df

RC SDM 10 Serviceability By Dr.Mongkol JIRAWACHARADET 244

n n


Es/Ec n 8 35 ../.2 835 = 280 ../.2

(Hairline crack) 0.25 ..

Gerely Lutz

3s cw 0.011 f d A (10.1)

w fs ./.2 0.60 fy fy 10.1

dc (.)

h2/h1

A (.2) 2yb/n

10.1

(10.1)

y y

Effective tension

area of concrete

dc

h h

Neutral

axis

Steel

centroid

w


10.1

..

0.016 0.4

0.012 0.3

0.007 0.2

0.006 0.15

0.004 0.1

ACI

(10.1) Gergely-Lutz ACI 1999

c

s

2,800s 38 2.5c

f

(10.2)

s30(2,800 / f ) fs (../.2) , s sf M / (A jd) s yf (2 / 3)f jd 0.87d cc (.) s (.)

ACI :

1.

2.

3.

ACI


10.2

4. 5,600 ../.2

5. z = 1.2 (10.1)

3s cw w

z f d A0.011 1.2 0.013

(10.3)

z

: z 31,000 ../. (w 0.41 ..)

: z 26,000 ../. (w 0.34 ..)

(10.1)(10.3) 2 . = 1.35 1.2 z

: z 31,000(1.2/1.35) = 28,000 . ./ . (w 0.41 . .) : z 26,000(1.2/1.35) = 23,000 ../. (w 0.34 ..)

10.3

AsAs

Eb b L / 10

h

s

s

h/2s

s

(Skin reinforcement)

h/2

s

s

s

s


6. h 90 . (Skin reinforcement, Ask) h/2 sk (10.2) 30 . cc

10.1

. 10.4 fy = 4,000 ../.2 ACI ?

10.4 10.1

s yf (2 / 3)f 2 4,000 / 3 2,667 ../.2

cc 4.0 + 1.0 5.0 .

2,800s 38 2.5 5.0 27.42,667

. < [ 30(2,800/2,667) 31.5 . ]

10.4 27.4 .

10.2 20 . DB12 s fy = 4,000 ../.2 2 . s

s yf (2 / 3)f 2 4,000 / 3 2,667 ../.2

cc 2.0 .

30 cm

3DB28

2DB25

DB10 Stirrup

5 cm

5 cm


2,800s 38 2.5 2.0 34.92,667

. > [ 30(2,800/2,667) 31.5 . ]

31.5 . < 3 3(20) 60 .

..1970 45% cf 50%

4,000 /.2 (SD40) 280 ./2 680 ../.2

( )

ACI 10.2 10.3

10.2 ACI

L/20 L/24 L/28 L/10 L/16 L/18.5 L/21 L/8

* fy 4,000 ../.2 0.4 + fy / 7,000


10.3

L/180

L/360

L/480

L/240

ACI (Immediate deflections)

(Creep) (Shrinkage) (Long-term deflection)

(Modulus of Elasticity)

ACI Ec

1.5c c cE 4,270 w f (10.4)


wc 1.45 2.48 /.. 2.32 /.. ACI

c cE 15,100 f (10.5)

(Cracking Moment)

(Modulus of rupture),

r cf 2 f (Cracking moment, Mcr )

r gcr

t

f IM

y (10.6)

yt

Ig

b h, yt h/2 Ig bh3/12

()

() ()

10.5

MM


EI EI 10.5

10.5() Ig (Transformed section) (Cracked-section moment of inertia, Icr) 10.6

10.6

10.7

10.7

M

Mcr

Mom

ent

Deflection D

Dcr De

Icr

Ig Ie

As

h

b

x

dN.A.

nAs

n = Es/Ec


x

2s s sx b

b x nA (d x) x nA x nA d 02 2

(10.7)

x

3

2

cr s

bxI nA (d x)

3 (10.8)

10.8

Icr

s s sB b / (nA ), r (n 1)A / (nA )

2x 2dB(1 rd / d) (1 r) (1 r) / B

3 2 2

cr s sI bx / 3 nA (d x) (n 1)A (x d )

Ig Icr Ig Icr ACI Branson :

3 3

cr cre g cr g

a a

M MI I 1 I I

M M

(10.9)

Mcr r g tf I / y Ig fr (Modulus of rupture) 2.0 cf 0.04

c cw f wc (../..) Ma

Ma EI EIg EIcr 10.9

10.9 EI Ma

As

A sh

b

nAs

(n- )A s

d

b

xd

EI

EIg

EIcr

MaMcr

EIe


(10.9) Ie Ma ACI Ie (10.9) . .

Ie Ie :

:

c m e1 e2I 0.70I 0.15(I I ) (10.10)

:

e m e1I 0.85I 0.15I (10.11)

Im, Ie1 Ie2 Ie

(Instantaneous deflection, Di) EI

Dmax

10.4

4

max

5wL

384EID ()

4

max

wL

185EID

( 0.4215L )

4

max

wL

384EID ()

L

w

L

w

L

w


3

max

PL

48EID ()

33

max

PL 3a a4

48EI L L

D

( a b )

x a(b L) / 3

2 2maxPa

3L 4a24EI

D ()

3

max

PL

48EI 5D

( x = 0.4472L )

3

max

PL

192EID ()

4

max

wL

8EID ()

3

max

PL

3EID ()

2ML

16EID ()

L

P

L / 2

L

P

a b

x

a

PP

L

a

P

L / 2 L / 2

P

L / 2 L / 2

L

w

P

L

L

M


10.10

: D = D0 + D1 + D2

10.10

2 DD D LD

(Camber) LD

L D L DD D D (10.12)

M1 M2

M1

M2

D

0D

1D

2D


10.3 10.11 10 fc = 280 ../2 fy = 4,000 ./2

10.11 10.3

L/16 10(100)/16 62.5 .

1.

3g1

I 40 60 720,00012

.4

2

a

0.7 10M 8.75

8 -

10.12

Ec 15,100 cf 15,100 280

252,671 ../.2

n Es/Ec 62.04 10

8.1252,671

2x

40 (8.1)(39.27) 52 x2

2x 15.71x 816.82 0

x 21.8 .

3 2

cr concrete steel

1I I I 40 21.8 8(39.27) 52 21.8

3

crI 424,663 .4

8 ton (LL)

10 m

5 m Beam weight

700 kg/m(DL)

52 c

m

60 c

m

40 cm

8DB25, As = 39.27 cm2

N.A.

x

40 cm

nAs


rf 2.0 280 33.5 ../.2

r gcr

t

f I 33.5 720,000M 8,040

y 30 100

..-.

3

cr cr

a a

M M8,0400.92, 0.78

M 8,750 M

(10.9)

Ie 0.78(720,000) + 0.22(424,663) = 655,026 .4

DD 4 4

c e

5wL 5 7 (10 100)0.55

384E I 384 252,671 655,026

.

(Camber)

2.

Mmax 8.75 + 8(10)/4 28.75 -

3

cr cr

max max

M M8,0400.28, 0.022

M 28,750 M

(11.8)

Ie 0.022(720,000) + 0.978(424,663) 431,160 .4

DD+L 4 3

c e c e

5wL PL

384E I 48E I

4 35 7 (10 100) 8,000(10 100)

384 252,671 431160 48 252,671 431,160

0.84 + 1.53 2.37 .

3.

DL DD+L DD 2.37 0.55 1.82 .

10.3 DL 10 100L

2.78360 360

. > 1.82 OK


10.4 10.3 3DB25 10.13

10.13 10.4

1.

s

b 40B 0.126

nA (8.1)(39.27) .

s

s

(n 1)A (7.1)(14.73)r 0.329

nA (8.1)(39.27)

x 22dB(1 rd / d) (1 r) (1 r) / B

22(52)(0.126)(1 0.329(4) / 52) (1.329) 1.329 / 0.126 20.4

.

Icr 3 2 2

s sbx / 3 nA (d x) (n 1)A (x d )

3 2 2(40)(20.4) / 3 (8.1)(39.27)(52 20.4) (7.1)(14.73)(20.4 4)

458,953 .4

2.

Mcr/Ma 0.92 (Mcr/Ma)3 0.78 ( 10.3)

Ie 0.78(720,000) + 0.22(458,953) 662,570 .4 4 4

D

c e

5wL 5 7 (10 100)0.54

384E I 384 252,671 662,570

D

.4 ( 10.3)

Mcr/Ma 0.28 (Mcr/Ma)3 0.022 ( 10.3)

Ie 0.022(720,000) + 0.978(458,953) 464,696 .4

DD+L 4 35 7 (10 100) 8,000(10 100)

384 252,671 464,696 48 252,671 464,696

52

cm

60

cm

40 cm

4 cm

d

3DB25

A s=14.73 cm2

8DB25

As = 39.27 cm2


0.78 + 1.42 2.20 .4 ( 10.3)

3.

DL DD+L DD 2.20 0.54 1.66 .

(Long-term deflection)

(Shrinkage) (Creep) (Sustained load) Dcp+sh ACI

cp sh i DD D (10.13)

1 50

(10.14)

i DD ACI 10.5

sA / bd

10.5

5 2.0

1 1.4

6 1.2

3 1.0

10.5 10.3 ACI

1. 10.3

(Di)D 0.55 .

(10.14) 5

2.0 2.01 50 1 50(0.0)


(10.15)

cp sh i D 2.0(0.55) 1.10D D .

10

10.1 ACI fy = 4,000 ../.2

10.2 ? cf = 320 ../.2 fy = 4,000 ../.2 4.0 .

10.3 cf = 280 ../.2 fy = 4,000 ../.2 ACI ?

2.5 cm clear

4.0 cm cover30 cm

2 DB28 and

2 DB25 bars

2 DB25 bars

DB10 Stirrup

2.5 cm clear

4.0 cm cover30 cm

2 DB28 and

2 DB25 bars

2 DB25 bars

DB10 Stirrup

20 cm

50 cmd = 42 cm

4 DB25

2 DB16

20 cm

50 cmd = 42 cm

4 DB25

2 DB16

30 cm

5 cm

55 cm

3 DB32

40 cm

5 cm

5 DB28

50 cm

10 cm

120 cm

30 cm

5 cm

55 cm

3 DB32

40 cm

5 cm

5 DB28

50 cm

10 cm

120 cm


10.4 DB16 2.5 . ACI fy = 4,000 ../.2

10.5 10.3 () , Ig () Icr () Ie Ma = 0.6Mcr

10.6 3.6 cf = 280 ../.2 fy = 4,000 ../.2

b

(.) d

(.) h

(.) As

(.2) A's

(.2) wD

(/.) wL

(/.) PD

() PL

() (1) 40 54 60 8DB28 2DB28 4.0 3.2 - -

(2) 45 64 70 6DB32 - 2.5 1.2 3.2 2.4

(3) 30 48 55 8DB25 2DB25 3.0 1.0 - -

(4) 35 54 60 8DB28 2DB28 3.5 1.3 2.5 2.2

10.7 7.2 2 / 1.6 / cf = 240 ../.2 fy = 4,000 ../.2 () () ()

35 cm

9 cm

56 cm

8 DB25

5 cm

2 DB20

35 cm

9 cm

61 cm

4 DB25

5 cm

2 DB25

4 DB32

35 cm

9 cm

56 cm

8 DB25

5 cm

2 DB20

35 cm

9 cm

61 cm

4 DB25

5 cm

2 DB25

4 DB32

PDPL

wD + wL

2.4 m 1.2 m

PDPL

wD + wL

2.4 m 1.2 m


2 20%

10.8 4 15 . 340 ../. 540 ../. [email protected] . 60% 30

cf = 240 ../.2 fy = 4,000 ../.2

10.9 10 . 8 bw = 30 . h = 50 . 2.6 /.( ) 7.6 /. 4DB28 6DB32 55% 24 cf = 320 ../.2 fy = 4,000 ../.2

10.10 1.4 /. 1.8 /. () () () 4 10% cf = 280 ../.2 fy = 4,000 ../.2

400 cm

bE

30 cm

15 cm

50 cm

400 cm

bE

30 cm

15 cm

50 cm

6.8 m

7.2 m

2DB25

2DB25+1DB20

4DB25

6.8 m

7.2 m

2DB25

2DB25+1DB20

4DB25

40 cm

8 cm

52 cm

6 DB25

40 cm

8 cm

52 cm

6 DB25

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