1 :

1 :

: 5.0 < L/S = m

= S

.

= LLL

2m LS = 2m/gk w =

m/gk Sw =

S S S

2m/gk w =

2m LS5.0 = g

S

m/gk Sw5.0 =

L

:

2< L/S = m

:)BA( C Do54 o54

2 Sm S2

: )BA( 2m/gk w =

= 4/2S 2/LS =

o54 o54

S - 2/LS = 4m S= 4/2

2 Sw3m

m/gk B A

L

32 =

m/gk

L

.

.

T = C

)dj( C M)dj(*C = M

)dj(*T =

: w

: I / )y*M( = ) y( / I = s

L P :

)

xxs / M = xam)xamy( / I = xxs )

( .

c f5 0

. tf : f .

c

CP

5300.0 ( ) :

(5300.0) ( ):

5300.0 = c.

CcitsalPP

ngiseD

5300 0

yf sA = T ff sy sy

gnihsurCCP5300.0 =uc

. 5300.0 ():

g su CC

sf sA = T ff sy sy

. .

. ( )

.

.

.

y / ] E / [ = )y / ( = y / ]E / )I/ yM([ =

) I E ( / M = :

.: : :

.

.

... )d(:

b=

c=

d=

D,h=

d

tsA=

mm 003 )(..3 ces

)mm21 : ( + M)mm21 : (

+UM

3/4mm 52 ro bd

: ( (

3

5

m

m

(

mm 53

3/4 mm 52

>

3/4 xam

mm 52>

( )

xam

: 06-D~)01+01+53(-D =d :09-D~)5.21+02+01+53(-D =d

( )

= L( )

L

yaw-enO02/L01/L 82/L 42/L bals

:

61/L8/L 12/L 5.81/L MAEB

.

( ) 14

: nim

sAc

y

f

f

0.52

1.4nim

=

=

XAM

nim 33.1

fy

. = nim

9 (fc < fr) 9

My

MI

My = f

b

Mmomentcrackingrupture)of(Modulusffwhen

for crg

M MIMyf

= fc

hcrMmoment crackingrupture) of (Modulusrffwhen

t

rgcr

tcrr y

fIM

IyMf ==

fs

yt

63.0 where 'cr

tg

ff

yI

= 12bhI

3

g = (n-1)As

)2/cf < ).pmoc( cf ;rf >)noisnet( cf(

rcM > M . rcM

ffe rc ffeI rcM:

yrraC fnoisserpmoC

: cf rcM M

toN yrraC

sf noisneTty

.

:

i T yrraC MMrc.

noisneTrc

( )

: : .( . ) . . yf < sf& c f5.0

ssc fAfbkd =

2*

: Ec= 5000 fc

c EAkdbE =cccsss EfEf == ;

sssc EAkdbE =2kd

kddkdStrain sc =

ssssc EAkddkdkdbE = )(2

)(2

kddEE

Akdkdbc

ss =

E

)(2

kddnAkdkdb s =n

EEratioModulus

c

s =

db

()2

= s bdkdkAnddk

()2

ddkdbAn

db= s bdkdk

=sA(1)

2

2

= knkdb

=

knkn += 2220(A.N) =++ 22 knnn ) (

( ) ( )

=++ 22 knnn ) ( .A.N

h AN

dk

d

nsA

k k . A.N s A N

2()2 bdk()3

3=+ rcs IbdkAnddk ()

fs vs. Ms M = Tarm = A f jdMs T arm Asfsjd

fs = Ms/Asjd; where jd = d(1-k/3)

f vs. M M = Carm = (f kdb/2)jdfc vs. Ms Ms Carm (fckdb/2)jd

fc = 2Ms/jkbd2; where j = (1-k/3)c s j ; j ( )

: My = Ms (when fs = fy) = Asfyjd

: cE/sE x sA = n x sA :gnittilps riah )1-n2( x sA:

n2

.

dc c C=fcbkd/2

(F)orce

h NA NA

kd

d d kd

d f

jd

y d-kd

y=fy/Es T=Asfyj

dx

( )dddkdd c =

( )( )dkddd s =

kd

dxdkd

dxd

c

c

=

( )( )kdd

dxdkdd

dxd s =

kd0035.0

kdkd

c

cc

==

==

u

( )fkdd

kdd

yys

ss

=====

yy

kdCCa)2ad(abfM

kd'

cn === , jdAE)kdd(jdAfTjdM)kdd(Ekdd

ssysyy

s

===

yy

DSU

DSUDSU: :

b4>h ) .

. ( .

( .S.F)

. .

. . 5300.0 . 5300 0

5300.0=u. .

: 58.0=s yfs=dyf58 0 f f6.0=c cfc=dcF

.

3K 58.0) cf

.( (

. /

. .

Stress

fc(MPa)

fcfc

cufctcufct

Straincu(0.0035) fct k1fck1f c

k2cCc

a

=

c

a

TM+

Cc = k1fc b*c at the location x = k2*c

.

)nM(

5300 =uc= kf'f 3c1dc 3' kfc

) (

cc 2k

5300. =uc

c1=a = cc Ckfcb 13 (')2/a

= cdc Cfbc 11 ()

f A T yff A T dyf

= cCT Fx0 = dyf sA=T syf sA=T

Fx0 Af

a

fbaAf

sdy

dcsdy=

=

dysyy

dcccc

ffffff

0.58'0.6'

====

MAf(da/2)fba(da/2)fb

a

rsdydc

dc

==0.58 fff dysyy =

.

fdb)A

fbAf

2s MAf(d1

dc

sdy .== rsdy

)

(

)2f

fMdbf(1

dc

dydy

21 = r

.( .

y y>s 3.y

= E

1

s

=ca

E

f 05805100076.

1) (

dc =>

0.790.52000.760.580.51000.76

1

1

=c =

ff

c => scy

fc 10.790.52000.76 Mfd

==

dc

dy2u

U

12R

ff

mdb ; RM

:

2

=

dy

U

f112Rm

m2 1

( b )c

abfC cdc =

0035.0cu =c

d

T=As fyd /s y y sf E = =

dcdc cu

bcub

+=+=

bdffAbcfT0F ydbydsb1cdx ==== C cd ycuycu ++

ycu

cu

yd

cd1b ff

+=

5y

ycu

f102

f0035.0 == , 3

700fycu

cu

yd

cd1b ff

+=

yyd

cd1b f700

700ff

+=

: .

MPa400fMPa30f'mm450d300 c ==== mmb 30 cmMPa400f MPa30f mm 450d 300 ycmmb 30 cm

45 cm4 28

: mm2463284A 2

2

s ==

0182.0450300

24634

available

s

==

70030609.0300025.097.0805.0300015.085.0

====

OK

0244.400700

70040085.0306.09.0805.0

max

max

=+

=

31

m.KN6.295295651878306.0805.02

40085.00182.0140085.04503000182.0M 2r ==

=

:

) decrofnier-rednu ( . : ) d f i d (.

)b(.

)b=( . . : 300.0

b = y =

sA

b < b > y > y <

= : b l > : RC < : d RC

= b : balance, > b : over RC, < b : under RC : max = b : min=max max b

1.4 / fy (Concrete first crack)0 25f /f

: min

:

w =36 5 kN/mw = 15 kN/m

. .MPa420fMPa21fmm600Dmm600b yc ====

kN/m7584)536(51)915(251wLL51DL251wkN/m9256.06.0ghtBeam's wei

=++=+===

wL =36.5 kN/mwD = 15 kN/m:

kN.m09.519820.775.84

uM8

2luwuM

kN/m75.84)5.36(5.1)915(25.1uwLL5.1DL25.1uw

===

=++=+=7.0 m

60

6M

92.0210025.097.0;82.0210015.085.0 cm546-60d

88

======

60 cm

553442085.m

97.22540600

61009.5192bduMR

=

==

As=? 0

c

m

01.042085

97.255.342115534

1

55.34216.082.

m

=

=

==As ?

6

41700216

2 mm3436av.s

A257322901.0540600sA

42085.55.34

===

Okbmin

003.0420

4.1min 017.0420700

70042085.216.92.082.0b

===+

=

:. m/Nk 51 m/Nk 62 .

apM 024=yf , aPM 5.42=cfm/Nk 51 = Dwm/Nk 62= Lw /Nk 51/Nk 62

m 0.01

L0001

:

aeBmsthgiew0.560.530052gk/m865gk/m~6Nk/m

26.5~56mcbh/25361

000161DL

3

nim

=====

M518.526Nk.mw1.52(516)1.56256.52Nk/m

ggg

u

u

= =++=

0.190.180.6520070.3910

0.580.5100520.18,0.790.5200520.19

======

b

11742256158024

MMdb518.52601

0.39100.58024007024

0.190.18

62

= ru==

b+1

2.18.652 .3910.5802410.3910.58024

k /hid800d400b mm8.345b165224711b42d/b 3 ====

105862M

5.862MkN/m9259.04.0ghtBeam's wei81090d~D- 900~90800D

6u =

===+=

420850f

286.3810400

105.862bdMR

yd

2

6

2u

=

==40 cm

0110286.34.292111

4.29256.081.0

42085.0f81.0

mcd

yd

===

286 mm4.3553810400011.A

011.042085.

286.34.292114.29

1

2s

b

==

=

= p 90 cm

4 282 2

Ok.39835220285286b5.3694A

86.35538 0000.

min

s

s

=+++==

4 2840 cm

Ok.003.0420/4.1 maxminmin ==

90 cm

28

l t C

dcf

2/a 3/a2

elgnairtC 3/a2 a elgnatcer

dyf sA=+ tcergniart MnCda2Cd2a3) ( ) (

3/2L 3/1L

L L

8/1L 8/1L

2L 1L

UnderstandingUnderstanding

when I read it I forget it

I b it when I see it I remember it

when I do it I understand itwhen I do it

End of Chapter 1 1End of Chapter 1-1