نوتة حسابية وأحمال الزلازل لبرج سكنى

" "

)dohteM murtcepS esnopseR ladoM deifilpmiS(

) 0002 PAS (

)(

- ) tfaR .C .R (

: +

/

)85( fo )1( egaP )80423930010-2+( moc.oohay@ywasi3ladem7a

fcu = kg/cm (After 28 days)fsy = kg/cm (Steel 36/52)

Flooring Cover = kg/m

Live Load = kg/m ()= kg/m ( - )

WALLS :

Wt. of Bricks = kg/mWt. of Mortar = kg/m ( TWO sides , 2 cm each )

-

Number of Floors = (Basement + Ground +11 Typical Floors)( + + )

Height of Basement Floor = mHeight of Other Floors = m

# Residential Building in Cairo - # Moderate (Medium) Density of Soil

. ( ) . #. ( ) . #

Net Bearing Capacity of Soil = t/m (At Foundation Level)( )

For "Working Stress Design Method" :fco = kg/cm fs = kg/cmfc = kg/cm qc = kg/cm

qmax = kg/cm = (for Slabs < 18 cm)

= (for Beams & Slabs 18 cm)

19As' / As = 0.0

300

14002000

D E S I G N D A T A :

2503600

0.2

150

13

3.503.00

17

60 200090 7

200

[email protected] (+2-01003932408) Page (2) of (58)

:

: snoitaluclaC cisaB

: S L L A W : ssenkciht mc 21

m/gk )2( . )0002( 20.0 + 0041 x 21.0 =

: ssenkciht mc 52m/gk = )2( . )0002( 20.0 + 0041 x 52.0 =

)wh( . )maeb( t - )roolf( h =

st - )roolf( h =: m00.3 = thgieH roolF , mc 07 = t htiw smaeB roF

'm/t )07.0 - 00.3( 52.0 ='m/t )07.0 - 00.3( 34.0 =

: )balS revelitnaC( ecarreT roF

21

'm/t = 5.2 x 07.0 x 21.0 = :

'm/t )07.0 - 00.3( 52.0 =

'm/t = 06.0 + 12.0 =

18.0

) (

18.0 )egde( w

06.0 2w

06.0 )mc 21( wW

12.0 1w07

)teparaP( )( .

wh

052 w

)gnikroW( )etamitlU(

.

wh

034 w

00.1 )mc 52( wW


)21 01( / cL = st balS revelitnaC :

#

#

#

#

# / )ffohsarG(

.

/

) ( )( . )(

.

= st

)elpmiS( )ytiunitnoC( . )8/2L w(

: .

) ( . ) (

)noisroT( .

sL sL04 53

)noitcelfeD( .

54 yaW-owT

balSsL

52

noituloS fo spetS

sL=

yaW-enO0353 balS

)metsyS lacitatS( . )diloS( )kcolB wolloH( )talF(

.

stsL

)st( ) ( :

) ( . . .

sL

) - - ( . : :


: 51.0 - r 5.0 = ) ( 2r / 53.0 =

) ( : )4r + 1( / 4r = - 1 = )4r + 1( / 1 =

#

#

:

)gnikroW(2k cf M 2k cf M sw llaw LL CF st r sL L .oN1S

2S

3S

. . .

)etamitlU(J 1C M J 1C M usw llaw LL CF st r sL L .oN1S

2S

3S

. . .

#

'm/.tfR

. )C .F(

) /( .

.

)2m/t( " " .

)( ).( .

. ) - ( )mrofinU(

.

'm/.tfR 'm/.tfR

'm/.tfR

LsL

r=


B2B1 Ls S1

S2

S3

L

Beam (B1) : Coefficient for Shear =

Coefficient for Moment =

Beam (B2) : : Coefficient for Shear = 1 - 1 / (2 r)

Coefficient for Moment = 1 - 1 / (3 r2) (r = L / Ls)

:

Load for Shear = Ca . (Ls / 2) . ws t/m'Load for Moment = Ce . (Ls / 2) . ws t/m'

r = 1

(Working) L ts FC LL

(Ultimate) L ts FC LL

SC2

. . .

Edge Load

Edge Load

No.

SC1

SC2

No. Rft./m'

SC1

k2

JMu

fc

C1

. . .

ws

wsu

0.67CaCe

0.50

M Rft./m'

:

. . .

ShortLong ShortLongShear Moment

Loads on Supporting Beams


:

. (Working)

As' = As(Hook)

Stage (1) : Uncracked Section : ( Neglecting Rft. )I (g) = 100 . ts3 / 12 cm4

f (ctr) = 0.75 (fcu) 2/3 kg / cmYt = cm

Mcr = f (ctr) . I (g) / Yt

Stage (2) : Cracked Section : ( n = Es / Ec = 10 ) (----) () (n)

(Neutral axis) Snv = 0.0 = 100 Z/2 + n . As' . (Z - 2) = n . As . (d - Z) Z = - - - cm

I (cr) = 100 Z3/3 + n . As' . (Z - 2)2 + n . As . (d - Z)2 cm4

K = (Mcr/Ma)3 (Ma = Applied Moment)

I (e) = K . Ig + (1 - K) . I cr cm4 (Effective Inertia)[ Note : Icr < Ie < Ig ]

Ec = 14000 (fcu) 1/2 kg / cm

Ec Ie = kg . cm

(all.) = Lc / 450 cm

(act.) = (w L4/8 + P L3/3) / EI (all.) (SAFE)

ts / 2

- - -

As2

ts N. A.Z

2As' = As

Ma

ws Edge Load

Lc


:

)3L + 'L + 1L = L (52 / L st

'L

3L 2L 1L

m/t .L .L + .C .F + CR . st = 3w = 1wm/t soC .L .L + .C .F + CR . )70.0 + st( = 2w

: gniyfilpmiS

m/t .L .L + soc / ].C .F + CR . )70.0 + st([ = ' 2w

)noitcelfeD( :

I E / ).M .B fo .M .B( =

+

.

:

: )/ ( . :

)noitcaeR citsalE( )mD.M.B( ) (

)dohteM maeB etagujnoC(

' 2w1w 1w

2R 1R3L 2L 1L

1w

2w

3w

H

1w ' 2w 1w


)balS talF( :

: yletamixorppA

01 / 2vaL . sw )ev+( M 'm / 21 # 7 hseM esU

)mottoB & poT( 8 / 2vaL . sw )ev-( M

: ekauqhtraE ot euD )( KO )ev+( M - - - = )+( M .xam

)( - - - = )-( M .xam

QE )-( M + )ev-( M = )ngiseD( M

.tfR poT lanoitiddA esU )'m / 21 # 7( - ).qer( sA = )sA( 'm / 61 # 4 hseM

)balS talF( .

.

.


# )( : 01 / L )41 21( / L 5 / L

.

#

#

#

#

)5b( )71b( .)07 x 52( : 5b

) - - - (

)metsyS lacitatS( . .

.

) 5b ( ) 71b ( )71b( )5b( .

24.6

)1b( )2b(

)3b( . . . .

)71b( )5b( )71b R(

)mD.M.B( .

72.215.3 88.2 30.3

)( )( . )( .

) ( .

: :

. ) (

.

) / ( ) (

.

.


:


: :

).cte . . . kroW lautriV ,noitcelfeD epolS ,noitubirtsiD tnemoM ,noitauqE M3( .

:

'm / t CR . t . b = thgieW nwO

) - - (

:

#

#

) (: elpmaxE

3 1 )noitubirtsiD tnemoM(

554.0 = 12 )F.D( - 1 = 32 )F .D( 545.0 = 12 )F .D()raehs rof daol esu( : ecroF gniraehS rof gnivloS

tm 23.3 = 21)MEF( 5.0 + 12)MEF( = 12Mtm 65.7 = 23)MEF( 5.0 + 32)MEF( = 32M

)545.0( )23.3 - 65.7( + 23.3 = 2M )554.0( )23.3 - 65.7( - 65.7 = 2M

D .F .Sm

)tnemoM rof daoL( )mD.M.B( . ) (

.

)raehS rof daoL( .

:

36.5tm

26.3

m 07.1 m 08.3

48.171.2

17.169.1

RO=

: :

m 58.2

10.2

89.4

94.4 04.7

00.4 378.0

2


Solving for Bending Moment : (use load for moment)

M21 = 3.92 mtM23 = 8.21 mt

M2 = 3.92 + (8.21 - 3.92) (0.545)M2 = 8.21 - (8.21 - 3.92) (0.455)

B. M. Dm

D E S I G N : Beam Section (12 x 70)

k1 = 0.29 fc = 72 kg/cm2 (OK) c1 = 3.73 c/d < 0.44 (OK)k2 = 1770 J = 0.792As = 5.36 cm2 As = 4.99 cm2

= 6.26

6.26

250 x 1266 = k1 6.26 x 10

5 9.39 x 105

12

#

c1

OR

Mu = 1.5 x 6.26 = 9.39 mt

mt

# #

=

#

Working

5.03

Ultimate

#

66

(fs = 2000 kg/cm2 , = 0.2)

1.42


)maeB ediW( : )maeB neddiH( .

#

)B( x )L .L + C .F( + )2S( bals morf daol + )1S( bals morf daol + .tw .o = w

#

) ( )C .F( )L .L( .

.

) (

.


##

.

.

)0002PAS( .

. ) ( .

)DACotuA( : ) - - - . . (

. .

) ( .

.

)reyaL( )semarF_PAS( .

)0002PAS( )9 noisrev( )DACotuA( )reyaL( .

)noituloS launaM( . )0002PAS( .

:

)kcaB ot dneSredrO warDslooT(

)kcoL( )reyaL( .

) . . .(

)reyaL( "dirG" .

)PAS( .


)sllehS( ) ( ) ( . )sllehS(

)sllehS( .

)reyaL( )sllehS_PAS( )0002PAS( )9 noisrev( )DACotuA(

)reyaL( .

) ( )eniL(

)3,0,0(@ . )ypoC(

.

)ecaFD3( ) ( . )PAS(

. )DACotuA( )PAS( .

) ( ) ( .

.

)( )tnioJ( . ""

)dnetxE-mirT-esarE-telliF( .

)( )tnioP( )elytS tnioPtamroF( . )stnioP( )reyaL(

)stroppuS( .

)sweiV D3weiV( )WN-EN-ES-WS( .

)llawraehS( )eroC(

.


)FXD( .tamrof-FXD sA gniwarD evaS

)PAS( .FXD tropmI eliF

.

lairetaM wohS / yfidoM etercnoC lairetaM enifeD3m/t 05.2 = emuloV tinu rep thgieW

2m/t 6 e 1.2 yticitsalE fo suludoM

5/1 6/1 = oitaR s'nossioP

esrevnI sexA lacoL llehS ngissA snoitces )aerA( llehS tceleS

m 61.0 = ssenkciht gnidneB = ssenkciht enarbmeM : mc61 balS roF

)Z( )m-noT( )lacipyT(

.

)sllehS( )DACotuA( .

)llehS( )sbalS( )sllawraehS( )eroC( . )61S( )52WS(

)03WS( )eroC( .

)weiV( )snoitpO yalpsiD teS ro stnemelE teS( )lliF( )sllehS( . )llehS(

.

. . . .


)emarF( . )( :21B RO 07x21B : emaN noitceSm 21.0 : )2t( htdiW m 07.0 : )3t( htpeD: sreifidoM teS / srotcaF noitacifidoM

)( :)yas 10000.0 RO 1000.0( eulaV llamS yreV = tnatsnoC lanoisroT #)egareva sa 8 nekat( )01 6( = sixa 3 tuoba aitrenI fo tnemoM #

#

#

1000.0 = tnatsnoC lanoisroT # 1000.0 = sixa 2 tuoba aitrenI fo tnemoM #1000.0 = sixa 3 tuoba aitrenI fo tnemoM #

#

noitceS emarF ngissAnoitceS )aerA( llehS ngissA

sllaW - 3 thgieW nwO - 1

daoL eviL - 4 revoC roolF - 2

)noitcA dirG( . .

)sllehS( )semarF( )tceleS(

.

:

)( .

)semarF( ) ( .

)emarF( ) ( )LOC(

)sreifidoM teS / srotcaF noitacifidoM( .

)( )( )ecroF laixA( .


snrettaP daoL / sesaC daoL citatS enifeD

:

)3m/t( CR x )3m( .loV = )TWO( snoitcaeR 3m 052 V 5.2 x V =

) + ( / )( /

/ #

#

revoC roolF

)reilpitluM thgieW fleS( )( .

)TWO( )( .

)( ) + + ( .

026

thgieW nwO

) ( . )reilpitluM thgieW fleS( )(

.

)( ) /(

. )C .F( ) ( .

)C .F( ) /( ) /( .

)C .F( ) ( ) /( . )C .F( ) /( .


saerA ediviD / sllehS hseM tidE

semarF ediviD seniL tidE / tidE .

mrofinU daoL citatS )aerA( llehS ngissA

mrofinU daoL citatS emarF ngissA

). . ( )ytiunitnoC( .

)llA tceleS( )emarf( )semarf( .

)sllaW( : ) ( )m/t( .

) /( . )( ) /( .

)C .F( )L .L( : )2m/t( :

LL riatS

) sbalS talF( ) - /( ) - /(.

daoL eviL

sllaW

) ( )( .

.

)L .D( ) + (

)m/t( . .

)L .L( )m/t( .

.

LD riatS


:

) (

) ( 2m/t 24.1 = )05.0 x 05.0( / )17.0 x 05.0(

)(

not 63.0 = 17.0 x 5.0 = FF F F F

)(

m 01.0 = ecnareloT stnioJ tidE stnioP tidE / tidE )stnioJ( .

noisurtxE wohS / edurtxE snoitpO yalpsiD teS weiV

.

09 yb etatoR sexA lacoL emarF ngissA

)daoL detartnecnoC( )stnioJ( :

)m/t( )ymmuD( )( .

)LD riatS( )LL riatS( : )m/t( .

.

.

)stnioJ( .

.

) ( .

) C.F L .L( ) ( ) (

: m/t 17.0 = )61.0 - 00.3( 52.0 = )llaw( W

= sw


.

)PAS( :

. ydoB ddA stniartsnoc tnioJ ngissA

2m/t 51.0 + )5.2 x 31.0( = C .F RO 2m/t 5.2 x 31.0 = TWO-

)33I ,22I( )33I ,22I(

)0002PAS( )9 noisrev( .

)PAS( :

)sixa 3 tuoba aitrenI fo tnemoM( .

)sixa 3 tuoba aitrenI fo tnemoM( )( .

) ( ) ( )aitrenI( . )mrofinU( )TWO(

)C .F( . :

)( : )( )( )b,a( )tniartsnoC( . )b,a( :

.


5 4 3 2 1

5 4 3 2 1

sesaeleR emarF ngissA tnemelE emarF tceleS

dexiF stniartseR tnioJ ngissA )troppuS( .

a

bc

)b( .

33M

dnE tratS

)esaeleR( .

.

)stroppuS( ).(

)stniartseR( )dexiF( .

)33I ,22I( )enarbmeM( )llehS( )ecroF lamroN( .

) ( .

: )emarF( . )33M( ) (

. )egniH etaidemretnI( )yaB gnitaolF( .


obmoC weN ddA snoitanibmoC daoL enifeD )L & D(

)LDriatS + sllaW + C .F + TWO( : D)LLriatS + L .L( : L

L + D = T

)L + D( 5.1 = T 5.1 = TLUL 6.1 + D 4.1 = TLU

sisylanA nuR / nuR ezylanA

sessertS / secroF wohS yalpsiD

)DDA( )rotcaF elacS( )daoL latoT( .

)etamitlU( )TLU( .

RO

)epahS demrofeD( .

)gnikroW( )etamitlU( .

)3-3 tnemoM( )2-2 raehS( .


.

)( : )raehS rof daoL( .

) ( .)( )PAS( :

snoitcaeR stnioJ yalpsiD

#

#

: dohteM GNIKROW )1(

)2mc/gk 55 ocf( ysf . sA 44.0 + ocf . cA = wNcA %1 sA gnimussa

cA 07 wN) mc ,gk : stinu (

: :

)llawraehS( )eroC( .

. daoL s'nmuloC fo ) %01 %5 ( nmuloC fo .tw nwO

.

)PAS( )(

.

) - - ( )noitanibmoC daoL latoT( .

)gnikroW( )etamitlU( .

.


: dohteM ETAMITLU )2(

ysf . sA 76.0 + ucf . cA 53.0 = uNcA %1 sA gnimussa

) mc ,gk : stinu ( #

#

# :

) ( .

. )balS talF( .

.

cA 501 uN )cA( . )t( )b(

.

) sroolF 8 ( : snoitces 'snmuloC fo noitamitsEskrameR ).hc( t ).qer( t b wN )pyt( wN .loC

08 26.97 03 2.761 0.91 107 68.26 03 0.231 0.51 2001 78.39 03 1.791 4.22 3.W .S 902 23.441 52 6.252 7.82 4EROC 6.263 2.14 5

ralucriC 06 06 06 06 4.561 8.81 03001 69.59 03 5.102 9.22 1306 14.75 03 6.021 7.31 23

).tw nwo gnidulcni( snot ) ( = = = = ) ( ]01.1[ x )sroolF fo .oN( x )pyt( N = ).tot( N) N 01% ( cA 07 ysf . sA 44.0 + ocf .cA = wNcA 501 ysf . sA 76.0 + ucf .cA 53.0 = uN

68.45

gniwarD ni nwohS sA

. . . . .


)tnemoM rof daoL(

)raehS rof daoL( ) %( .

)( .

)0002PAS(

.

: ) ( )tnemoM rof daoL(

.


.

.

#

)---( .

) ()(

)(

)(

) (

iX Y

iY

X

) iY . iN (

)Y,X( )smutaD( )iY,iX(

.

= GCXiN = GCY ) iX . iN (

) iN (

:

:

)NOIGER( . )YLOPB(

)NOIGER( .

)PORPSSAM( )noigeR( . . )

( )tnioP( .

" "

)0002PAS(

.

)mutaD( ) ( .

) ( . :

.

)L .D( )L .L( . .

)DACotuA( )YLOPB( .

:

) iN (

) dohteM murtcepS esnopseR ladoM deifilpmiS (


not va)L .L( . )aerA( L .T = roolF / L .D

) %( .not L .T x 58.0 roolF / L .D

PAS )obmoC LD( .

LDriatS + sllaW + C .F + TWO = roolF / L .D

)( )stnioJ( )eerF( )stniartseR( .)( )dexiF( .

)( )nuR( .)(

.

1M N

:

: )L .D( .2M

N/1M : )X( .N/2M : )Y( . : 1M 2M

:

.

: )C .F( )/(

)L .L( )/( .

.

N

: )DACotuA(

) ( .

:

dexiF

:

)PAS(

:

tnioJ


ces 57.0 H . tc = 1T )1T( )X( )Y( :

)ces 2 RO cT4( fo tsellams 1Ttc : . : )50.0 = tc(

H : .cT : )( .

)1 epyT( :ces 02.1 = DT ces 01.0 = BT= S ces 52.0 = CT

)-( )( . )00.1 = (

)00.5 = R( )-( )( .

)00.1 = ( )-----( )( . cT 2 1T fi 58.0 = )00.1 = ( cT 2 > 1T fi 00.1 =

)R( ) ( )( )A-xennA( .

)1T( )( )B-xennA( )--( .

)-( . ) C ( . ) (

. :

" " )-( )2 epyT(

)1 epyT( .

:

)1 epyT( .

)( )( )S ,DT ,CT ,BT( )-( )( .

5.1


: DT < 1T < CT

ga 2.0 )V( :

= V )V( )W( . =

:

)V( :

iF : )i( )X( )Y( : )yF = xF(iW : )i( .

iH : )i( .

yL %5 = ye xL %5 = xe YxL : )X( . ) yF(

yL : )Y( . ) xF( yF : X

)Z( )xF( ye . xF = xzM )Z( )yF( xe . yF = yzM

iF

)ga( )g( . )--( )-( .

)( )C-xennA( . g 51.0 = ga )III( enoZ oriaC )T( S )1T(

)---( . )DT ,CT ,BT ,1T( .

)--( )V( )etamitlU( )gnikroW( ).( )= . .(

g / W . . )1T( S . W . ) rotcaF (

ye

xe

ga . . )1T / CT( . )R / 5.2( . S = )1T( S

) - -

( .

.

)yticirtneccE( )Y ,X( )%(

.

=

) V = iF : KCEHC ( ) iH . iW ( iH . iW

V

xF


. (SAP2000)

. () (Working)

Calc

ula

tion o

f SEIS

MIC

Forc

e

(acc

ordi

ng

to N

ew E

gypt

ian C

ode)

Ct

=

0.05

[Fr

om

Co

de - An

ne

x (B

)]H

=

19.00

m

T1 =

0.45

5se

c [C

urv

e ty

pe(1)

:]

T B =

0.10

sec

L x =

33.70

m (av

.)

T C =

0.25

sec

L y =

20.50

m (av

.)

T D =

1.20

sec

S =

1.50

R =

5.00

=

=

=

=

1.00

= = =

=1.

0077

0 t

19.00

m

=

=

=

=

0.85

5 th

.3.

0077

0 t

16.00

m

ag

=0.

15g

4 th

.3.

0077

0 t

13.00

m

3 rd

.3.

0077

0 t

10.00

m

T C 12 :

M (-) = q L / 12 , M (+) = q L / 24 , Neglect Torsion

Coeff. of Max. Moment (x 1/10000)

o


Coefficients for Two-Way Solid Slabs according to (Marcus) :

= (-0.3350) r2 + (1.4514) r - 0.7179

= (3.0375) . (0.1298) r

(Excel)

For Design of Beams : [ 1 ] WORKING :

T & L - sections :

fc ( 2/3 ) ( fc )all. calculate z = kz M / B

if z ts if z >>>> ts b = B b = Br = r . B

2000 1800 1600 1400 1200 fs 0.112 0.115 0.122 0.130 0.140 ( kz ) av

r = 1 [( 1 b/B ) . ( 1 ts/z )2] ( r 1 ) and design as in R - section [ 2 ] ULTIMATE : (c1 & J) Chart

c / d = 5.6 / [ c12 + c1 c12 4.5 ]

get J = ( 1/2.3) [ 1 + 1 ( 4.5 / c12 ) ] = ( 1 / s ) [ 1 0.4 ( c/d ) ]

Note : c/d = 2.8 / ( c12 . J . s )


from Eqn. : d = k1 (M/b)0.5 - - - - - get (k1)fc = c1 (k1) c2 , k2 = c3 (k1) c4

Equations for (Working Stress Design Method) / (k1-k2) Table

B - - - - ts

t

b

ts / t =

b / B =

Ix = . B t 3 WHERE :

= 3/12 + (1 - )3/12 + 0.25(1 - )/( + - )

IX = B ts3 / 12 + b ( t - ts )3 / 12 + Af Aw t 2 / 4 ( Af + Aw ) Af = B ts = Area of Flange

Aw = b ( t - ts ) = Area of Web

x - - - - - - - - - - - - - - - - x

Y = . t

= 0.5 ( 2 + - 2 ) / ( + - )

- - - - - - - -

Y

NOTE :

C e n t r o i d & I n e r t i a o f T s e c t i o n

c4

c3

c2

c1

fs = 2 0 0 0 kg/cm2fs = 1 8 0 0 kg/cm2fs = 1 6 0 0 kg/cm2

0.1005 0.0870 0.0745

1950.95441970.63221991.2833

0.0895 0.0737

1747.5058

-1.2497 -1.1771 -1.1033

= 0.4 = 0.4 = 0.4 = 0.4 = 0.2 = 0.2 = 0.2 = 0.2 = 0.0 = 0.0 = 0.0 = 0.0

1770.4871

0.1065

1794.2216

-1.1862 -1.1001-1.2701

= 0.4 = 0.4 = 0.4 = 0.4 = 0.2 = 0.2 = 0.2 = 0.2 = 0.0 = 0.0 = 0.0 = 0.0

0.0711

1542.24531569.0417

0.09140.1135

1597.2377

-1.2953 -1.1960 -1.0930

= 0.4 = 0.4 = 0.4 = 0.4 = 0.2 = 0.2 = 0.2 = 0.2 = 0.0 = 0.0 = 0.0 = 0.0

15.841414.857514.0442 17.311716.630916.026416.569415.763315.0745


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