ុ ន ុក Self weight ស់កកខណ កកខណ

7.08kN/m 7.08kN/m (11.5m) (11.5m)2 8 11



= 117.0 kN.m



f cs

2313 313.4k .4kN  (0.230 .230m m)2  117.0k 7.0kN N-m 0.23 .230m =  1   2 2 4 1.668m  0.010m  0.0167m =  6.52 MPa



f pES = 8.04 8.04 (  6.52 6.52MP MPa) a) = 52.4 MPa

និងដយ ងដយងនជ ងនជ ី ដល ដលកេី កេី ២ f pipi

= 1302 MPa  52.4 MPa = 1249.6 MPa

Pi

= (20 Strands  98.71 mm2)  1249.6 MPa = 2466.9 kN

2466.9kN  (0.230m)2  117.0kN-m 0.230m  1  f cs =   1.668m2  0.010m2  0.0167m4 =  7.05 MPa



8.04 (  7.05MP 7.05MPa) a) f pES = 8.04

= 56.7 MPa

និងដយ ងដយងនជ ងនជ ី ដល ដលកេី កេី ៣ f pipi

= 1302 MPa  56.7 MPa = 1245.3 MPa

Pi

= (20 Strands  98.71 mm2)  1245.3 MPa = 2458.5 kN

f cs = 

2458.5 58.5kkN  (0.23 .230m) 0m)2  117.0k 7.0kN N-m 0.23 .230m 1      1.668m2  0.010m2  0.0167m4

=  7.02 MPa



f pES = 8.04 8.04 ( 7.02MP 7.02MPa) a) = 56.5 MPa

និងដយ ងដយងនជ ងនជ ី ដល ដលកេី កេី ៤ f pipi

= 1302 MPa  56.5 MPa = 1245.5 MPa

Pi

= (20 Strands  98.71 mm2)  1245.5 MPa = 2459.0kN

2459.0k .0kN  (0.230m)2  117.0kN-m 0.23 .230m   1 f cs =    1.668m2  0.010m2  0.0167m4 =  7.02 MPa BUT Borith

12





8.04  ( 7.02MPa 7.02MPa)) f pES = 8.04

= 56.5 MPa Stress គណង ដលកេី ដយងដញតម ញតមកហតង់ ហតង់ Stress កេី ៣ ៣ នដដលកេី កេី ៤ ៤ ដស ដស  56.5 MPa លងល ។ ែូចដនក ចដនកហតងែលតឹ ហតងែលតឹមត មតវគឺ វគឺ 4.3% ចនកក នកកណត់ ណត់កកហតង់ ហតង់កលបង កលបង 10% ងដលងពី ងពីែែូ ងូ ដយន់ ន  P  0.90P គឺជងតម ជងតមែលដយងកដ ងកដញ ។ i

j

ែូចដនក ចដនកហតង់ ហតង់ដយ ដយ elastic shortening គឺ f

pES

 56.5 MPa

កហតង់ ហតង់នខែលដក នខែលដកតដងដមឥេធ ងដមឥេធ ិពលនកលកិ ពលនកលកិ  ឬ Anchorage seating loss គឺតតវនដគ វនដគ គណមយៈូមន មនៈ  f = E (3.24) ែល L ជវងនខ ដសនឹនឹង 13.8 m L 6mm ម Specify និង  ជវងអិលក់ លក់ ឬ ឬ កលកិ  នតម 6mm A

pA

ps

A

f = pA

6.0mm 13800mm

 200000MPa

= 87.0 MPa

ែូចដនក ចដនកហតង់ ហតង់ដយ ដយ Anchorage seating គឺ f

pA

 87.0 MPa

កហតង់ ហតង់ដយកកិ ដយកកិតគឺ តគឺតតវនពិ វនពិ  និងត ងតវនយកមកសិ វនយកមកសិក ក ដែមបីមបីននូ ននូវតម វតមកង ងងសិ ងសិេធេធភព ភព ខែលន   ់ពីពនក ី នកហតង់ ហតង់ជស ជស ។ ែូ ចែលនសិកកន កកនងមក កហតង់ ហតង់ដយកកិ ដយកកិតស់ តស់ខ ខ  នឹង ងពង់ ពង់ នឹងដត ងដតង គឺន នល់ ល់ជ ជ ងែល់ ង ែល់សិ សិេធេភពស់ ភធ ពស់ខ ខ មូង ង ួមទង ង លលក លួួ លកណៈូ ណៈូ និងផ ងផ ស់  នី ូវខមេី វខមេីងែលនក ងែលនកណត់ និ និងគណ ងគណ ។ ូូមន មនស់គណកក គណកកហតង់ដយកកិ ដយកកិតគឺ តគឺ f pF = f pi

 (   k L)

(3.22)

ែលកហតង់ ហតង់ដយកកិតដកតនដ តនដងដយក ងដយក ២ ៗគឺ ៗគឺ Wobble និង Curvature effects ែលនៈ - គឺជ coefficient of friction between the tendon and the duct due to the curvature effect (use  = 0.2) - K គឺជ coefficient of friction between the tendon and the surrounding concrete due to wobble effect or length effect. (use k = 0.004/m)

BUT Borith

(ACI 318M-08_Commentary Table R18.6.2/ page 288)

13



  ី ី ១.៦ ១.៦ : Approximate Evaluation of the Tendon's Central Angle តង ី ី ១.៣ ១.៣ :  ិំ ំហង់ដយស ដយស ិ ិតែ តែងរ ងរ ិ ិួួយៗ យៗ L(

វងខដង)

0.40 m

9.20 m

0.40 m

 rad

0.0087

0.2010

0.0087

 k L) (  

0.0033

0.0769

0.0033

 (    k L)

0.0835

មគណមសិក ក កហតដយក ហតដយក ងកកិ ង កកិត គឺដក ដកតន តន 8.35% នភពន់ដែមដដពលទញ មដដពលទញ ខ (8.35% of f ) pi pi

1302MPa a  0.08 0.0835 35 f pF = 1302MP

= 108.9 MPa

ែូចដនក ចដនកហតង់ ហតង់ដយ ដយ Friction គឺ f

pF

 108.9 108.9 MPa

១.២.២.២ Time-dependent loss   

កហតង់ ហតង់ស់ ស់ខដយឥេធ ខដយឥេធ ិពល ពល ស័យដល យដលយៈដពលយូ យៈដពលយូ (Time dependent) នីែគឺ ែគឺៈ Creep loss (ួមច់ មច់ដត ដតង ដយដោងង្ ុ ុ ដយដោងង្ េន ុ េន ុកយៈដពលយូ) Shrinkage loss (ួមច់ មច់ដត ដតង ដយសត និ និងតិ ងតិកម កមគីមីស់ ស់សស ីមមង់ង ត៏ត់ ៏ ក ុ ុ កងយៈដពលខ ងយៈដពលខី) Steel relaxation (ដនឿយត់ ឬត់ ឬត់ងក ងក ង ង  ស់ខដពលដ ខដពលដ យៈដពលយូ យៈដពលយូ)

BUT Borith

14



កហតង់ ហតង់ែលដក ែលដកតដ តដងដយ ងដយ Creep តវនគណមូ វនគណមូមន មនែូចងដមៈ ចងដមៈ f pCR = kCR

ែល

Eps EC

(3.11b)   = nk f f  ស់ ់ដោងង្ ុ ុ ដោងង្ ែលជដេដត ែលជដេដតងដក ងដកងង Post-tensioned member

 f cs  f

k CR = 1.6

csd

CR

cs

csd

Eps = 200000 MPa Ec = 27800 MPa

Eps

n

=

n

= 7.2

ែល E ជម ូឌឌលដអឡស លដអឡសចស់ ចិ ស់ដត ដតង f ' = 35 MPa c

Ec

លដៀ ូមឌឌលដអឡសចខ ចិ ខ ជមួយនឹ យនឹង ូមឌឌលដអឡស លដអឡសចដត ិចដតង នមកពីគណក គណកហតង់ ហតង់ elastic shortening ដលកេី កេី ៤ ងដល

f cs = 7.02MPa f csd =

c

MDL  e

ែល M ជម ូមមង់ង ែលដក ់ ែលដកតពី តពី self-weight + superimpose dead load DL

Is

MDL = =

WDL  L2 8 (7.08kN/m (7.08kN/m  4.17kN/m) 4.17kN/m)(11.5m)2 8

= 186 kN-m

f csd =

e

= 240 mm

Is

= 0.0167 m4

ដមលក ុ លក ុងូេី េី ១ ១.៧ ងដម) (ដមលក ុ លក ុង ១ ២. ២.១.២ ងដល)

(

186kN-m 186kN-m 0.230m 0.230m 0.0167 m4

= 2.32 MPa

 7.02MPa  f = 7.21.6   7.02MP a  2.32MP 2.32MPa a pCR   = 54.2 MPa

ែូចដនក ចដនកហតង់ ហតង់ដយ ដយ Creep គឺ f

pC

= 54.2 54.2 MPa

កហតង់ ហតង់ែលដក ែលដកតដ តដងដយ ងដយ Shrinkage តវនគណមូ វនគណមូមន មនែចងដមៈ ចូ ងដមៈ Time-dependent Method:

 V  f pSH = 8.2 10 106 KSHEps  1 0.06  (100  RH)  S  

(3.14)

គិតក តកហតដយ ហតដយ shrinkage ដយ 7 ៃ  ់ពីពក់ ី ក់ដត ដតង (moist-cured concrete) BUT Borith

15


សនត់


KSH = 0.77

humidity correction factor

RH = 77%

សដណ ដណមក ុ ុ មកងដត ងដតង

(Table 3.6)

Eps = 200000 MPa =29000000 psi

V A  he he =  2A 2 S

(A)  កពស់ (h ) ជឌស់កលខណ កលខណ ដស ដស ក  ក (A) ពស់ (h S ជឌស់ ស់កលខណ កលខណ (ូកា កា លទ ទ ង ង ដល ដល និ និងដម = 2A) V

e

he = 300mm = 11.811 in

V 11.811in  5.91 in = S 2





f 8.2106  0.7 0.77 2900 290000 000 00 1 0.0 0.06 5.91 .91 (100 100 77) 77) pSH = 8.2 = 2718.1 psi = 18.7 MPa

ែូចដនក ចដនកហតង់ ហតង់ដយ ដយ Shrinkage គឺ f

pS

= 18.7 18.7 MPa MPa

កហតង់ ហតង់ែលដក ែលដកតដ តដងដយ ងដយ Steel relaxation តវនគណមូ វនគណមូមន មនែូចងដមៈ ចងដមៈ (PCI [ Ref. 8.35])

f pR (t i , t j ) = fp (t i )  fp (t j )

= f py py

fp (t i )  fp (t i )

  t  j   0.55   log    t i  k  f py    

= 0.9f pu pu = 0.91860 MPa

k = 45

តមដ

(PCI Prestress losses [ Ref. 8.35])

(Prestress Concrete Analysis and Design/Table 2.6)

= 1675.5 MPa f p (t i ) = f pipi = 0.7f pu pu = 0.71860 MPa

(ACI-11/18.5.1/ page 293)

= 1302 MPa

ដយៈដពល 1 ៃ ដស ដស 24 ដ ដ ង 

f pR (1 , 24) =

1302MPa  1302MPa 45

  24     0.55   log    9.10 MPa  1674MPa   1

យៈដពលដងដេៀតក ុ ុ យៈដពលដងដេៀតកងងងងដម ងងងងដម ក៏គណមូ គណមូមន មនដនែ ដយយៈដពល t និង t គិតជដ តជដ ង ។ ដយៈដពល 3 ៃ ដស ដស 72 ដ ដ ង i i



j

f ps ( 3 ) = f ps ( t i )  f pR ( t i , t j )

= 1302.0 MPa  9.10 MPa = 1292.9 MPa

BUT Borith

16



តង ី ី ១.៤ ១.៤ : Typical time-step computations of relaxation loss for a strand of constant length, fixed at it ends

ែូចដនក ចដនកហតង់ ហតង់ដយ ដយ Steel relaxation គឺ f = 35.3 35.3 MPa pR

តង ី ី ១.៥ ១.៥ : ងេ  ី ីំំហង់ ហង់តន តន  ី ីួយួ ៗ Prestressing loss in

Loss

Percentage of loss

Post-tensioned

(MPa)

(% of f pu pu)

Elastic Shortening

56.5 MPa

3.0%

Anchorage Seating Loss

87.0 MPa

4.7%

Friction Loss

108.9 MPa

5.9%

Steel Relaxation Loss

35.3 MPa

1.9%

Shrinkage loss

18.7 MPa

1.0%

Creep Loss

54.2 MPa

2.9%

Total Loss

360.5 MPa

19.4%

ា ក់ តម Total Loss ក ុ ុកងងងដល ងងងដលដន ដន គឺដយ ដយងនសន ងនសនតតម ់តមមតខ (ែូចជ ចជ number of strands, tendon's central angle (), eccentricity of tendon (e) ក៏ចទ ចទងម ងមខត់ ខត់ សិ សិនដនពងី នពងីកក ុ ុ កកងកណី ងកណីដ ដងផ ងផ ត់ អត់ជ់ ជ់) ដែមបីមបីចក តមកហតង់ ។ ដែមបីមបីសិសកដយស ិកដយសកិកិតដគត តដគតវគណកក វគណកកហតង់ ហតង់ដ ដងវ ងវញដដពលែលដគ ញដដពលែលដគ ឹ ែ ឹងតម ងតមមតែលសនតងដល ់ ងដលដយ ។ សិកស់ កស់ដយ ដយងខ ងខ  គឺគុ ុ នកដ ឺនកដស់ ស់ software ដយរួយកតម មតែលដយងសន ងសនតងដល ់ ងដលែូែដច ដូ ចដយងខ ងខ  មិមុ ុ នកតម និ កតមកហតង់មមង ដេៀតដេ នន័យតម យតមសនតតឹ់ តឹមត មតវដ វដយ ។ BUT Borith

17



ដយងច់ ច់តតវដ វដ ដ ដ ងផ ងផ ត់ ដតកកហតង់ ហតង់ស់ ស់ខសថ ខសថិតដចដ តដចដ តមែលអន តឲដស់ ស់ មកណត់ ណត់ដយ ដយ 0.50f pu pu

≤

f se se < 0.60f pu pu

(ACI 318M-14_20.3.2.3.1/ page 331)

f se se

= 0.7f pu pu  Total Loss

f se se

= 0.7f pu pu  19.4% f pu pu = (0.506 f pu pu ) = ( 0.506  1860 MPa) = 941.5 MPa

0.50f = 930 MPa ដយតមែលកដញ ដស 941.5 MPa ជងតម ជងតមែល Code ដយដតិតច ិចត ដស 0.50f ។ ែូចដនដយ ចដនដយងយកតមក  ងសិ ង សិេធេភពស់ ភធ ពស់ខ f = 941.5 MPa មកដស់ ស់ដែដែមបីមបីគណកច គណកចនួនួនែលកល នែលកល ខណ ខណ តវែូ វែូចងដម ចងដម ។ pu pu

pe pe

តមក  ងសិ ង សិេធេភពស់ ធភពស់ខ ខ f = 941.5 MPa pe pe

១.២.៣ កគ កគរ រឌឌ ១.២.៣.១ សិកកកល កកកល ងំ បស់ខប ខប 

សទ់  Requirements (2-hour fire rating, assume carbonate aggregate)

(IBC 2003)

Unrestrained slabs = 11/2'' = 40 mm = 3/4'' = 20 mm

សទ់ងដម ងដម សទ់ងដល ងដល

 Tendon profile:

ដស់ ស់ខងដន ខងដន គឺត់ ត់តង់ តង់កន កនងសសដ ឲមិ ឲមិនដក នដកតនក តនក ងម ង ូម មង់ងែលដក ់ ែលដកតដងពីច ចក ក ិតស់ តស់ខ ខ ។ Reversed parabolic shape:

  ី ី ១.៧ ១.៧ : Continuous Post-Tensioned BUT Borith

18



តង ី ី ១.៦ ១.៦ : យៈព់់ កសបង ់ ់ កសបង Tendon Ordinate

Tendon (CG) Location***

Cantilever left-support - anchor

160 mm /2  150 mm = 280 mm

Interior support - top

410 mm  115 mm = 295 mm

Interior mid-span - bottom

50 mm

Cantilever right-support - anchor

160 mm /2  150 mm = 280 mm

(CG): Center of gravity ***

ចយស់ យស់គិតពី តពី  តកលខណ តកលខណ ងដម (Slab Band) ឬ ពមម ដ អ័កស់ កស់ខ ខ a = e = 15 mm, ស់ cantilever slabs (ចយពី យពី អ័ អ័កខងដម កខងដម ដអ័កខងដល កខងដល) END

aINT = 295 mm  50 mm Span ងក ុ ុ (ស់ Span ងកង)ង) e គឺជច ជចយងអ័ យងអ័កស់ កស់ខដអ័ ខដអ័កស់ កស់កលខណ កលខណ ដយតម តមនឹង ងលដម លដម span = 245 mm

 Prestress Force Required to Balance 70% of self weight DL 60% to 80% of DL (only self-weight)

ស់កលខណ កលខណ (good approximation for hand calculation)

កណត់ ណត់យកមកដ យកមកដ 70% គឺ Wb

= 0.70 WSW = 4.96 kN/m2 = 4.96 kN/m2  5.550 m = 27.51 kN/m

(5.550 m ជេេឹងងន ុ ងងន ុកស់កលខណ កលខណ )

 Force needed in Tendons to counteract the load in the interior bay P

= =

WbL2 8aINT 27.51kN/m 27.51kN/m (11.5m) (11.5m)2 8  0.24 0.245m 5m

= 1856.2 kN

ជក ជក ងែលត ង ែលតវខដល វខដលមមខត់ ខ ត់កលខណ កលខណ 1 strip

ឲច ឲចនួននខដយ នួ ខដយងន n

= P / Peff

Peff = f pe pe  Aps

(f pe pe

ជស ជស ខសិេធេធភព ភព និង A ជកឡស់ ស់ខមួ ខមួយដែ យដែម) ps

= 941.5 MPa  98.71 mm2 = 92.9 kN n

=

1856.2kN Strands  19.97 St 92.9kN

ដស់ ស់ចចនួន នខ នួ ខ " 20 Strands " BUT Borith

19



 Average pre-compression limits P/A

តូច ចត ត

= 0.90 MPa = 2.10 MPa

(ACI 318M-14_8.6.2.1/ page 104)

 Check Precompression Allowance Actual force

ស់ខគឺ ខគឺ

Pactual = (20 Strands)  92.9 kN = 1858 kN

Pactual

1858kN = A 1.668m2 = 1.11 MPa > 0.9 MPa

ស ស ស់ ់ខ ខជងស ជងស អន ត ែូដច ដចចនួនួនដ នដស់ ស់ខគឺ ខគឺគ់ គ់ោន់ ោន់ដ ដយតម យតម 0.9 MPa គឺជ ស ស ស់ ់ខអន ខអន ត តូច ចត ( ដគក់ដែដែមបីមបីដត ដតងកលខណ ងកលខណ ក ឲន ន មដ ) ។ ដយតម តមិ តមិន ដយដលស 2.1 MPa ។  Check force needed in Tendons to counteract the load in the cantilever slab P

=

=

Wb L2

cantilever slab) ស់ cantilever

(

2aEND

27.51kN/m 27.51kN/m  (1.15m) (1.15m)2 2  0.15 0.15m m

តវក វក ងខតិ ង ខតិចជងល ចជងលងងក ុ ុ ងកង) interior span និង cantilever slab គឺ the amount ស់គណដន គណដន តមវក វក ងខដែ ង ខដែមបីមបីដល ដលក ពិតស់ interior = 1124.6 kN < 1858 kN

(cantilever slab

of load that will be balanced:

Wb = =

8aINTP L2 8  0.24 0.245m 5m1858 1858kN kN (11.5m) 2

= 27.0 kN/m

Wb WDL

=

27.0kN/m (7.08 (7.08kN kN/m /m  5.550 5.550m) m)

= 69%

2

 0.69

តមដនដចដ នដចដ  60% to 80% acceptable for this design

ែូដច ដច: Effective prestress force, P = = 1858 kN និង W = 27.0 kN/m eff

BUT Borith

b

20



១.២.៣.២ សិកកកល កកកល ងំ Moments [Equivalent Frame Method]

ក ុ ុកងគណកក ងគណកក ងក ុ ុ ង កងស់ ងស់មមខត់ ខត់ ដោងង្ ុ ុ ដោងង្ កលខណ កលខណ ដន ក ុ ុមស់ មស់ដយ ដយងខ ងខ  នដរ ុ ុ នដរសដើ សដើសយក សយក Equivalent Frame Method ។    មតមនែូចងដម ចងដម នមកពីភព ូូ ភព (b) ែលដេព័ពងដល ័ ងដល ។ ។ - វងដ L = 11.5 m  យពីអ័អកក័  A ដ F - វងេេឹងស between centerlines b = 5.55 m - កមសសសងដម L = 3.2 m ស់ សងដម និងដល ងដល - កស់កលខណ h = 260 mm កលខណ - កស់ slab slab band h = 410 mm  ក Stiffness ស់កលខណ កលខណ សិកក កក Stiffness ដនអនដមមដសៀវដស់ ដមមដសៀវដស់ដក ដក [Antoine_E._Naaman] - "PRESTRESSED col

s

sb

CONCRETE ANALYSIS ANALYSIS AND DESIGN" / page 678

4EcI s

ks =

L

=

4Ec  1.67  1010 mm4

សនត L ់ L = span length, center to center of support

11500mm





= 5.80 5.809 9 106 Ec mm-N/r -N/rad ad



ក Stiffness ស់សស សស 4EcI

kc =

ែល

L

(1500mm)3 bh3 700mm (1500mm) I= = = 19.69 1010mm4 12 12

L = Lstory - hsb = 3200mm - 410mm = 2790 mm

kc =

4Ec 19.68 .68 1010 mm4 2790mm





= 282. 282.26 26106 Ec mm-N mm-N/r /rad ad



ក Stiffness of torsional member (slab strip), C x = កស់កលខណ កលខណ equivalent h = 300 mm y = េ សសមដ យ Span = 1500 mm c2 = េ ស សមេេឹង Span = 700 mm e

3  x x y 0.63   C =  1 0.6 y  3 

(11.7)

3  300m 300mm m  (300 (300m mm)  1500 1500m mm  =  1 0.63   1500mm  3 

= 1.18 .18 1010mm4

BUT Borith

21





  3  L2 (1  (1 c2/L2 ) 

9EcC

kt = 

=



(11.6)

  9Ec 1.18 .18 1010 mm4   3  5550mm(1  5550mm (1 700mm/5550mm) 700mm /5550mm)   





= 28. 28.67 67106Ec mm-N mm-N/ra /rad d

 The Stiffness of the equivalent column 1

k ec

=

k ec =

1

 kc

+

1

(11.5)

kt

1

   

1



េេួលនគឺ លនគឺ

1

+  k c k t 



1 Ec

  1 1    6 6  2 (28 (2 8 2.2 2. 2 6 1 0 ) 2 8.6 8. 6 7 1 0     

   ូ មមមង់ង ដក ដ់ កតពី តពីន ុ ន ុក Dead Load Moment distribution ស់ uniform dead load នមកពីេ េងន់ ង ន់ូូកន ុ កន ុកួមោ មោ ង ន ុ ន ុកផផ ល់ស់ ស់កលខណ កលខណ ជមួយនឹ យនឹង superimposed dead load គឺ k ec = 27.2 27.299  106 Ec mmmm-N/r N/rad

WDL = WSW + WSD = (0.3m5.55m23.6kN/m3) + (4.17kN/m25.55m)

ន ុ ន ុកដស យដលកលខណ កលខណ )

= 62.44 kN/m

(

PDL = (2.35kN/m22.94m5.55m) = 38.34 kN

ន ុ ន ុករា ងងដៅ ង ងដៅ ដឥែ ឥែ ១០០មម ូកយអសងង កយអសងង)

(

  ី ី ១.៨ ១.៨ : Loading due to Dead Load

BUT Borith

22


 Distribution factor (DF)

=

kij

k

jk

(Cantilever slab)

DF AG = DFFH = 0

DF AF =

joint និមួ ដតង់ joint មយៗដង យួ ៗដង តនដយ តនដយ ratio of stiffness


ks kec + k s

5.809 5.809106 Ec 27.29 .29 106 Ec  5.80 .809 106 Ec

= 0.18

DFec =

=

kec kec + k s

27.29 27.29106 Ec 27.29 .29 106 Ec  5.80 .809 106 Ec

= 0.82 DFcol =

DFec 0.82 = 2 2

(ចកដមគណ ដសសងដម និងដល ងដល)

= 0.41

 Fixed-End Moments

ស់អង្ អង្ត់តនិន់ ិមួមយៗ យួ ៗ

  ី ី ១.៩ ១.៩ : Fixed-End Moments of Each Member BUT Borith

23


-


interior span ពី ូមមមង់ង អវ អ់ វរនតង់ ា នតង់គល់ គល់េេ កងដល កងដលស់ ស់ interior span  ត់អ័អ័កក (A - F) MDL =

62.44kN/m2  (11.5m)2

WDLL2

=

12

12

= 668.1 kN-m -

cantilever slab សងងពី ូមមមង់ង អវ អ់ វរនតង់ ា នតង់គល់ គល់េេ កងដល កងដលស់ ស់ cantilever slab  ត់អ័អកក័  (G - A) និង (F - H) MDL =

WDLL2 2

 62.44kN/m2  (1.15m ) 2    38.34kN 1.15m  PDLL =     2  

= 85.4 kN-m -

interior span ពី ូមមមង់ង ់វរនច ា នចក ក លល លល ង កងដមស់ កងដមស់ interior span  ត់អ័អកក័  (A - F) MDL =

WDLL2 24

 62.44kN/m2  (11.5m )2   =    24  

= 344.1 kN-m

 Moments distribution

ស់ slab frame ដ សស

  ី ី ១.១០ ១.១០ : Moment Distributed of Dead Load

BUT Borith

24



ូូេី េី ១.១១ ងដមជ តមែមម ូមមងែលដក ់ែលដកតនពី តនពីន ុ ន ុក dead load ។ តម ូមមមង់ង ែលត ់ ែលតវយកដដ ស់ក ុ ុកងដ ង ដងផ ងផ ត់ stress ដល កលខណ កលខណ និងយកដ ងយកដ combined ដែមបីមបីកសសែក កសសែក គឺយកម យកម ូមមង់ង ដជ់ ់ ដជ់  ស់សស សស (moment in clear span) គឺ

  ី ី ១.១១ ១.១១ : Diagram Moment due to Dead Load ូមមមង់ង ដក ដ់ កតពី តពីន ុ ន ុក Live Load Moment distribution ស់ uniform Live load នមកពីេ េងន់ ង ន់ ដមស់ ស់ន ុ ន ុកដស ឬ ន ុ ន ុកចល័តដដល តដដល កលខណ កលខណ ។ 

WLL = 1.92 kN/m2  5.55 m = 10.66 kN

ន ុ ន ុកចល័តដែ តដែដដល ដដលកលខណ កលខណ )

(

  ី ី ១.១២ ១.១២ : Loading due to Live Load BUT Borith

25


-


interior span ពី ូមមមង់ង អវ អ់ វរនតង់ ា នតង់គល់ គល់េេ កងដល កងដលស់ ស់ interior span  ត់អ័អ័កក (A - F) MLL =

10.66kN/m2  (11.5m)2

WLLL2

=

12

12

= 117.5 kN-m -

cantilever slab សងងពី ូមមមង់ង អវ អ់ វរនតង់ ា នតង់គល់ គល់េេ កងដល កងដលស់ ស់ cantilever slab  ត់អ័អកក័  (G - A) និង (F - H) MLL =

WLLL2

10.66kN/m2  (1.15m)2 =

2

2

= 7.1 kN-m -

interior span ពី ូមមមង់ង ់វរនច ា នចក ក លល លល ង កងដមស់ កងដមស់ interior span  ត់អ័អកក័  (A - F) MLL =

WLLL2 24

10.66 .66kN/m2  (11.5m) .5m)2 =

24

= 58.7 kN-m



  ី ី ១.១៣ ១.១៣ : Moment Distributed of Live Load

BUT Borith

26



ូូេី េី ១.១៤ ងដមជ តមែមម ូមមង់ងែលដក ់ ែលដកតនពីន ុ ន ុក live load ។ តម ូមមមងែលត ់ែលតវយកដដ ស់ក ុ ុកងដ ង ដងផ ងផ ត់ stress ដល កលខណ កលខណ និងយកដ ងយកដ combined ដែមបីមបីកសសែក កសសែក គឺយកម យកម ូមមង់ង ដជ់ ់ ដជ់  ស់សស សស (moment in clear span) គឺ

  ី ី ១.១៤ ១.១៤ : Diagram Moment due to Live Load ូមមមង់ង ដក ដ់ កតពី តពីន ុ ន ុក Balancing Load Moment distribution ស់ uniform Balancing load នមកពី ក ក ងខដយទញដល ង ខដយទញដលក កលខណ W =  27.0 kN (ន ុ ន ុកដលក កលខណ កលខណ  ុ ុយពី យពីេិេសដេ សិ ដេញនែ ញនែ ី ី) 

b

  ី ី ១.១៥ ១.១៥ : Loading due to Balancing Load

BUT Borith

27


-


interior span ពី ូមមមង់ង អវ អ់ វរនតង់ ា នតង់គល់ គល់េេ កងដល កងដលស់ ស់ interior span  ត់អ័អ័កក (A - F) Mbal =

WbL2 12

27.0kN/m2  (11.5m)2 =

12

= 329.6 kN-m -

cantilever slab សងងពី ូមមមង់ង អវ អ់ វរនតង់ ា នតង់គល់ គល់េេ កងដល កងដលស់ ស់ cantilever slab  ត់អ័អកក័  (G - A) និង (F - H) Mbal =

WbL2 2

27.0kN/m2  (1.15m)2 =

2

= 17.9 kN-m -

interior span ពី ូមមមង់ង ់វរនច ា នចក ក លល លល ង កងដមស់ កងដមស់ interior span  ត់អ័អកក័  (A - F) Mbal =

WbL2 24

27.0kN/m2  (11.5m) 2 =

24

= 148.8 kN-m



  ី ី ១.១៦ ១.១៦ : Moment Distributed of Balancing Load

BUT Borith

28



ូូេី េី ១.១៧ ងដមជ តមែមម ូមមង់ង ់ ែលដកតនពី តនពីន ុ ន ុក load balancing ។ តម ូមមមង់ង ែលត ់ ែលតវយក វយក ដដស់ ស់ក ុក ុង ដ ងផ ងផ ត់ stress ដល កលខណ កលខណ និងយកដ ងយកដ combined ដែមបីមបីកសសែក កសសែក គឺយកម យកម ូមមង់ង ដ ់ ដ ជ់ ស់ ស់សស សស (moment in clear span) គឺ

  ី ី ១.១៧ ១.១៧ : Diagram Moment due to Balancing Load តង ី ី ១.៧ ១.៧ : ងេល ល ៉៉ ៉ង់  ើ ើ  ី ីទ ទ ុ ុងៗ ងៗ ែងរខងន ងរខងន ុ ុង (interior span) ូមមមង់ងនមកពី ់ នមកពីន ុន ុក

ូមមមង់ង ដគល់ ដ់ គល់តម តម (At support) ូមមមង់ង ដក ដ់ ក លល លល ង (At mid span) គិតពី តពីអ័អកសស ក័ សស ដ អ័កក គិតពី តពី ងម ងមខ ដ  សស សសងមខ

Dead Load

602.0 kN-m

366.5 kN-m

344.1 kN-m

Live Load

106.0 kN-m

65.8 kN-m

58.7 kN-m

Load Balance

296.9 kN-m

187.7 kN-m

155.4 kN-m

តង ី ី ១.៨ ១.៨ : ងេល ល ៉៉ ៉ង់  ើ ើ  ី ីទ ទ ុ ុងៗ ងៗ ែងរខងរៅំ ងរខងរៅំងងខង ងងខង (cantilever slab) ូមមមង់ងនមកពី ់ នមកពីន ុន ុក

ូមមមង់ង ដគល់ ដ់ គល់តម តម ូមមមង់ង ដក ដ់ ក លល លល ង គិតពី តពីអ័អកសស ក័ សស ដ អ័កក គិតពី តពី ងម ងមខ ដ  សស សសងមខ

Dead Load

85.4 kN-m

29.7 kN-m

-

Live Load

7.1 kN-m

2.5 kN-m

-

17.9 kN-m

6.5 kN-m

-

Load Balance

BUT Borith

29



១.២.៣.៣ Check stress at jacking និង at service load Set Design Parameters កណត់ ណត់ Set ចនួននៃ នួ ៃទញខអន ទញខអនដមម ដមម "PRESTRESSED CONCRETE A FUNDAMENTAL APPROACH APPROACH / 5 Edition"



th



   f 'c   t    

f 'ci =  

t

(2.4a)

ស់សស ីមមង់ង ត៏ត់ ៏ Type-I ជមួយទ យទដយដ ដយដសដណ ដណម (moist-cured type- )  = 2.3 ស់ស Type-III ជមួយទ ស ីមមង់ង ត៏ត់ ៏ Typeយទដយដ ដយដសសដណ ដណម (moist-cured type- )  = ដមគណស័ ណស័យនឹ យនឹងមតែលតវោ វោ នឹងដមគ ងដមគណ : ( = 4.0   = 0.85 and  = 2.3   = 0.92) Admixture ែូចដនដយ ដយយដតងស់ ងស់កលខណ កលខណ ដន គឺដ ដស់ ស់មមង់ង ត៏ត់ ៏ Type-I ដយមិនដ នដ គីគ មីីមី Admixture ចដនដយង ចទញកចននៃ នួ ៃ ែលដត ែលដតងត ងតវដក វដកន Strenght ែល់ f ' = 28 MPa (Strenght 28 ៃគឺគឺ f ' = 35 MPa) ។ កលបង់ t = 10 ៃ  = 4.0

I

III

c



c

   35 MPa   4.0 4. 0 0.85 0. 85 10   10

f 'ci =  

= 28 MPa (f ' = 28 MPa) ដយងច់ ែូចដន ចដន ដយដពលពីក់ ក់ដត ដតងកលខណ ងកលខណ ន 10 ៃ (f ងច់ដ ដ មទញខន មទញខន ។ ា ក់ ដដ ដស់ ស់ដត ដតងយេឹ ងយេឹក ក គីគ មីីមី Admixture គឺដយ ដយងកម ុ កម ុងេិញដត ញដតង ដយដយងអករ ករយងដត យងដតង យដសច ដគដ យពិ យពិដ ដ (Trial mix) មងដយមងដេៀតូតទល់ តទល់តចូ តចូលលកខណ ខណ ែលដយងចង់ ងចង់ន ន គឺ ដយដពលក់ដត ដតងន ងន 3  4 ៃដយ ដយ Strength ដតងដក ងដកនែល់ នែល់ 80% ន Strength ដ 28ៃ ឬ f 'f ' > 28 MPa ។ ci

ci

 Allowable stresses: Class U At time of jacking: (f 'ci = 28 MPa) Compression

Æ 0.60f 'ci = 0.6028 MPa

(ACI 318M-14_Table 24.5.3.1/ page 408)

Æ 16.8 MPa Tension

Æ 0.25f 'ci = 0.2528 MPa

(ACI 318M-14_Table 24.5.3.2/ page 409)

Æ 1.32 MPa At service loads: (f 'c = 35 MPa) Compression

Æ 0.45f 'c = 0.4535 MPa

(ACI 318M-14_Table 24.5.4.1/ page 409)

Æ 15.7 MPa Tension

Æ 0.50f 'c = 0.5035 MPa

(ACI 318M-14_Table 24.5.2.1/ page 407)

Æ 2.95 MPa

BUT Borith

30



តង ី ី ១.៩ ១.៩ : ងេល ល Stress ុញា ់ុ ុងរឌ ងរឌ រុងរតំ ងរតំង កក ុ ុងលក ងលកខណ ខណ

ក ងដត ក ង ដតង

(Conditions)

(Strength)

(Compression) សងត់ត់ (Compression)

ទញ (Tension)

 28 MPa

16.8 MPa

1.32 MPa

35 MPa

15.7 MPa

2.95 MPa

ដៃទញខ ទញខ

(At time of jacking)

  ់ពីពដម ី ដមស់ ស់ន ុ ន ុក (At service loads)

តមស  (Stress) អន តមតន់ ន់

Stage 1: Stresses immediately after jacking (DL + PT)

 Midspan Stresses ftop = fbot =

(  MDL  Mbal )



S (  MDL  Mbal )

P A



S

P A

ស់ដល ដលង ងក ុ ងក ុង ftop =

(  344. 344.1k 1kNN-m m  155. 155.4k 4kNN-m) m) 0.0876m3



1858 1858kN kN 1.668m2

=  3.27 MPa compression < 16.8 MPa fbot =

(  344. 344.1k 1kNN-m m  155. 155.4k 4kNN-m) m) 0.0876m3



តូចជង ចជង Stress អន ត OK)



(



(



(



(

1858 1858kN kN 1.668m2

= 1.04 MPa tension < 1.32 MPa


 Support Stresses ftop = fbot =

(  MDL  Mbal )



S (  MDL  Mbal ) S

P A



P A


(  366. 366.5k 5kNN-m m  187. 187.7k 7kNN-m) m) 0.0876m3



1858 1858kN kN 1.668m2

= 0.93 MPa tension < 1.32 MPa fbot =

(  366. 366.5k 5kNN-m m  187. 187.7k 7kNN-m) m) 0.0876m3




1858 1858kN kN 1.668m2

=  3.16 MPa compression < 16.8 MPa


ស់ដល ដល ង ងដៅទងសងង ងសងង BUT Borith

31


ftop =

(  29.7 29.7kN kN-m -m  6.5k 6.5kNN-m m) 0.0876m3




1858 1858kN kN 1.668m2

=  0.85 MPa compression < 14.4 MPa fbot =

(  29.7 29.7kN kN-m -m  6.5k 6.5kNN-m) m) 3

0.0876m






(



(



(



(



(



(



(

1858 1858kN kN 2

1.668m



Stage 2: Stresses at service load (DL + LL + PT)

 Midspan Stresses ftop = fbot =

(  MDL  MLL  Mbal )



S

P A

(  MDL  MLL  Mbal ) P



S

A


(  344.1 344.1kNkN-m m  58.7k 58.7kNN-m m  155. 155.4kN 4kN-m -m))



0.0876m 3

1858 1858kN kN 1.668m 2


fbot =


(  344.1k 344.1kN-m N-m  58.7k 58.7kN-m N-m 155.4kN 155.4kN-m) -m) 1858 1858kN kN



0.0876m 3

1 . 6 6 8m 2

= 1.71 MPa tension < 2.95 MPa


 Support Stresses ftop = fbot =

(  MDL  MLL  Mbal )



S

A

(  MDL  MLL  Mbal ) S

P



P A


(  366.5k 366.5kN-m N-m  65.8k 65.8kN-m N-m 187.7kN 187.7kN-m) -m) 1858 1858kN kN



0.0876m 3

1 . 6 6 8m 2

= 1.68 MPa tension < 2.95 MPa fbot =

(  366.5 366.5kN kN-m -m  65.8 65.8kN kN-m -m  187.7 187.7kN kN-m -m))



3

0.0876m


1858 1858kN kN 1.668m


2


ស់ល ល ង ងដៅទងសងង ងសងង ftop =

(  85.4 85.4kN kN-m -m  7.1k 7.1kNN-m m 18.6 18.6kN kN-m -m)) 0.0876m3



1858 1858kN kN 1.668m2


BUT Borith

តូចជង ចជង Stress អន ត OK) 32


fbot =


(  85.4 85.4kN kN-m -m  7.1k 7.1kNN-m m  18.6 18.6kN kN-m -m)) 0.0876m3



1858 1858kN kN 1.668m2





(

តង ី ី ១.១០ ១.១០ : ងេល លរៀៀព រៀៀព  (Stress) ន ុ ុងុ ងុក់ ក់ុ ុងរឌ ងរឌ រុងរតំ ងរតំង កក ុ ុងលក ងលកខណ ខណ

ស ដតន់ ស ន់

ដលង

េីង

(Conditions)

(Stresses)

(Spans)

(Locations)

សងត់ត់ (Compression)

ដៃទញខ ទញខ (At time of jacking)

ទញ (Tension)

ងក ុ ុ ងកង ងដៅ ងក ុ ុ ងកង ងដៅ

សងត់ត់   ់ពីពីដម ដម ស់ន ុ ន ុក (At service loads)

(Compression)

ទញ (Tension)

ងក ុ ុ ងកង ងដៅ ងក ុ ុ ងកង ងដៅ

ក ល គល់តម តម គល់តម តម ក ល គល់តម តម គល់តម តម ក ល គល់តម តម គល់តម តម ក ល គល់តម តម គល់តម តម

តមស  (Stresses) គណ អន ត 3.27 MPa 3.16 MPa

16.8 MPa

1.38 MPa 1.04 MPa 0.93 MPa

1.32 MPa

3.94 MPa 3.91 MPa

15.7 MPa

1.94 MPa 1.71 MPa 1.68 MPa

2.95 MPa

-

គ់ Stresses are within the permissible code limits ។ មខត់ ខត់មិមនត និ តវ វ add nonprestressed bonded reinforcement there, However, nonprestressed bonded reinforcement គឺតវដកន វដកនងគល់តម តម ែលតវគណ វគណ ែូចងដម ចងដម ។

BUT Borith

33



១.២.៣.៤ សិកភដបបស់ កភដបបស់កខណឌ កខណឌ (Deflection Evaluation) The midspan deflection of the column strip or middle strip in an equivalent frame is computed as the sum of three parts: deflection of panel assumed fixed at both ends, plus deflection of panel due to the rotation at th e two support lines

។

  ី ី ១.១៨ ១.១៨ : Panel Layout Plan that Chose to Calculate Deflection BUT Borith

34



សិក ក Deflection ដនអនដមមដសៀវដពី ដមមដសៀវដពី គឺ និង "PRESTRESSED

"PCI DESIGN HANDBOOK HANDBOOK Precast and Prestressed Concrete / 6th Edition" CONCRETE A FUNDAMENTAL APPROACH / 5th Edition"

មតែលត តែលតវស់ វស់គណភព គណភព នែូចជ: ចជ: - h = 260 mm កស់កលខណ កលខណ - b = l = 5800 mm វងេេឹងនដោងកលខណ ងនដោងកលខណ - h = 410 mm slab band កស់ slab - b = 1500 mm វងេេឹង slab band k =  27.29 7.2910 E  mm-N/ra /rad Column stiffness factor, E គិតជ តជ N/mm - w = 7.08 kN/m ន ុ ន ុក self-weight - w = 4.17 kN/m ន ុ ន ុក Superimposed dead load - w = 1.92 kN/m ន ុ ន ុក Live load - w = (w + w ) = 11.25 kN/m ន ុ ន ុក Total Dead load - P = 1858 kN ក ងស់ ក ង ស់ខស - a = 245 mm ែឃ ស់ស់ខ ខ s

sb

sb

6

ec

2

sw

2

SDL

2

LL

D

2

c

c

sw

2

SDL

INT

សិកកភព កកភព initial អនដមមដសៀវដ ដមមដសៀវដ "PRESTRESSED CONCRETE A FUNDAMENTAL APPROACH / 5 Edition" ទ ទងអស់ ង អស់ ។ ។ ស់ prestressed Class U (uncrack) slab, it shall be permitted to calculate deflection based on " I " ។ W L I = I 9.34) ែល (  ' = 384EI th

g

4

cs

g

cs

ដយងនម ូមមង់ងនិន់ ចលភពនដោងមួ ិចលភពនដោងមួយទ យទងមូ ង មូល Ig

bh  (580 (5800 0mm  1500 1500mm mm))  (2 (260mm 60mm))3   1500 1500mm mm (410 (410mm mm))3  = =   12  12 12   

= 1.47 .47 1010 mm4



ភពដយន ុ ុក uniform ដក លល ភពដយន លល ងែលសនតដច ដ់ ចងតម Fixed ទងសងង ង សងង ូមឌឌលដអឡស លដអឡសចដៃ ចិ ដៃទញ ទញ ដពលដតងនយ 10 ៃ f '  28 MP MPa E = 4700 4700 f ' ូមឌឌលដអឡស លដអឡសចស់ ចិ ស់ដត ដតងគ់ ងគ់យ យ 28 ៃ f ' =35MPa E = 4700 4700 f ' ci

ci

c

BUT Borith

c

35



តង ី ី ១.១១ ១.១១ : លភដ់ ភដ់ទ ទ ុ ុ  ិ ិួួយៗ ម យៗ ម់់ចុ ចុងររឌ ងររឌ Fixed ំងងខង ងងខង  ត់ពីពទញភ  ទី ញភ មៗ f ' = 28MPa

35MPa  ត់ពីពដ  ដី ស់ ស់ន ុ ន ុក f ' = 35MPa c

ci

Deflection at

Prestressed force

Self-weight

Superimposed

(load balancing)

= W

Live load

Dead load

8P  aINT

= ( wsw  l )

= ( wSDL  l )

= ( wLL  l )

= - 27.5

= 41.1

= 24.2

= 11.1

L2

(kN/m)

L

(mm)

11500

11500

11500

11500

E

(MPa)

24780

24780

27800

27800

5.1

2.7

1.2

 ' =



W  L4 384EIcs

(mm)

-

3.4

ភពដនតវសតដនឹ វសតដនឹងភព ងភព  ស់ column strip និង  ស់ middle strip c

c =  '  s =  '

s

Mcol,strip E I c cs

(9.34a)

Mframe Ec Ic

Mslab,strip Ec Ics Mframe Ec Is

ខទងអស់ ងអស់ 20 Stands តវនយដក ុ ុ វនយដកង Column strip ទងអស់ ង អស់ ែូដច ដចដមគណម ណ ូមមង់ងដដល ដ់ ដល

Mcol,strip =

ឬ MM

និង

col,strip

= 1.0

frame

20strained of Mframe = 1.0Mframe 20strained

Mslab,strip Mframe

=0

ដយម យ ូមមមង់ង និន់ ចលភពស់ ិចលភពស់ Middle Strip និង Column Strip នតមមិនដស នដសដេដ េ ដកស់កលខណ កលខណ មិនដស នដសោ  ដ Column Strip នកស់ Slab band 410 mm និងេេឹ ងេេឹង 1500 mm គឺ  5800mm  1500m  1500mm m  (260mm (260mm))3    1500mm ( 410mm)3  bh 2 Ic = =   12  12 1 2     





= 1.07 1010 mm4

Is = Ics  Ic = 1.47 1010 mm4  1.07 1010 mm 4 = 0.40 .40 1010 mm4

BUT Borith

36



តង ី ី ១.១២ ១.១២ : លភដងច ភដងច Column & middle strip ម់ចុ ់ ចុងរ ងរ Fixed ំងងខង ងងខង Deflection at

Prestress

Column Strip,  c (mm) Slab Strip,  s

(mm)

-

Self-weight

Superimposed dead load

Live load

7.0

3.7

1.7

0

0

0

4.7 0

ភពស័យជមួ យជមួយម ង  ិងលទ លទងសងង ង សងង



តង ី ី ១.១៣ ១.១៣ : ងេល ល ៉៉ង៉ ់ net ់ទ ទ ុ ុ  ិ ិួយៗ ួយៗ  ី ីក ក់ ់ង៉ ង៉ ៉៉ងំ់ ំងងខងែ ងងខងែង ូមមមង់ង នមកពី ់ នមកពីន ុ ន ុក

ូមមមង់ង ដគល់ ដ់ គល់តម តម (At support) Interior span

់ net (M = M ) ូមមមង់ង net A

Cantilever slab

F

(Interior - Cantilever)

Total Dead Load

602.0 kN-m

85.4 kN-m

Live load

106.0 kN-m

7.1 kN-m

98.9 kN-m

Load balance

296.9 kN-m

17.9 kN-m

279.0 kN-m

Self-weight = WSW    Total dead load   WDL 

Superimposed dead load = WSDL 

  Total dead load   

WDL

-

7.08    85.4 kN-m   11.25 

7.08    602 kN-m   11.25 

= 378.9 kN-m

4.17    602 kN-m   11.25 

= 53.7 kN-m

325.1 kN-m

4.17    85.4 kN-m   11.25 

= 31.7 kN-m

= 223.1 kN-m

191.5 kN-m

តង ី ី ១.១៤ ១.១៤ : លភដ់ ភដ់ទ ទ ុ ុ  ិ ិួយៗ ួយៗ អរ័យ យ ឹ ឹង៉ ង៉ ៉៉ងងែ់ ងែ ិគ់ គ់ររឌ ររឌ ំងងខង ងងខង Deflection at M A = MF  A =

 F =

 '' =

MA

K ec MF K ec



BUT Borith

A

  F   L 8

Prestress

Self-weight

Superimposed DL

Live load

(kN-m)

279.0

325.1

191.5

98.9

(rad)

0.00037

0.00043

0.00025

0.00013

(rad)

0.00037

0.00043

0.00025

0.00013

1.2

0.7

0.4

(mm)

-

1.1

37





សភពមេិ ភពមេិសដ សដ Long cy = c   ''

(9.36a)

 sy =  s   ''

(9.36b)

តង ី ី ១.១៥ ១.១៥ : លភដុ ភដុ ់ទ ទ ុ ុ  ិ ិួយៗត យួ ៗត ិ ិ  Long Deflection at

Prestress

Self-weight

Superimposed

Live load

Dead load

cy = c   '' (mm)

-

3.7

8.3

4.4

2.1

 sy =  s   '' (mm)

-

1.1

1.2

0.7

0.4

ដយងន ងនមតស់ តស់ េិ េិសដ សដ Short b

= l = 11500 mm

L

= 5800 mm

h

= 260 mm

wb = 70%(Wsw) = 0.7 [(0.26m11.5m)23.6kN/m3] = 49.4 kN/m aINT = h - cgs = 260 mm - 40 mm = 220 mm P =

Wb l2 8aINT

49.4kN/m 49.4kN/m (11.5m) 11.5m)2  3712 kN = 8  0.22 0.22m m

ដយងនម ងនម ូមមង់ង ន់ ចលភពនដោងមួ ិចលភពនដោងមួយទងមូ ងមូល Ics



bh 11500 11500mm mm (260mm (260mm)) 3 = = = 1.68 1010 mm4 12 12

ភពដយន ុ ុក uniform ដក លល ភពដយន លល ងែលសនតដច ដ់ ចងតម Fixed ទងសងង ង សងង ូមឌឌលដអឡស លដអឡសចដៃ ចិ ដៃទញ ទញ ដពលដតងនយ 10 ៃ f '  28 MP MPa E = 4700 4700 f ' ូមឌឌលដអឡស លដអឡសចស់ ចិ ស់ដត ដតងគ់ ងគ់យ យ 28 ៃ f ' =35MPa E = 4700 4700 f ' ci

ci

c

BUT Borith

c

38



តង ី ី ១.១៦ ១.១៦ : លភដ់ ភដ់ទ ទ ុ ុ  ិ ិួួយៗ ម យៗ ម់់ចុ ចុងរ ងរ Fixed ំងងខង ងងខង  ត់ពីពទញភ  ទី ញភ មៗ f ' = 28MPa

 ត់ពីពដ  ដី ស់ ស់ន ុ ន ុក f ' = 35MPa

ci

Deflection at

Prestressed force

c

Self-weight

Superimposed

(load balancing) =

W

Live load

dead load

8P  aINT

= (wsw  b)

= (wSDL  b)

= (wLL  b)

= 194.2

= 81.4

= 48.0

= 21.1

L2

(kN/m)

L

(mm)

5800

5800

5800

5800

E

(MPa)

24780

24780

27800

27800

0.7

0.3

0.2

 ' =



W  L4 384EIcs

(mm)

-

1.6

ភពដនតវសតដនឹ វសតដនឹងភព ងភព  ស់ column strip និង  ស់ middle strip c

c =  '

 s =  '

s

Mcol,strip E I c cs

(9.35a)

Mframe Ec Ic

Mslab,strip E I c cs

(9.35b)

Mframe Ec Is

ខត់មេិសដនក សដនក ុ ុមដយ មដយងខ ុ ុខ មិមននគណសិ និ នគណសិកកដេ កកដេ ដយខមេិសដនដយ សដនដយងពយដស ងពយដសោ  (distribute) ដពញដោងកលទងមូ ងមូល ។ នន័យ យ ខក់ក ក ល តវនយដក ុ វនយដក ុង Column strip និងក់ ងក់ ក លដេៀតយដល middle strip ។ ែូដច ដចដមគណម ណ ូមមមង់ង ដដល ដ់ ដល Mcol,s l,strip

ឬ

Mcol,strip  Mmid,strip  0.5 Mframe

Mframe



Mmid, id,strip trip Mframe

 0.5

ដយម យ ូមមមង់ង និន់ ចលភពស់ ិចលភពស់ Middle Strip និង Column Strip នតមដសនឹង ូមមមងនិ់នចលភពនដោងមួ ចិ លភពនដោងមួយ ទងមូ ង មូលចកនឹង ២ គឺ

Is  Ic 

Ics 2

ឬ

Ics Is



Ics Ic

 2.0

តង ី ី ១.១៧ ១.១៧ : លភដងច ភដងច Column & middle strip ម់ចុ ់ ចុងរ ងរ Fixed ំងងខង ងងខង Deflection at

Prestress

Self-weight

Superimposed dead load

Live load

Column Strip,  c (mm)

-

1.6

0.7

0.3

0.2

Slab Strip,  s (mm)

-

1.6

0.7

0.3

0.2

BUT Borith

39



ដយ Span មេិសដន សដន នវងហក់លោ លោ (5300 mm, 5800, 5875mm) ឲដគសន ឲដគសនត់តម តម net moment ដតង់សសនីមួ មយៗ យួ ៗ ែល លពី លសងនម ូមមង់ង អវ អ់ វរនទ ា នទងសងង ងសងងសស សស នតមតូចដស ចដសត  ត ដសសូស ននូ  ។ ែូចដនដគន ចដនដគន តម net rotate  = 0   '' = 0.0 mm (ភពដយម ង Slab)  ិងលដគល់ លដគល់តមស់ តមស់ Slab)  សភពមេិ ភពមេិសដ សដ Short cx = c   ''

(9.36a)

=    ''

(9.36b)



sx

s

តង ី ី ១.១៨ ១.១៨ : ុភដរង់ ភដរង់ Column  ិង middle strip ់ទ ទ ុ ុ  ិ ិួួយៗត យៗត ិ ិ  Short Column ិ Deflection at

Prestressed force

Self-weight

(balance load)

Superimposed

Live load

dead load

 cx (mm)

-

1.6

0.7

0.3

0.2

 sx (mm)

-

1.6

0.7

0.3

0.2



   sx  cy

  

sy



 cx

(9.37)

ែូចដន ចដន   

 

 E  W  sx   cy NS

BUT Borith

sy

  cx

40



តង ី ី ១.១៩ ១.១៩ : លភដ ភដ ( ) រង់ចំចំុចុ ណ រឌ រឌ ់ទ ទ ុ ុ  ិ ិួយៗ យួ ៗ i

Conditions

Prestressing

Deflection due to Gravity Loads

balance load

Self-weight

Superimposed DL

Live load

(Wbal)

(Wsw)

(WSDL)

(WLL)

-

4.3

9.0

4.7

2.3

 Long

(mm)

 Short

(mm)

-

2.7

1.9

1.4

0.6

  Long   Short   (mm)  i =    2  

-

3.5

5.5

3.1

1.5

សិកដ កដងផ ងផ ត់ភព ភព កលខណ កលខណ ដតងដក ងដកង ងងដនអន ងដនអនដមមងដក ុ ុ ដមមងដកងដសៀវដ ងដសៀវដ " PCI Design Handbook Precast And Prestressed Concrete " (6th Edition)_Table 4.8.4.1/ page 4-94 ។ ែលដគនដ ង ផ ត់ ជីែែក់ ក់លស លសន់ ន់ៗ គឺៈ (1a). ដ ងផ ងផ ត់ដដពលដគទញខភ ដពលដគទញខភ មៗ (At Release) ដយមិនទន់ នទន់នដ នដស់ ស់ន ុ ន ុកអីទងអស់ ង អស់ គឺនតេ នតេងន់ ងន់ self-weight ស់កលខណ កលខណ និងក ងក ងដល ង ដលកស់ កស់ខ ខ ។ (2a). ដ ងផ ងផ ត់ដដពលទញខួចចដ ចចដ ពី ១ ១ ដ ២ខ ដគដដពលងសង់ (At erection) ដពលដ នេងន់ ងន់ self-weight ជមួយក យក ងដល ង ដលកស់ កស់ខ ខ និងនដស់ ស់ន ុ ន ុក Superimposed dead load ែូចជ ចជ ដៀ ូ ព័ ព័នធនធ M/E និងដៀរ ងដៀរា ងឥែ ង ឥែជដែម ។ (3a). ដ ងផ ងផ ត់ដដពលងសង់ួចដ ចដយ នយៈដពលយូ់ ់ពីព ៥ ី ៥ ឆឆ ដ ដ ងដ ងដ (At Final) នន័យដពល យដពល កលខណ កលខណ ងដមន ុ ងដមន ុកែលដដលយូ យូ (sustained load) ដ ឲនភពនថ ឲនភពនថមដយឥេធ មដយឥេធ ិ ពល Creep & Shrinkage in concrete និងតង់ ងតង់ភពស ភពសតិ យឺតស់ខក ុ ុ ខកងយៈដពលយូ ងយៈដពលយូ ។

BUT Borith

41



តង ី ី ១.២០ ១.២០ : Suggested simple span multipliers to be used as a guide in estimating long-term cambers and deflections for typical prestressed members

(1a). At Release :

  1.00i (bal)  1.00i (sw)

(2a). At Erection:

  1.80i (bal)  1.85i (sw)  1.00i (SDL)

(3a). At Final :

  2.45i (bal)  2.70i (sw)  3.00i (SDL)  1.00i (LL)

តង ី ី ១.២១ ១.២១ : លភដ ភដ () ន ុ ុងេ ងេឌ ឌ យៈ ិ ិួួយៗ យៗ Deflection (  ) at

Deflecti-on by loads i

(1a). Release

(A) Wbal

3.5 mm

-

Wsw

5.5 mm

WSDL

3.1 mm

WLL

1.5 mm

Results

BUT Borith

-

(2a). Erection

(3a). Final

Multiplier

Results

Multipier

3.5 mm

1.80(A)

= - 5.3 mm

2.45(A)

= - 8.6 mm

5.5 mm

1.85(A)

= 10.2 mm

2.70(A)

= 14.9 mm

1.00(A)

=

3.00(A)

=

9.3 mm

1.00(A)

=

1.5 mm

2.0 mm

3.1 mm

8.0 mm

Results

17.1 mm

42



តង ី ី ១.២២ ១.២២ : ទ ងផ ទ ងផទទ ់ជួ ជួយល យលភដុ ភដុញា  ន ុ ុងេ ងេឌ ឌ យៈ ិ ិួយៗ យួ ៗ Deflection at

Calculate

Allowable*** [ACI 318M-14]

(mm)

(mm)

(1a). Release

2.0

(2a). Erection

8.0

(3a). Final

17.1

Æ L/360 = 31.9 Æ L/360 = 31.9 Æ L/480 = 23.9

Description

Ok Ok Ok

និង L/480 ជតមភពអន ត នន័យដ យដតមភពស់កលខណ កលខណ តូចជង   ចជងណ ណងឹ គឺ ស់ែលដដល ែលដដលកលខណ កលខណ ែូចជ ចជ  ូ រ រា ងឥែ ង ឥែ ឬ ឬ រា ងកា ង កាក និ ់ និងទ ងទ  ង ច មិននដខូ ននដខូច ។

Allowable*** L/360

១.២.៣.៥ សិក ក Ultimate Strength The primary post-tensioning

ូមមមង់ង M ់ M លដមវងល លដមវងលង 1

M1 = P  e

e

ដតង់ ់គល់ គល់តម តម (ចៃ ចៃ យពី neutral axis ដអ័កស់ កស់ខ ខ)

= 15 mm

M1 = 1858 kN  0.015 m = 27.54 kN-m

ូមមមង់ង ដន ដ់ នលជ ជ ត់តង់ តង់ដចដ ចដ ល ល ង Msec = Mbal  M1 = 296.9 kN-m  27.9 kN-m = 269.0 kN-m

  ី ី ១.១៩ ១.១៩ : Moment due to Secondary Post-Tensioning BUT Borith

43


Combined loads


ជមួយដមគ យដមគណ (factored moments) ដែមបីមបីយកម យកម ូមមងដសិ ់ដសិកកច កកចនួននែក នួ ែក ែលកល

ខណ ខណ តវដ វដស់ ស់ ។ Mu = 1.2 MDL + 1.6 MLL + 1.0 Msec

ដតង់ midspan: M = 1.2 (344.1 kN-m)  1.6 (58.7 kN-m)  1.0 (260.0 kN-m) u

= 766.8 kN-m

ដតង់ support:

Mu = 1.2 (366.5 kN-m)  1.6 (65.8 kN-m)  1.0 (269.0 kN-m) = 814.1 kN-m

តង ី ី ១.២៣ ១.២៣ : ងេល ល Combined for ultimate strength desing



េីងម ង ូមមមង់ង ដតង់ ដ់ តង់

តម ូមមម ងស ស់  គិតា តា លនដមគ ណ

ក លដល លដល ង (Midspan)

766.8 kN-m

គល់តមទ តមទងសងង ងសងង (Support)

814.1 kN-m

គណ minimun bonded reinforcement Bonded reinforcement is meant to ensure flexural continuity and ductility and to limit crack width and

spacing due to overload, temperature or shrinkage s hrinkage

។

ូមែលកលខណ ែលកលខណ ដនគឺដ ដ Slab band (wide shallow beam) ។ ដក ុ ដក ុងសិក ក Strip design ែលជ band slab ម Recommend ែលែកដចញពី " ADAPT Technical Note /page /page 04 " គណកសសែក គួតដ តដ ដម equivalent uniform slab thickness (h ) ។ h Û 300 mm មគណងដល e

e

Minimum negative moment at column reinforcement required ft  0.5 f 'c As,min = 0.00075Acf

ែល

(ACI 318M-14_8.6.2.3/ page 105)

Acf = max[ (L /2 , l2 )he ] = (11500mm /2) 300 mm = 1725000 mm2

As,min = 0.00075 1725000 mm2 = 1294 mm2 BUT Borith

44



ដស់ ស់ែកស ែកសគឺ គឺ 12DB12 Top (A = 1356 mm )  ងតិច ដស់ ស់ែក ែក 4DB12 Top ដយគ យគ តមិនឲដល នឲដលស 300 mm 1/6 of clear span វងែកែលតវក់ វក់តតន់ ន់ ូមមមម ង់ង ់វរន ា ន ងខី 1/6 2

s

ACI 318M-14_8.7.5.3/ page 110) ( ACI ACI 318M-14_8.7.5.5.1/ page 111) ( ACI

Minimum positive moment reinforcement required



(ACI 318M-14_Table 8.6.2.3/ page 105)

លងងក ុ ុ ងកង 0.17 f c = 0.17 0.17 35 MPa= 1.0 1.0 MPa MPa = 1.71 MPa > 0.17

y

=

=

Nc

តវគណកែកដ វគណកែកដស់ ស់ែូែចងដម ចូ ងដម

'

f t

=

f t



ft  f c



 he

where (f t & f c is stress at service load)

1.71 MPa



1.71 MPa  3.94 MPa



 300 m m = 90.8 mm

1   ft  y   l2  2

1 =   1.71N 1.71N mm2  90.8 90.8 mm  5550m 5550mm m = 4311 431121 21.0 .0 N 2  

  431121.0 N Nc     2211 mm2 A s,min =  0.5 f  0.5 0.5  390 390 N 2 y   mm

  ី ី ១.២០ ១.២០ : Stress Distribution ***

ស់ Slab with bonded tendons, it shall be permitted to reduce A

s,min by

the area of the bonded prestressed

។ (កឡស់ ស់ខស ខសទ ទង 20 Strands)

reinforcement (Aps) located within the area used to determine Nc for positive moment (ACI 318M-14_Table 8.6.2.3) Aps

= nuber of strands  Aps = 20  98.71 mm2 = 1974 mm2

***

ម Code ងដលនន័ នន័យកឡ យកឡែក ែក non-prestressing គួតដ តដដពញមួ ដពញមួយេេឹ យេេឹង Strip = 5550 mm As,used

= As,min - Aps = 237 mm2

ដយេីងខដយ ង ខដយងក់ ងក់តក ុ ុ តកង Slab Band នេេឹងត ងត 1500 mm ដសនងឹ 27% (1500/5500) នេេឹងស ងស ែល ដស 5550 mm ែូចដនដយ ចដនដយងគិត កឡស់ ស់ខត ខត 27% ដេ ែលយកមករួយកឡ យកឡែក ែក non-prestressing ។ As,used

= As,min - 27% of Aps = 2211 mm2 - 0.27  1974 mm2

BUT Borith

45



= 1678 mm2 = 15-DB12@370mm

យក ុ ុ យកងមួ ងមួយេេឹងដស 5550 mm

ACI 318M-14_8.7.2.2/ page 106) គ តែក maximum @450mm គ ( ACI ី 1/3 of clear span ( ACI ACI 318M-14_8.7.5.5.1/ page 111) វងែកែលតវក់ វក់តតន់  ន់ ូមមម ង់ង់វរានក នក លល លល ង ង ងខ 1/3 តដែមបីមបីសម សមលងសង់ែកដនដយ ែកដនដយងយដពញមួ ងយដពញមួយកលខណ យកលខណ  លងងដៅ (cantilever slab) នត compression stressed ' .17 f c ( ft  0.17

=> Not required)

Minimum positive moment reinforcement not required

(ACI 318M-14_8.6.2.3/ page 105)

ែូចដនម ចដនមខត់ ខត់តន់ ន់ ងដមនកលខណ ងដមនកលខណ ល ល ងងដៅ (cantilever slab) មិនត នតវក់ វក់ែក ែក ។ 





 Mn =  A s fy +A psfps  d e  



a



2 

de

= effective depth

dp

ែល z ជចយគិ យគិតពី តពីអ័អកខ ក័ ខ (Tendon) ដអ័ក កពង់ ពង់ខ ខ (Duct)  d /2  z)] = h  [cover  d , d ជេ កម ក មសស់ ់ ស់ពង់ ព ង់ខ ខ (Duct) = 300 mm  [20 mm 12 mm (20 mm /2  4 mm)] ,d ជេ ស់ែក ែក (Rebar) = he  [cgs  z] e

,

rebar

duct

duct

rebar

= 254 mm dr

= he  (cover  drebar /2) = 300 mm  (20 mm 12 mm /2) = 274 mm

de

= dr  [(dr  dp) /2] = 274 mm  [(274 mm  254 mm) /2] = 264 mm

  ី ី ១.២១ ១.២១ : Geometry and Reinforcement Aps = 98.71 mm2(number of Strands) = 98.71 mm2  (20 Strands) = 1777 mm2

fps

   f  dr f y    p pu         '    p = fpu 1      1  f 'c dp f ' c  

BUT Borith

(ACI-318M-14_20.3.2.3.1/page 331)

46



តង ី ី ១.២៤ ១.២៤ : Values of 

p (ACI-318M-14_Table

f py f pu

 dr dp

=

0.90f pu 1860MPa

= 0.90  0.90



20.3.2.3.1/page 331)

 p = 0.28

ដ ងផ ងផ ត់ដគល់ ដគល់តម តម = 274 mm (កមសសិ bounded reinforcement) ់ សិេធេភពស់ ធភពស់ bounded = 254 mm (កមសសិ bounded Tendons) ់ សិេធេភពស់ ធភពស់ bounded

តង ី ី ១.២៥ ១.២៥ : Values of for equivalent rectangular concrete stress distribute 

1

 1 = 0.85 

 p =

 =

d'

A ps bdp A s

=

=

bdr

0.05 (35MPa (35MPa  28MPa 28MPa)) = 0.80 7

1777mm2 5550mm  254mm 1356mm2 5550mm  274mm

= 0.00126

(ACI-318M-14_Table 22.2.2.4.3/page 349)

ែល b = l = ជវងេេឹងស ងសស់ ស់ Strip 2

= 0.00089

ដជង ជង 0.15d ែកដតន់ ន់សង សងត់ត់មិមនគិ និ គិតា តា ល p

d'

= (120 mm + 12mm /2) = 126 mm > 0.15(174 mm) = 26.1 mm



 '

(ACI 318M-14_20.3.2.3.1/ page 331)

មិនគិ នគិតា តា ល

 0.28    1860MPa 274mm 390MPa fps = 1860MPa 1 0.00089     0.00126   35MPa 25 2 54mm 35MPa  0.80    = 1809.4 MPa a

BUT Borith

=

 A f

s y

 Aps f ps



0.85f'c b

47



a

1356 1356mm mm  390M 390MPa Pa  1777 1777mm mm  1809 1809.4 .4MP MPaa  = = 22.7mm

c

=

2

2

0.85 0.85 35MP 35MPaa  5550 5550mm mm

a

= 27.6 mm 0.85 = hs  Cover  db

dt

= 260 mm -20mm -12mm = 228 mm

 d c t  c 

=

 t

   0.003 = 0.023  0.005   

 = 0.9 (tension-controlled section)

  M = 0.9  13 1356mm2  390MPa  17 1777mm2 1809.4MPa 







  264mm 

22.7mm     = 851.4 kN-m 2  

851.4 kN-m N-m  M u  814 814.1 kNkN-m  M = 851

ែកែលដស់ ស់មគណងដល មគណងដលដគល់ ដគល់តម តម គឺគ់ គ់ោន់ ោន់ដ ដយស់ យស់េ់ េ់ក ក ងម ង ូមមមង់ង ងដៅ ់ ងដៅ ។ ពយែកកត កតន់ ន់ងដល ងដលជ់ ជ់សស សស   ងតិច 1.5h (h ជេ ស់  ស់សស) សស) គឺ 1.5  700 mm = 1050 mm ដយ (ACI 318M-14_8.7.5.3/ page 110) គ តស់ែកមិ គ ែកមិនឲដល នឲដលស 300 mm 12mm គ ដស់ ស់ែក ែក ង 10 ដែមេ មេ  12mm គ ត 100 mm គិតពី តពីអ័អ័កដអ័ កដអ័កក ដស់ ស់ែកស ែកសគឺ គឺ 20DB12 Top (As = 2261 mm ) ដគល់តមទ តមទងសងង ងសងង 2

 dr dp 

ដ ងផ ងផ ត់ដក ដក លល លល ង = 274 mm (កមសសិ bonded reinforcement) ់ សិេធេភពស់ ធភពស់ bonded = 254 mm (កមសសិ bonded Tendons) ់ សិេធេភពស់ ធភពស់ bonded =

A s bdr

=

1678 mm2 5550mm  27 274mm

= 0.011

 0.28    1860MPa 274mm 390MPa   fps = 1860MPa 1 0.0011   0.00126  35MPa 25 2 54mm 35MPa  0.80    = 1807.8 MPa

1678mm mm  390M 390MPa Pa  1777 1777mm mm  1807 1807.8 .8MP MPaa 1678 = 2

a

2

0.85 0.85 35MP 35MPaa  5550m 5550mm m

= 23.4 mm

c dt

=

a

= 27.6 mm

0.85 = hs  Cover  db

= 260 mm -20mm -12mm = 228 mm BUT Borith

48



 d c  t   0.003 = 0.022  0.005   = 0.9 (tension-controlled section)  c      23.4mm  2 2  M = 0.9 0.9  1678m 678mm m  390M 390MP Pa  1777m 777mm m 180 1807.8M 7.8MPa Pa   264m 264mm m   2     t

=





= 878.0 kN-m

 M = 878.0 878.0 kN-m kN-m  Mu = 793. 793.0 0 kN-m kN-m

ែកែលដស់ ស់មគណងដល មគណងដល គឺ គឺគ់ គ់ោន់ ោន់ដ ដយស់ យស់េ់ េ់ក ក ងម ង ូមមមង់ង ងដៅ ់ ងដៅ ។ ដស់ ស់ែកស ែកសគឺ គឺ 15DB12@370 mm Bottom (A = 1696 mm ) ដគល់តមទ តមទងសងង ងសងង 2

s

តង ី ី ១.២៦ ១.២៦ : ុងេ ងេ៉ ៉ ៉៉ង ់ M ជួយ យ ឹ ឹង M n

លកខណ ខណ ទង ៤ Mn  Mu

Mn  f M Msc

u

តមក ង (Strength) Mn

= 851.4 kN-m

Mu

= 292.0 kN-m

ពីពណ៌ ពណ៌ដល ដលមមខត់ ខ ត់ (OK) គ់ោន់ ោន់ (OK)

(OK) គ់ោន់ ោន់ (OK)

Mn = 851.4 kN-m f M Msc = 292.0 kN-m

តង ី ី ១.២៧ ១.២៧ : ងេល ល  nonprestress reinforcement រូវរើ វរើរ់ រ់ន ុ ុងរឌ ងន រឌ េីងត ងតវពយែក វពយែក

តមចនួន ួនែកែលត នែកែលតវដ វដ

េេឹងពយែក ងពយែក

វងដស់ ស់ែក ែក

គល់តមទ តមទងសងង ងសងង

20DB12 At Top

1/6 clear span

(Support)

(As = 2261 mm2)

យសងងសស  ង 10 ដែមគ មគ ត 100 mm

ក លដល លដល ង

13DB12@400 mm At Bottom

ដពញេេឹង

1/3 clear span

(Midspan)

(As =1696mm2)

BUT Borith

ឬ យដពញទងអស់ ងអស់

49



១.២.៣.៦ សិក ក Shear Strength

ដក ុ ដក ុងកលខណ កលខណ និងដរ ងដរងង Shear strength ដរ វញ ញដវណ ដវណ សស ន ុ ន ុកមូល ុ ុ ល  ឬ ឬ កឡតិ តិកម គឺ ដក ដកតដចញពី តដចញពីមូមលដត លូ ដតជដច ជដចនដក ុ ុ នដកងលក ងលកខណ ខណ ពីគឺ គឺៈ 

Wide-beam action, or one-way shear



Two-way action, or two-way shear

  ី ី ១.២២ ១.២២ : (a) Beam-type Beam-type failure. (b) & (c) Punching Punching shear around columns សិកស់ កស់ one-way action ចដម ដមខត់ ខត់ដោ ដោ ក់ែលត ែលតវគណ( វគណ(Critical shear section) គឺគិគតច ិតច យ d ពី ជយស់ ជយស់មមខត់ ខ ត់សស ។ ក ងត់ ង ត់េេឹ េេឹង (shear force) ដចេីេីង critical section គឺនមកពី នមកពី ultimate reaction (V ) ដដល កឡ កឡ (Tributary Area) of A (the critical shear section) ។ u

c

  ី ី ១.២៣ ១.២៣ : Tributary Area and Critical Sections for One-Way Shear BUT Borith

50




ន ុ ុកែលនអដពដពដល ន ដលកលខណ កលខណ ពមទងគិ ងគិតា តា  លទ លទងេ ង េងន់ផ ល់ស់ ស់កលខណ កលខណ ងែន w = 7.08 kN/m ន ុ ន ុកផផ ល់ស់ ស់កលខណ កលខណ w = 4.17 kN/m ន ុ ន ុកនថមែូ មែូចជ ចជ  ូ យអ យអ រា ង និង M/E w = 1.92 kN/m ន ុ ន ុកដមស់ ស់ដស ដស (1m ) ន ុ ុកសនដមគ ន នដមគណគិ ណគិតក ុ ុ តកង ១មតដ តដ (1m 2

SW

2

SDL

2

LL




2

qu

= 1.2(wSW + wSDL) + 1.6wLL = 1.2 (4.17 kN/m2 + 7.08 kN/m2) + 1.6 1.92 kN/m2 = 16.57 kN/m2

និង មតដងដេៀតស់ តដងដេៀតស់ក ក V និង V មកដ តផ តផ ត់  = 1.0 ស់ normal concrete  = 0.75 ស់ shear reduction u

M0 = =

Mu =

qu  l2  L2

n

Total static moment

8

16.57kN/m 16.57kN/m2  5.550m (11.50m) (11.50m)2 8

0.65

 1  1     ec  

 M0

មេិសវង សវង

= 1520.5 kN-m (STRUCTURAL (STRUCTUR AL CONCRETE Theory and Design_17.8.7/ page 612)

 ce =

Mu =



0.65  1   1    4.7 

 1520.5 = 814.9 kN-m

dp

= 254 mm

d

= 264 mm

bw

= l2 = 5550 mm

ln

= 4600 mm

(ACI 318M-14_8.10.3.2/ page 120)

kec



27.2 27.299  106 Ec

 ូមមមង់ង ់លង  លង(distribution) ដតង់គល់ គល់តម តម ( ks  kb )

5.809 10 1 06 E c  0

= 4.7

រដសិេធេភពស់ ភធ ពស់ ខ រដសិេធេភពស់ ភធ ពស់ ែកជមួយខ យខ េេឹងម ងមខត់ ខត់ែលង ែលងង ដមលក ុ ុ លកងូ ងូេី េី ១.២៣ ១.២៣ ងដល

ក ងត់ ក ង ត់ែលនអ ែលនអដពដពដល ដលមខត់ ខ ត់ដោ ដោ ក់ (Critical shear section) Vu

= qu (ln  l2) = 16.57 kN/m2(4.6 m 5.550 m) = 441.5 kN

BUT Borith

51





លេធ ិភពេ់ ភពេ់នឹនឹងក ងក ងត់ ង ត់អន អន ត មលកខណ ខណ និមួមយៗ យួ ៗ 

Vc1 =  0.05    f 'c  4. 4.8 

(ACI 318M-14_Table 22.5.8.2/ page 355)

Vu  dp 

 

Mu

  bw  d  

 441.48kN 441.48kN 0.254m 0.254m =  0.051.0 35MPa  4.8MPa   5550mm 264mm  814.9kN-m   = 1384.4 1384.4 kN





Vc2 = 0.05    f 'c  4.8  bw  d

  =  0.05 0.05 1.0 1.0 35MPa 35MPa  4.8 4.8MPa MPa  5550 5550mm mm 264m 264mm   = 7466.4 7466.4 kN





Vc3 = 0.42    f 'c  bw  d   =  0.42 0.421.0 1.0  35MP 35MPa a   555 5550mm 264 264mm  

= 3640 3640.7 .7 kN



លេធ ិភពេ់ ភពេ់នឹនឹងក ងក ងត់ ង ត់អន ត ស់ដត ដតង 

Vc = min Vc1, Vc2 , Vc3



  = min 1384.4kN, 1384.4kN, 7466.4kN, 7466.4kN, 3640.7kN 3640.7kN = 1384.4 kN  



លេធ ិភពេ់ ភពេ់នឹនឹងក ងក ងត់ ង ត់អន ត ស់ែក ែក Vs = 0.066 f 'c  b w  d

(ACI 318M-14_22.5.1.2/ page 352)

= 0.066 0.066 35MPa 35MPa  5550mm 5550mm  264mm = 572.1 kN



លេធ ិភពេ់ ភពេ់នឹនឹងក ងក ងត់ ង ត់អន តស (ដតង ែក) +

Vn = Vc  Vs

(ACI 318M-14_22.5.1.1/ page 351)

= 1384.4 kN  572.1 kN = 1956.5 kN  Vn = 0.75 0.75 1956 1956.5kN .5kN

= 1467.4 kN

ដយ V = 1467.4 kN > V = 441.5 kN ែូដច ដច ដយងដ ងដញម ញមខត់ ខត់កលខណ កលខណ គឺគ់ គ់ោន់ ោន់ដយ មិននងមួ ងមួយេិ យេិស (one-way shear) ។ ដយ Shear reinforcement not required ចដទ ដទងពី ងពី សស ។ n

BUT Borith

u

52



មខត់ ខត់ដោ ដោ ក់ែលត ែលតវគណ( វគណ(Critical shear section) គឺ ពី ជយស់ ជយស់មមខត់ ខត់សស សស ែូចែលន ចែលន ញក ុ ុកងូ ងូងដម ងដម ។ Shear stresses ែលគិតា តា  ល Shear force ដ critical section និង fraction of transfer moment transferred by shear to the columns ។ ក ងត់ ង ត់េេឹ េេឹង (shear force) ដចេីេីង critical section គឺនមកពី នមកពី ultimate reaction ដតង់គល់ គល់េេ ឬ សស ែក ន ុ កុ នដមគណែលដដល ណែលដដល កលខណ កលខណ ែលខ័ណ ដយ ត ត b of A (the critical shear section) និងនតម ងនតមដស b = (c  d )(c  d ) ។ d 2

o

c

o

1

e

2

e

  ី ី ១.២៤ ១.២៤ : Tributary Area and Critical Sections for Two-Way Shear 

មតនថ តនថមដេៀតស់ មដេៀតស់ក ក v និង v មកដ តផ តផ ត់ u

n

d = de = 254 mm hs = 260 mm c1 = 1500 mm c2 = 700 mm b1 = (c1  d)

= 1.500 m  0.254 m = 1.754 mm b1 = (c1  d)

= 0.700 m  0.254 m = 0.954 m

BUT Borith

53





ស ត់េេឹ ស េេឹង នដមគណដក ណដកតនដយេ តនដយេងន់ឈពី ឈពីដល ដល (Gravity Loads) ែលនអដពដពដល ដលមមខត់ដោ ដោ  ក់ (Critical shear section) Vu = qu l1  l2  b1  b 2   1.2  Pwall100





= 16.57 kN/m2  [(6.9 m 5.55 m)  (1.754 m 0.954 m)]  1.2 38.34 kN) = 1675.0 kN Ac = 2(c1  c2  2d)d = 2[1.5 m  0.7 m  20.254 m)] 0.254 m = 1.38 m2 v u,g =

Vu

=

1675.0kN 1.38m2

A c

= 1.21 MPa



ស ត់េេឹ ស េេឹង នដមគណដក ណដកតនដយដ តនដយដក ក ងពី ង ពី ូមមមម ង់ង ច់ ់ ច់ដ ដ ងដតង់គល់ គល់តម តម transfer) ែលនអដព ដពដល ដលមមខត់ ខ ត់ដោ ដោ ក់ (Critical shear section)

(shear-moment

bo = 2  (b1  b2 )

= 2 (1.754 m  0.954 m) = 5.46 m Jc = =

d  (c1  d)3



(c1  d)  d3

6



d (c 2  d)(c1  d) 2

6

0.25 0.254 4  (1.5 (1.5  0.25 0.254) 4)3

(ACI 318M-14_R8.4.4.2.3/ page 100)

2 

(1.5 (1.5  0.25 0.254) 4) (0.2 (0.254 54))3

6

6



0.25 0.254 4 (0.7 (0.7 0.25 0.254) 4)(1 (1.5 .5 0.25 0.254) 4)2 2

= 0.643 m4

c3 = c4 =

(c1  c 2 ) 2 (1.5 (1.5 m  0.7 0.7 m)

c3 = c 4 =

2

= 1.1 m

1

  = 1 

1

2

c1  de

3 c 2  de 1

  = 1 

1

2 1.5m 1.5m  0.25 0.254m 4m 3 0.7m .7m  0.25 .254m

  = 0.47

v u,s =

BUT Borith

   Msc  c 3

Jc 54



ដយតម M ជ factored moments in columns គឺគណែូ គណែូចងដម ចងដម se

Msc = 0.08  qDu  0.5qLu  l2  ln2  q'Du  l '2  l'l'n 2 









(ACI 318M-14_8.10.7.2/ page 123)

qDu = 1.2  ( WSW  WSD )

= 1.2(7.08 kN/m2 + 4.17 kN/m2) = 13.5 kN/m2 q'Du = qDu  13.5 kN/m2 qLu = 1.6 1.6  (WLL ) = 1.6 1.6 1.92kN .92kN/m /m2 = 3.07kN .07kN/m /m2 q'Lu = qLu = 3.0 3.07 kN/m N/m 2 l '2 = l2 = 5.550 m l '2 = 1. 1 .15 m 0.08

  qDu  0.5qLu  l2  ln2  q'Du  l '2  l 'n2     1    1     ec   0.08 = 5.55m (0.4m) 2    13.5  0.5  3.07kN/m2  5.55m (10m) 2  13.5kN/m2 5.   1   1     4.76 

Msc =

















= 550.9 kN-m v u,s =

0.47 0.47  550.9 550.9kN kN  m 1.1m 1.1m 0.643m4

= 0.44 MPa



ស ត់េេឹ ស េេឹងស ងស ែលនអដពដពដល ដលមមខត់ ខ ត់ដោ ដោ ក់ (Critical shear section) vu =

Vu A c



   Mu  c 3

(ACI 318M-14_R8.4.4.2.3/ page 100)

Jc

vu = v u,g  v u,s = 1.21 MPa  0.44 MPa = 1.65 MPa



លេធ ិភពេ់ ភពេ់នឹនឹងក ងក ងត់ ង ត់អន អន ត មលកខណ ខណ និមួមយៗ យួ ៗ ែូចងដម ចងដម v c1

= 0.29 f 'c  0.3fp c 

Vp b0 d

ែល f '

c

ACI 318M-14_22.6.5.5 /page 365) ( ACI

MPa  5. 5 .92 MP MPa , but shall not  35 MP

exceed 5.8 MPa

ដយតម bV d តូច ែូចដនមិ ចដនមិនគិ នគិតា តា ល និង p

0

fpc = BUT Borith

P A

shall not exceed 3.5 MPa 55



(

ACI-14_19.2.4.2/page316)  = 1 Normalweight ACI-14_19.2.4.2/page316)  1836 1836103N  = 0.29 1.0  (5.8MPa)  0.3    0 6 2   1.66  1. 668 8 10 mm m m  

= 2.0 MPa

 Vp  d  v c2 = 0.083  1.5  s   f 'c  0.3fp c   b0  b0 d 

 s = 40

ស់សសងក សសងកង

 400.254m  = 0.083 1.5   1.0 (5.8MPa)  5.46m  

= 1.6 MPa

v c,max = 0.17 f 'c

(ACI 318M-14_Table 22.6.6.1/ page 366)

= 0.17 0.17 1.0 1.0 35MPa 35MPa = 1.0 MPa



លេធ ិភពេ់ ភពេ់នឹនឹងក ងក ងត់ ង ត់អន តស់ដត ដតង vc



= min v c1, v c2 , v c ,max

ACI 318M-14_22.6.5.5 /page 365) ( ACI



= min2.0 MPa, 1.6 MPa, 1.0MPa  = 1.0 MPa  

vc = 0.751.0 MPa = 0.75 MPa

ដយ v = 0.75 MPa < v = 1.65 MPa នន័យលេធ យលេធ ិភពេ់ ភពេ់នឹនឹងក ងក ងត់ ង ត់អន អន តស់ដត ដតងមិ ងមិនគ់ នគ់ ោន់ជមួ ជមួយនឺ យនឺងក ងក ងត់ ង ត់ងដៅដេ ងដៅដេ ។ ែូ ដចមខត់ ខត់តតវដ វដស់ ស់ែកកង ែកកង (Stirrup reinforcement) ដែមបីមបីមកេ់ មកេ់ ជមួយតម យតមែលដលស នមកពី v  v = 0.82 MPa ។ គណសសែក Stirrup reinforcement ែូចងដម ចងដម ។  លេធ ិភពេ់ ភពេ់នឹនងក ងឹ ក ងត់ ង ត់អន អន តស់ែក ែក ដយងទញដចញពី ងទញដចញពីមន ូូមនដ ងផ ងផ ត់ងដម ងដម c

u

u

c

v   v s  v c   v u  v s  u  v c    A v  f y t b0  S

vu





A v 

f yt

vs =

b0  S

(ACI 318M-14_22.6.7.2/ page 366)

 vc

v  u  vc      

b0  S  

ែល

A v  f y t

ែល

A v

ជកឡស់ ស់ែកកង ែកកង

ជក ជក ងស់ ង ស់ែកកង(ែក ែក ងអ ង អដ ដ) d 254mm គ តយែកកង គិតពី តពីអ័អ័កដអ័ កដអ័កក S  = = 127 mm គ 2 2 fy t = 390M 390MP Pa

BUT Borith

56



សនតយ់ ក S = 100 mm មកដ  1.57MPa

5460mm 100mm  

 0.75

A v 

 1.0MPa  

390MPa

= 1531 mm2

ដស់ ស់ែកកងដរ ែកកងដរងពី ងពី 10DB12 mm (A = 2261 mm ) គ់ួនួ េិសែូ សែូចៗោ ចៗោ ដ ងផ ងផ ត់លេធ ល ិេធភពេ់ ភពេ់នឹនងឹ ក ក ងត់ ង ត់អន អន តស (ដតង ែក) 2

v



+

 vn  vu

  v s  v c   v u  

ែល

A v  f y t vs =

b0  S



2261 2261mm mm2  390M 390MPa Pa 5460 mm mm 100 mm mm

 1.6 MPa

 0.75 0.75 1.6 1.6 MPa MPa  1.0 1.0 MPa MPa   1.57 1.57 MPa MPa 



1.95 1.95 MPa MPa  1.57 1.57 MPa MPa

ដយ v = 1.95 MPa  v = 1.57 MPa ែូដច ដចដយងដ ងដញែកេ់ ញែកេ់ក ក ងត់ ង ត់ែលនដ ែលនដស់ ស់ង ង ដល គឺ គឺគ់ គ់ោន់ ោន់ដ ដយ ស់េ់ េ់ ងពី ងពីេិេិស (two-way shear) ។ n

Fraction

u

ស់ភពន់ ភពន់ន ន nominal moment គឺតតវនា វនា នដយ Flexure គឺ

Mu =  f  Msc sc

1  f =

1

1



2

b1

3

b2

1

2

1.764m

3

0.96 .964m

 0.53

មសិកងដល កងដលដយ ដយងន ងន Mse = 550.9 kN-m

(factored moments in columns)

0.53  550. 550.9kN9kN-m m  f Mse = 0.53

= 292.0 kN-m

ដយ M = 851.4 kN-m >  M = 292.0 kN-m ដយងេេួ ងេេួលន លន តម ូមមមង់ង ែលនស់ ់ ែលនស់េ់េល់ េល់ នឹងម ង ូមមមង់ង ែលដ ់ ែលដ អដពដព ែូ ែូដច ដចដយងដ ងដញម ញមខត់ ខត់កលខណ លខណ គឺ គ់ោន់ ោន់ដ ដយ ។ f

BUT Borith

sc

57



តង ី ី ១.២៨ ១.២៨ : ុងេ ងេ Shear Strength ់រឌ រឌ ុងរុ ងរុងរតំ ងរតំង លកខណ ខណ

តមក ង (Strength)

Vn  Vu

vn  vu

Mn  f M Msc

Vn

= 1467.4 kN

Vu

= 441.5 kN

vn

= 1.95 MPa

vu

= 1.57 MPa

ពីពណ៌ ពណ៌ដល ដលមមខត់ ខ ត់ (OK) គ់ោន់ ោន់ (OK)

(OK) គ់ោន់ ោន់ (OK)

(OK) គ់ោន់ ោន់ (OK)

Mn = 851.4 kN-m f M Msc = 292.0 kN-m

១.២.៣.៧ សិកជប កជបាស់ ាស់ែកក ុ ុ ែកកង Slab Band

ដយសិកដល កដលក ក ងត់ ង ត់េេឹ េេឹង ស់កលខណ កលខណ គឺដយ ដយងេេួ ងេេួលននូវលេធ វលេធល ល កលខណ កលខណ ច់ ច់តតវ ែកកង ឬែលេ់នឹនងឹ ក ក ងត់ ង ត់េេឹ េេឹង ។ ដយងនឹ ងនឹងសិ ងសិក ក និង គណសសែកស់កលខណ កលខណ តង់េីេី ង Slab Band ដយក៏ យក៏ែូែចូ Drop Panel ែ ។ ដយង ងច់ ច់គឺគតឺ តវនែកសី វនែកសីតតណ ភព ឬែកស់េ់ េ់នឹនឹងភពួ ងភពួមឌ មឌ ស់ ដតង ដលគឺដយ ដយង ងច់ ច់តតវែកសី វែកសីតតណ ភព អប  ។ b = 1500 mm ជេ ស់  ស់សសយកង សសយកង min

w

d = 254 mm ACI 318M-14_8.7.5.6.3.1/ page 111) ូូមន មនដស់ ស់កឡ កឡែក ែក អប យកតមនូ នូមន មនងដមទងពី ងពី ( ACI

A s = =

A s =

0.37 f 'c bw d f y 0.37 0.37 35MP 35MPa a  700m 700mm m  254m 254mm m 390MPa

2.1 b wd f y

=

2.1 2.1 700mm 700mm  254m 254mm m 390MPa

= 998 mm2

= 958 mm2

តមកឡែក ែក អបគឺ A A = 998 mm ដយងដ ងដស់ ស់ែក ែក ងអ ង អដ ដ 9DB12@160 mm Bottom (A = 1017 mm ) ក់យក ុ យក ុង Slab Band ទងពី ង ពីេិសរ សរ វញ កសសទងសងង ងសងង ។ s

2

s

BUT Borith

2

58



១.២.៣.៨ សិក ក End Blocks at Support Anchorage Zones

កង ងងសង ងសងត់ត់ចចចច ណ ណ  ចែ៏ ច ែ៏ក ុ ុកងអ័ ងអ័កដ កដ យដកតនដតង់ តនដតង់មខត់ ខត់េមដដល េមដដលកកត់ ត់ែ៏ែត៏ ូចន ចនស់ ស់ចចង ស់កលខណ កលខណ ែល លមកពីក ក ងដក ង ដកង ងង (ដពលដគទញខ) ែ៏  ។ ។ ដយផ ដយផ ស់  កង ងង សងត់តមអ័ ់មអ័កពី កពីចចណ ណ  ចដពយដស ច ដពយដស មិនសនឹ នសនឹមៗ មៗ ដង តដយនក តដយនកង ងងទញេេឹ ងទញេេឹង (transverse tensile stress) ក ុ ុកងេិ ងេិសឈ សឈ ែូចដនដ ចដនដយ longitudinal bursting cracks ក៏ដក ដកតនដ តនដ anchorage zone ។ ដដពលែលកង ងង ង ជងម ូឌឌលត់ លត់ស់ ស់ដត ដតង end block នឹងដមដ ងដមដ យ ដលកលងតដគក់ កលងតដគក់ែកឈសមស ែកឈសមស ។ សិកដនអន កដនអនដមមដសៀវដ ដមមដសៀវដ "Building Code Requirments eor Structural Concrete (ACI 318M-14)" AASHTO_LRFD_2012_Bridge_Design_Specifications_6th_Ed ridge_Design_Specifications_6th_Ed"" ជមួយនិ យនិង " AASHTO_LRFD_2012_B

  ី ី ១.២៥ ១.២៥ : (a) Compression Compression Stress Transfer. (c) Stress Stress Trajectories អន តអតិដតង់ ដតង់ anchorage device seating មិនត នតវ វជតម ជតមនសមីទ ទងពី ងពីែលន ែលន ញែូចងដមៈ ចងដមៈ Bearing stress

f n1 = 0.7f'ci n1 f n2 = 2.25f' ci n2 BUT Borith

A A g

AASHTO_5.10.9.7.2-2/ page 5-143) ( AASHTO_5.10.9.7.2-2/ AASHTO_5.10.9.7.2-3/ page 5-143) ( AASHTO_5.10.9.7.2-3/ 59



ជដស ីសសងស់ ងត់តស់ ់ ស់ដត ដតងដៃ ងដៃដគទញខ ដគទញខ ែលក ែលក ងដននមកពី ង ដននមកពីដ ដ ដតស ដតសគូ សូ ក ក ( test cylinders) ដក ុ ុ ដកងមន ងមនពិពី ិដ៍ ដ៍ទល់ ទល់តនក តនក ង  28 MPa ដេអន អន តឲទញន (ដមលក ុ ុ លកងងេី ងងេី ១.២) ១.២) A = កឡអតិ អតិនច នចណកស់ ណកស់ េេ ែលនងណីត ត សដែៀងោ សដែៀងោ នឹងកឡងន ុ ងន ុក A = gross area ស់ bearing plate A = effective net area ស់ bearing plate ែលតវនែកកឡ វនែកកឡ A A ពីកឡ កឡដហងដដល ដហងដដល bearing plate f ' f 'ci = 28 MPa

g

b

duct

  ី ី ១.២៦ ១.២៦ : Geometry of Anchorage Zones in slab section (  ិ ិ))

  ី ី ១.២៧ ១.២៧ : Dimension of Slab Anchorage (  ិ ិ)) BUT Borith

60



( A ដមលក ុ ុ លកងូ ងូេី េី ១.២៨ ១.២៨ ងដម ដយដយ យដយងសិ ងសិក ក ដនគឺគិគតជក ិតជក ុ ុម ែូចដនដពលកឡ ចដនដពលកឡនត នតតោ តោ ដគត់កឡ កឡដដល ដដល យកតកឡ effective ដមលក ុ ុ លកងូ ងូេី េី ១.២៧ ងដល) ។ A

= 2005 mm  260 mm = 521300 mm

Ag1 = (247 mm  90 mm) = 22230 mm2 Ag2 = (190 mm  79 mm) = 15010 mm2 Ag3 = (145 mm  79 mm) = 11455 mm2

ែងន (A



Ag = 3

g1 +

ែងន (350 mm  90 mm)

(កល ៣ កន ុ យុ  ២)

Ag2 + Ag3) + 2

= 3(22230 mm2 +15010 mm2 + 11455 mm2) + 2(350 mm  90 mm) = 209085 mm2 Aholl1 = (132 mm  37 mm) = 4884 mm2 Aholl2 = (97 mm  37 mm) = 3589 mm2

កឡតីតីដណកង ដណកង + កឡដអលី ដអលី)

Aduct = (

= (70 mm  35 mm) + (  8 mm  35 mm /2) = 2890 mm2

ែងន (A



Aholl = 3

holl1 +

ែងន 8   (12.7mm)  2

Aholl2 + Aduct) + 2



4

= 3(4884 mm2 +3589 mm2 + 2890 mm2) + 2(1013 mm2)



(កល ៣ ដយកន ុ កន ុយ 2 ែល 8 ជចនួននួ Strands)

= 36115 mm2 Ab = Ag - Aholl = 209085 mm2 - 36115 mm2 = 172970 mm2



f n1 = 0.7f' n1 ci

A A g

= 0.7 0.7  28MPa 28MPa



f n2 n2

521300 = 30.95 MPa 172970

= 2.25f'ci = 2.25  28 MPa = 63.0 MPa

ែូចដនដយ ចដនដយងយកតមតចមកសិ ូចមកសិកគឺ កគឺ f n

= min fn1 , fn2   30.95 MPa  

  ី ី ១.២៨ ១.២៨ : Geomatry Bearing Area (  ិ ិ)) BUT Borith

61



()

 Factored bearing resistance of anchorages Pr Pr

=  f f n Ab

ែល Resistance Factored  

Pr = 0.7  30.95 MPa  172970 mm2 = 3747 kN

AASHTO_5.10.9.7.2-1/ page 5-143) ( AASHTO_5.10.9.7.2-1/ = 0.7 AASHTO_5.5.4.2/ page 5-26) ( AASHTO_5.5.4.2/ (ជក (ជក ងអន ង អន ត)

( ) ស់ដក ដកង ងងស ងសទ ទង 20 stands

 Factored prestressed force Ppu

 1.2( 0.94f 94f )A   1.2(0. py ps    P = max max 1. 1.2(0. 2(0.880f )A   pu pu ps     1.2(jacking force)   

ACI 318M-14_25.9.2.1/ page 445) ( ACI

 1.2(0 .94  [0.9  1860MP 1860MPa]) a])(2 (200  98.71 98.71mm mm 2)   1.2(0.94   2 = P = max  1.2 1.2((0.80 .80  1860MP 0MPa)(20  98.71 .71mm )   pu   1.2(0.7 .7  1860MP 1860MPa) a)(20 (20  98.71 98.71mm mm 2 )  1.2(0   

 3728kN      3746kN 6kN  = 3746kN 6kN (     3085kN    

ខទង 20 Strands)

ដយងដ ងដញ ញ P = 3746 kN P = = 3747 kN ែូចដនកឡ ចដនកឡងន ុ ងន ុក (ដតង)ង) េគ់ោន់ ោន់េ់ េ់េល់ េល់ជមួ ជមួយនឹ យនឹងក ងក ង ដកង ងងដ ងដយ (មិនដ នដ ឲដត ឲដតងដជ់ ងដជ់នឹនឹង anchorage zone ដ ឬ កដយ) ។  កតមក  ងទញមេិ ង ទញមេិសឈ សឈ (T ) pu

≈

r

burst

  ី ី ១.២៩ ១.២៩ : Definition of terms used to define the general zone (  ិ ិ)) dburst = 0.5(h -2eanc)

(ACI 318M-14_R25.9.4.3.1b /page 447)

ែល e

ជចក ក ិត ង anchorage device ដេីរ រ េងន់ ងន់ (c.g.c) ស់ម មខត់ ខ ត់កលខណ កលខណ anc =

BUT Borith

75

62



= 0.5(260mm -275mm) = 130 mm

ជក ជក ងទញដច់ ង ទញដច់ដត ដតងមេិ ងមេិសឈ ដយក ដយក ងដក ង ដកង ងង Factored prestressed force (P ) ស់ដក ដកងងមួ ងមួយពង់ ពង់ (1 Tendons = 4 stands) Tburst =

pu

 1.2( 0.94f 94f )A   1.2(0. py ps    P = max max  1. 1.2(0. 2(0.880f )A   pu pu ps     1.2(jacking force)   

ACI 318M-14_25.9.2.1/ page 445) ( ACI

 1.2(0 .94  [0.9  1860MP 1860MPa]) a])(4 (4  98.71 98.71mm mm 2)   745.6kN   1.2(0.94       2   P = max 1.2 1.2((0.80 .80  1860MP 0MPa)(4  98.71 .71mm ) =  749.0kN .0kN  = 749.0k .0kN    pu      1.2(0.7 .7  1860MP 1860MPa) a)(4 (4  98.71 98.71mm mm2 )  1.2(0   616.9kN      -

គិតតម តតម T ម code ACI តិច ចតគឺ តគឺ burst

Tburst  0.35 Ppu = 0.35  749 kN

(ACI 318M-14_25.9.4.4.3 /page 449)

= 262.2 kN -

កលបងដស់ ស់ែកកងដរ ែកកងដរងពី ងពី េ  10 mm (A = 78.5 mm ) ែូចដនដយ ចដនដយងចទញនែូចូ ចូមន មនងដម 2

v

n

=

Tburst

ចនួននែកកងដរ ួនែកកងដរងពី ងពី ែលតវ) វ)

(

 

fs  2 A v

ា ក់ ដតម តម T យកម code ACI, = 0.35 P ដ f = f = 390 MPa (full yield strength of reinforcement) ត ដគណម គណម Strut-and-Tie method , f = [  f f = 0.6 f ] - ចនួ ននែកកងដរ នួ ែកកងដរងពី ែលតម T យកម Strut-and-tie method និង ម code ACI គឺ 262.2 262.2 10 N n = = 3 ដែម   burst

pu

s

y

s

y

y

burst

3

390 N

 2   113 mm2    mm 2

ែូដច ដច ដស់ ស់ែកកងដរ ែកកងដរងពី ងពីនថ នថម 2 ក់ងម ងមខ និង 2 ក់ងដម ងដមឲស ឲសគឺ គឺ 7 7 ដែម (7-DB12) AASHTO_Figure C5.10.9.3.2-1/ page 5-127) ចយពយែកកងគឺ យពយែកកងគឺ = = max[ 1.5h , 2.5d ] ( AASHTO_Figure 

s

burst

= max[ 390 mm , 325 mm ] = 390 mm AASHTO_Figure C5.10.9.3.2-1/ page 5-127) គ តែកកងពយតវត គ វត Æ min[ 12 in , 24 d ] ( AASHTO_Figure Ok គឺដស ដស 390mm / 7 ដែម = 55.7 mm Æ min[ 300 mm , 2410 mm = 240 mm ] ែូដច ដច ដស់ ស់ែកកងដរ ែកកងដរងពី ងពី 7 DB10@50 mm ទងកល ង កល និង កន ុ កន ុយស់ Tendon និមួមយៗ យួ ៗ ។ ចដែក ដែក longitudinal 4 ដែម (ដមលក ុ ុ លកងូ ងូេី េី ១.៣០ ១.៣០ ងដម) ក់ដែដែមបីមបីចង់ ចង់ែកកង ែកកង និងដ ងដ េ់ េ់ជ compression រួយដត DB14 ម ACI code ។ យដតងងែ ងងែ កណត់ ណត់យកេ យកេ  DB14 

b

-



BUT Borith

63



  ី ី ១.៣០ ១.៣០ : Detail anchorage zone reinforcement for groups tendons slab BUT Borith

64



១.២.៣.៩ សិកបងូ កបងូតបស់ តបស់ខប ខប (Elongation)

វងច់លូលូត (elongation) ស់ខ ខ ស៏យដល យដលវង វង និងូ ងូងកដងស់ ដងស់ង ង ។ វងច់ លូតស តស គឺ តវគិ វគិតូ តូកា កា លជមួយវងែលដក យវងែលដកតពីឥេធ ឥ ិេធពល ពល Shortening of concrete due to shrinkage ( ) និង Elastic shortenning of concrete ( ) ។ វងច់លូ លតនេ ូតនេក់ ក់េេនងជមួ ន ងជមួយនឹ យនឹងតម ងតមកកិតងខ តងខ (Strainds) ជមួយនឹ យនឹង ងពង ពង (duct) ដយតម យតមកកិត តលស័ លស័យនឹងម ងម កកដងស់ ដងស់ខ ។ ដយូងស់ ងស់ខ ខ មិនត់ នត់តង់ តង់ ឬ ឬ ដងែូចោ ចោ ដតដនដ ដនដយដគតវដ វដ សិ សិកកវងច់ កកវងច់លូលតម ូតមងមួយក យកត់ៗ (Segments) ដេូ ូក ា  ាលោោ មដយ ។ សិក ក elongation ដនអនដមម [ ដមម [T._Y._Lin,_Ned_H._Burns] ''Design of Prestressed Concrete''  ច់លតស់ តូ ស់ដពលដគទញ ដពលដគទញ SH

ES

F2 = F1  e(  kL )

Fa = F2 

s =

e (  kL )  1   kL

Fa  L Eps Aps

  ី ី ១.៣១ ១.៣១ : Frictional Loss ជក ជក ងែលត ង ែលតវទញខ វទញខ (ដងកលខ ែលដគភា់ជមួ ជមួយ ស ីនដពលទញ) នដពលទញ) F ជក ជក ងដ ង ដកក កកត់ ត់ងច ងចង នតមដសស នឹន ឹង F គណជមួ ណជមួយដមគ យដមគណែលត់ ណែលត់ង់ ង់ដយក ដយក ងកកិ ង កកិត F ជក ជក ងមម ង មម ដក ុ ុ ដកងចដ ងចដ កត់ ត់ខដង ខដង ងក ងក ង ង លពី លពី F ដ F L ជវងខមួយក យកត់ៗ ែលដគត់យកមកសិ យកមកសិក ក F1 2

a

1

1

2

  ី ី ១.៣២ ១.៣២ : Geometry of segments length BUT Borith

65



ស ស ទញ ១ ខ (Strand) កឡស់ ស់  ១ ខ (Strand) ជក ជក ងទញ ង ទញ ១ ខ (Strand)

f pipi = 1302 MPa Aps = 98.71 mm2 F1 = Aps  f pipi = 98.71 mm2  1302 MPa = 128.52 kN

ូមឌឌលដអឡស ល ដអឡសចស់ ិចស់ខ ខ

Eps = 200000 MPa  = 0.2

coefficient of friction between the tendon and the duct due to the curvature effects

k = 0.00

coefficient of friction between the tendon and the surrounding due to the wobble wobble effect or

length effect

(Table 4-7 / page 109)

តង ី ី ១.២៩ ១.២៩ :  ិរវងសច់ រវងសច់ (Elongation) ់ ករង ់ ករង់រវង រ់ វង ិ ិួួយៗ យៗ Location

O to P

P to Q

Q to R

R to S

S to T

(ដមលមូ លមូងដល ងដល) L,

(mm)

1035

1265

9218

1265

1035



rad)

0.0087

0.0

0.2010

0.0

0.0087

F2 = F1  e (  kL ) ,

(kN)

2555.3

2542.4

2354.0

2342.1

2328.3

(kN)

2562.9

2548.9

2447.0

2348.0

2335.2

(mm)

6.7

8.2

57.1

7.5

6.1

Fa = F2 

S =



S

e (   kL )  1   kL

Fa  L

,

,

Eps Aps

,

(mm)

85.6

ដយងេេួ ងេេួលន លន វងលូត (Elongation) ែលដកតដ តដងដយច់ ងដយច់លូតស់ តស់ដពលដគទញគឺ ដពលដគទញគឺ  = 85.6 mm S

BUT Borith

66



ឥេធ ិពល ពល Shortening of concrete due to shrinkage is អនដមមដសៀវដស់ ដមមដសៀវដស់ដក [Antoine_E._Naaman] - "PRESTRESSED CONCRETE ANALYSIS AND 

DESIGN"

SH =

ែល

L

 S (t )  L

= 13800 mm

ជវងសស់ ស់ដោងកលខណ ដោងកលខណ ែលតវត់ វត់ខ ខ

 t   b  t   SUKSHKSS  

S (t ) = 

(Table 2.9 /page 72)

ៃទញ ទញ ់ក់ ក់ដត ដតង តមដ

t  7days b = 35 KSH = 1.40-0.01H 0.01H

humidity correction factor

សនត់

H = H = 77%

relative humidity



KSH = 1.40-0.01(77) = 0.63

size and shape factor

តង ី ី ១.៣០ ១.៣០ : Size and shape factors for creep and shrinkage

(Table 2.10)

V   S  

Note: Volume-to-surface,   V



A  hs

S



2A

hs

(A)  កពស់ (h ) ជឌស់កលខណ កលខណ ដស ដស ក  ក (A) ពស់ (h S ជឌស់ ស់កលខណ កលខណ (ូកា កា លទ ទ ង ង ដល ដល និ និងដម = 2A) V

2

s

hs = 260 mm V



260mm

S



2

 13 cm

KSS Û 0.69

ដយដគន Ultimate shrinkage strain of concrete material ( )   11   2  w  1279 10 ែល w គិតជ តជ (N/m )  1337  SU

4

SU



3



សនត់

w = 150 kg/m3

(8.38)

ណេឹ ណេឹកត កតវយជមួ វយជមួយដត យដតងក ុ ុ ងកង 1m

3

= 1471 N/m3 BUT Borith

67


 11  SU = 2  1471 1279 1337 






10

4



= 3.6 3.6 104



 4   3.6  10  0.63  0.69  35  7 

 S (t ) = 

7

=2.6 =2.6 105

SH = 2.6105 (13800mm 0mm) = 0.4 mm

ដមឥេធ ិពល ពល Shortening of concrete due to shrinkage គឺ 

SH



= 0.4 mm

ឥេធ ិពល ពល Elastic shortening of concrete is P

= Aps  f pipi = (98.71 mm2  20 Tandon)  1302 MPa = 2570400 kN

 ES =

P L A c  Ec

=

2570400N 14800mm 166800 1668000mm 0mm2  27800 27800N/m N/mm m2

ដមឥេធ ិពល ពល Elastic shortening of concrete គឺ 

ES

 0.82 mm

= 0.82 mm

តង ី ី ១.៣១ ១.៣១ : ងេរវងសច់ រវងសច់ (Elongation) ់ ករកឥធ ់ ករកឥធ ិ  ិ ិួយៗ យួ ៗ Elongation

ដមឥេធ ិពល ពល

អិលត់ លត់ដវ ដវញ Elongation

ច់លតស់ តូ ស់ខ ខ ដមក ដមក ងទញ ង ទញ

Shortening of concrete

Elastic shortening

Loss due to

due to shrinkage

of concrete

anchorage set

85.6 mm

0.4 mm

0.82 mm

6 mm

BUT Borith

េូទត់ ទត់ស ស 81 mm

68

Two-Way Post-Tensioned Slab Design

Recommend Documents