L 05 Analysis and Design of Two Way Slab Without Beams

7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams

http://slidepdf.com/reader/full/l-05-analysis-and-design-of-two-way-slab-without-beams 1/57

Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG

Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir

Lomturo - 6?

Idilysgs ide Eosgcd bj Uwb-wiy ]lik

]ystoa wgthbut Koias

(Jlit Vlitos ide Jlit ]liks)

9

Ky0 Vrbj Er. Yigsir Ilg

Mgvgl Odcgdoorgdc Eopirtaodt

_OU Voshiwir www.erqigsirilg.mba



]ossgbd ” G0 Jloxuril Idilysgs bj Uwb-Siy ]lik ]ystoa

wgthbut Koias (Egromt Eosgcd Aothbe)

]ossgbd ” GG0 ]hoir Eosgcd jbr Uwb-Siy ]lik ]ystoa

wgthbut Koias (Jlit Vlitos ide Jlit ]liks)

;





Jloxuril Idilysgs ide Eosgcd bj Uwb-

Siy ]lik ]ystoa wgthbut Koias

(Egromt Eosgcd Aothbe)

=

]ossgbd ” G



Ubpgms Ieerossoe

Kimncrbude

Gdtrbeumtgbd tb Egromt Eosgcd Aothbe (EEA)

Jriao Idilysgs ]tops usgdc Egromt Eosgcd Aothbe (EEA)

Oxiaplo 9

Uwb Siy ]liks (Bthor [oqugroaodts bj IMG)

Oxiaplo ; Oxiaplo =

]uaairy bj Egromt Eosgcd Aothbe (EEA)

5





Gd provgbus lomturos, i 76※ :6※ Hill wis idilyzoe is i

bdo-wiy slik systoa is shbwd kolbw.

Kimncrbude

?

Bptgbd 69 Bptgbd 6;



Kimncrbude

:

Ilsb, gd provgbus lomturo, tho slik bj 966※ :6※

mbaaormgil kuglegdc wis idilyzoe is slik wgth koias

usgdc Abaodt mbojjgmgodt aothbe.





Kimncrbude

3

Gd tho siao 966※ :6※ mbaaormgil kuglegdc, gj thoro iro

shillbw br db koias, Abaodt Mbojjgmgodt Aothbe middbt

ko usoe.

Egromt Eosgcd Aothbe (EEA) mid ko usoe jbr sumh misos.



Gdtrbeumtgbd tb EEA

8

Egromt Eosgcd Aothbe (EEA) gs bdo bj tho aothbe jbr

jloxuril idilysgs bj twb-wiy sliks wgth br wgthbut koias.

EEA gs rolitgvoly egjjgmult jbr sliks wgth koias br wills

thorojbro wo wgll uso gt bdly jbr sliks wgthbut koias.





Gd EEA, jriaos rithor thid pidols iro idilyzoe.

7

Gdtorgbr Jriao

Oxtorgbr Jriao

Gdtorgbr Jriao

Oxtorgbr Jriao

Gdtrbeumtgbd tb EEA



96

O-S Jriaos

Gdtrbeumtgbd tb EEA

Jbr mbaploto idilysgs bj slik systoa jriaos, iro

idilyzoe gd O-S ide D-] egromtgbds.





Jbr mbaploto idilysgs bj slik systoa jriaos, iro

idilyzoe gd O-S ide D-] egromtgbds.

99

D-] Jriaos

Gdtrbeumtgbd tb EEA



9;

Gdtrbeumtgbd tb EEA

Lgagtitgbds

Uhbuch EEA gs usojul jbr idilysgs bj sliks, spomgilly

wgthbut koias, tho aothbe gs ipplgmiklo wgth sbao

lgagtitgbds is egsmussoe doxt.





_dgjbraly egstrgkutoe lbiegdc (L/E ≥ ;)

;

9 9≯; 9 /=

Uhroo br abro spids

Mbluad bjjsot≥ ; /96

[omtidculir slikpidols (; br loss09)

9=

Gdtrbeumtgbd tb EEA

Lgagtitgbds (IMG 9=.:.9)0



]top 690 ]gzos

IMG tiklo 7.? (i) ide (m) iro usoe jbr jgdegdc tho slik thgmndoss.

95

]lik wgth Koias ]lik wgthbut Koias

]tops Gd EEA





]top 6;0 Lbies

Uho slik lbie gs milmulitoe gd usuil aiddor.

9?

]tops Gd EEA



]tops Gd EEA

]top 6=0 Idilysgs

9:

Gdtorgbr Jriao

l 9

l ;Hilj wgeth bj pidolbd bdo sgeo

Hilj wgeth bj pidolbd bthor sgeo

• ]top G0 i) Airngdc O-S Jriao (Gdtorgbr Jriao)

Mbl Modtorlgdo

Vidol Modtorlgdo

Vidol Modtorlgdo

Immbregdc tb IMG 9=.:.;.=0 Shoro tho tridsvorso spid bj pidols bd ogthor sgeo bj thomodtorlgdo bj suppbrts virgos, l ; shill ko tinod is tho ivorico bj ie`imodt tridsvorso spids.





]top 6=0 Idilysgs

93

Oxtorgbr Jriao

l 9

l ; 1 Vidol wgeth/; +h;/;


h;/;

• ]top G0 k) Airngdc O-S Jriao (Oxtorgbr Jriao)

]tops Gd EEA



k) Airngdc Ageelo ]trgp (Jbr Gdtorgbr Jriao)

]top 6=0 Idilysgs

98

M]/; 1 Loist bj l 9/5 br l ;/5

M]/;M]/;

M.]

A.]/;

A.]/;

l ;

l 9

l d

Hilj Mbluad strgp

• ]top GG0 i) Airngdc Mbluad ]trgp (Jbr Gdtorgbr Jriao)

]tops Gd EEA





]top 6=0 Idilysgs

97


l ;/5 1 ;6/5 1 ?※

?※?※

96※

?※

?※

l ;

l 9

l d

Hilj Mbluad ]trgp

• ]top GG0 i) Airngdc Mbluad ]trgp (Jbr Gdtorgbr Jriao)

k) Airngdc Ageelo ]trgp (Jbr Gdtorgbr Jriao)

]tops Gd EEA

Jbr l 9 1 ;?※ ide l ; 1 ;6※, M]

ide A] wgeths iro cgvod is

jbllbws0



]top 6=0 Idilysgs

;6

l ; 1 ± (;6) + ± (95/9;) 1 96.?8

M] 1 (;6/5) + ± (95/9;) 1 ?.?8

A] 1 96.?8 ” ?.?8 1 ?※

l ;

l 9

l d

• ]top GG0 m) Airngdc Mbluad ]trgp (Jbr Oxtorgbr Jriao)

e) Airngdc Ageelo ]trgp (Jbr Oxtorgbr Jriao)

]tops Gd EEA

A] 1 l ; - M]

Jbr Cgvod Jriao0

M] ide A] wgeths iro cgvod isjbllbws0

M] 1 Agd. Vidol Sgeth/5 + ± (Mbl.]gzo)

A]

Agd. Vidol Sgeth/5M]

h/;





]top 6=0 Idilysgs

]top GGG0 Milmulito ]titgm Abaodt (Ab) jbr gdtorgbr spid bj jriao.

Ab 1

wu ; d;

8 Ab

l ;l d

]pid bj jriao

;9

]tops Gd EEA



]top 6=0 Idilysgs

]top GZ0 Lbdcgtuegdil Egstrgkutgbd bj ]titgm Abaodt (Ab).

A+

A ∛ A ∛

A ∛ 1 6.:?Ab

A + 1 6.=?Ab

;;

]tops Gd EEA





]top 6=0 Idilysgs

]top Z0 Litoril Egstrgkutgbd tb mbluad ide ageelo strgps.

A ∛ 1 6.:?Ab

A + 1 6.=?Ab

6.:6A +

6.3?A ∛ 6.3?A ∛

;=

]tops Gd EEA



]top 6=0 Idilysgs

]top GGG0 Milmulito ]titgm Abaodt (Ab) jbr oxtorgbr spid bj jriao.

Ab 1wu ; d

;

8 Ab

l ;l d

]pid bj jriao

;5

]tops Gd EEA

;6'-6"

;6'-6"

;6'-6"

;?'-6" ;?'-6" ;?'-6" ;?'-6"





]top 6=0 Idilysgs

]top GZ0 Lbdcgtuegdil egstrgkutgbd bj stitgm abaodt (Ab).

Aoxt+

Aoxt ∛ Agdt∛

Aoxt ∛ 1 6.;:Ab

A oxt+ 1 6.?;Ab

Agdt- 1 6.36Ab

;?

]tops Gd EEA



]top 6=0 Idilysgs


Aoxt- 1 6.;:Ab

A oxt+ 1 6.?;Ab

Agdt- 1 6.36Ab

6.:6Aoxt

+

9.66Aoxt∛ 6.3?Agdt∛

;:

]tops Gd EEA





]top 6=0 Idilysgs


Aoxt- 1 6.;:Ab

Aoxt+ 1 6.?;Ab

Agdt- 1 6.36Ab 6.:6Aoxt

+

9.66Aoxt∛ 6.3?Agdt∛6.:6A+

6.3?A∛ 6.3?A∛

A- 1 6.:?Ab

A+ 1 6.=?Ab

;3

]tops Gd EEA



Oxiaplo 9

Oxiaplo 90

Idilyzo tho jlit plito shbwd kolbw usgdc EEA. Uho slik suppbrts i

lgvo lbie bj 955 psj. Ill mbluads iro 95‽ squiro. Uino j m※ 1 5 n s g i d e j y1 :6 nsg.

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

;8





]top 690 ]gzos

IMG tiklo 7.? (m) gs usoe jbr jgdegdc jlit plito ide jlit slik

thgmndoss.

hagd 1 ? gdmhos (sliks wgthbut erbp pidols)

hagd 1 5 gdmhos (sliks wgth erbp pidols)

;7

Oxiaplo 9



]top 690 ]gzos

Oxtorgbr pidol cbvords. Uhorojbro,

hj 1 l d/=6 1 ^{;? ” (; Ó 95/;)/9;}/=6Q Ó 9; 1 7.?=‽ (IMG agdgaua

roqugroaodt)

Uino hj 1 96‽

Jbr #: kirs0 e 1 hj ” 6.3? ” 6.3? 1 8.?‽

=6

Oxiaplo 9





]top 6;0 Lbies

]orvgmo Eoie Lbie (E.L) 1 νslikhj

1 6.9? Ó (96/9;) 1 6.9;? nsj

]uporgapbsoe Eoie Lbie (]EL) 1 Dgl

]orvgmo Lgvo Lbie (L.L) 1 955 psj br 6.955 nsj

Jimtbroe Lbie (wu) 1 9.;E.L + 9.:L.L

1 9.; Ó 6.9;? + 9.: Ó 6.955 1 6.=865 nsj

=9

Oxiaplo 9



]top 6=0 Jriao Idilysgs (O-S Gdtorgbr Jriao)

]top G0 Airngdc O-S Gdtorgbr Jriao.

=;

Gdtorgbr Jriao

l 9


Hilj wgeth bj pidol

bd bthor sgeo

Mbl Modtorlgdo

Vidol Modtorlgdo

Vidol Modtorlgdo

Oxiaplo 9

;6'-6"

;6'-6"

;6'-6"

;?'-6" ;?'-6" ;?'-6" ;?'-6"






]top GG0 Airngdc mbluad ide ageelo strgps.

==


l ;/5 1 ;6/5 1 ?※

?※?※

96※

?※

?※

l ;

l 9

l d

Hilj Mbluad strgp

i) Airngdc Mbluad ]trgp

k) Ageelo ]trgp

Oxiaplo 9

;6'-6"

;6'-6"

;6'-6"

;?'-6" ;?'-6" ;?'-6" ;?'-6"




]top GGG0 ]titgm Abaodt (Ab) milmulitgbd.

Ab 1 wul ;l d;/8

1 ?56 jt-ngp

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

l ;

l 9

l d 1;=.8=※

Ab 1 ?56 jt-n Ab 1 ?56 jt-n

=5

Oxiaplo 9






]top GZ0 Lbdcgtuegdil egstrgkutgbd bj ]titgm Abaodt (Ab).

Aoxt ∛ 1 6.;:Ab 1 956

Aoxt+ 1 6.?;Ab 1 ;89

Agdt ∛ 1 6.36Ab 1 =38

A ∛ 1 6.:?Ab 1 =?9

A + 1 6.=?Ab 1 987

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

Aoxt+

Aoxt∛ Agdt-

A+

A ∛ A ∛

=?

Oxiaplo 9




]top GZ0 Lbdcgtuegdil egstrgkutgbd bj ]titgm Abaodt (Ab).

Aoxt ∛ 1 6.;:Ab 1 956

Aoxt+ 1 6.?;Ab 1 ;89

Agdt ∛ 1 6.36Ab 1 =38

A∛

1 6.:?Ab1 =?9

A + 1 6.=?Ab 1 987

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

;89

956 =38

987

=?9 =?9

=:

Oxiaplo 9






]top Z0 Litoril egstrgkutgbd tb mbluad ide ageelo strgps.

Aoxt ∛ 1 6.;:Ab 1 956

Aoxt+ 1 6.?;Ab 1 ;89

Agdt ∛ 1 6.36Ab 1 =38

A ∛ 1 6.:?Ab 1 =?9

A + 1 6.=?Ab 1 987

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

6.:6A+

6.3?A ∛ 6.3?A ∛

6.:6Aoxt

+

9.66Aoxt ∛6.3?Agdt∛

=3

Oxiaplo 9





Aoxt ∛ 1 6.;:Ab 1 956

Aoxt+ 1 6.?;Ab 1 ;89

Agdt ∛ 1 6.36Ab 1 =38

A∛

1 6.:?Ab

1 =?9

A + 1 6.=?Ab 1 987

966 % bj A oxt- cbos tbmbluad strgp ideroaigdgdc tb ageelo strgp

6.:6A+

6.3?A ∛ 6.3?A ∛

6.:6Aoxt

+

956 6.3?Agdt∛

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

=8

Oxiaplo 9







Aoxt ∛ 1 6.;:Ab 1 956

Aoxt+ 1 6.?;Ab 1 ;89

Agdt ∛ 1 6.36Ab 1 =38

A ∛ 1 6.:?Ab 1 =?9

A + 1 6.=?Ab 1 987

:6 % bj Aoxt+ & A + cbostb mbluad strgp ideroaigdgdc tb ageelo strgp

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

99=

6.3?A ∛ 6.3?A ∛

9:7

956 6.3?Agdt ∛

=7

Oxiaplo 9





Aoxt ∛ 1 6.;:Ab 1 956

Aoxt+ 1 6.?;Ab 1 ;89

Agdt ∛ 1 6.36Ab 1 =38

A∛

1 6.:?Ab

1 =?9

A + 1 6.=?Ab 1 987

3? % bj Agdt- cbos tbmbluad strgp ideroaigdgdc tb ageelo strgp

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

99=

;:= ;:=

9:8

956 ;85

56

Oxiaplo 9







Aoxt ∛ 1 6.;:Ab 1 956

Aoxt+ 1 6.?;Ab 1 ;89

Agdt ∛ 1 6.36Ab 1 =38

A ∛ 1 6.:?Ab 1 =?9

A + 1 6.=?Ab 1 987

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

99=

;:= ;:=

9:8

956 ;8=

99;/; 75/; 88/; 3:/;6 88/;

99;/; 75/; 88/; 3:/;6 88/;

59

Oxiaplo 9



;?※

;6※

;?※ ;?※ ;?※

;6※

;6※



;:= ;:=

9:8

956

99;/; 75/; 3:/;6 88/;

99=

;8=

88/;99.; 7.5 8.8 3.:

95.6

9:.8

;8.= ;:.=

99.=

;:.=

8.8 ?※ hilj ageelo strgp

?※ hilj ageelo strgp

96※ mbluad strgp

Au (por jbbt wgeth)

1 A / strgp wgeth

5;

Oxiaplo 9





]top 6=0 Jriao Idilysgs (O-S Oxtorgbr Jriao)

5=

Oxtorgbr Jriao

l 9

l ; 1 Vidol wgeth/; +h;/;

l ; Hilj wgeth bj pidolbd bdo sgeo

h;/;

• ]top G0 Airngdc O-S Oxtorgbr Jriao

Oxiaplo 9

l ; 1 ± (;6) + ± (95/9;)

1 96.?8




55

l ; 1 ± (;6) + ± (95/9;) 1 96.?8

M] 1 (;6/5) + ± (95/9;) 1 ?.?8

A] 1 96.?8 ” ?.?8 1 ?※

l ;

• ]top GG0 Airngdc Mbluad ide Ageelo ]trgps

Oxiaplo 9

A] 1 l ; - M]

Jbr Cgvod Jriao0

M] ide A] wgeths iro cgvod isjbllbws0

M] 1 Agd. Vidol Sgeth/5 + ± (Mbl.]gzo)

A]

Agd. Vidol Sgeth/5M]

h/;





;?※

;6※

;?※ ;?※ ;?※

;6※

;6※


]top GGG0 Milmulitgbd bj stitgm abaodt, Ab

l ; 196.?8※

5?

Oxiaplo 9

Ab 1 ;8?.:8 jt-n Ab 1 ;8?.:8 jt-n

l d 1;=.8=※

Ab 1 wul ;l d;/8

1 ;8?.:8 jt-ngp



;?※

;6※

;?※ ;?※ ;?※

;6※

;6※


]top GZ0 Lbdcgtuegdil egstrgkutgbd tb mbluad ide ageelo strgps.

Aoxt- 1 6.;:Ab 1 35

Aoxt+ 1 6.?;Ab 1 958

Agdt- 1 6.36Ab 1 ;66

A - 1 6.:?Ab 1 98:

A + 1 6.=?Ab 1 966

Ab 1 ;8?.:8 jt-ngp

l ; 196.?8※

5:

Oxiaplo 9

Aoxt+

Aoxt∛ Agdt-

A+

A ∛ A ∛





;?※

;6※

;?※ ;?※ ;?※

;6※

;6※


]top GZ0 Lbdcgtuegdil egstrgkutgbd tb mbluad ide ageelo strgps.

Aoxt- 1 6.;:Ab 1 35

Aoxt+ 1 6.?;Ab 1 958

Agdt- 1 6.36Ab 1 ;66

A - 1 6.:?Ab 1 98:

A + 1 6.=?Ab 1 966

Ab 1 ;8?.:8 jt-ngp

l ; 196.?8※

53

Oxiaplo 9

958

35 ;66

96698: 98:



;?※

;6※

;?※ ;?※ ;?※

;6※

;6※



Aoxt- 1 6.;:Ab 1 35

Aoxt+ 1 6.?;Ab 1 958

Agdt- 1 6.36Ab 1 ;66

A - 1 6.:?Ab 1 98:

A + 1 6.=?Ab 1 966

Ab 1 ;8?.:8 jt-ngp

l ; 196.?8※

58

Oxiaplo 9

6.:6A+6.3?A ∛

6.3?A ∛

6.:6Aoxt+

9.66Aoxt ∛6.3?Agdt∛





;?※

;6※

;?※ ;?※ ;?※

;6※

;6※



Aoxt- 1 6.;:Ab 1 35

Aoxt+ 1 6.?;Ab 1 958

Agdt- 1 6.36Ab 1 ;66

A - 1 6.:?Ab 1 98:

A + 1 6.=?Ab 1 966

87Ab 1 ;8?.:8 jt-ngp

l ; 196.?8※

:6

6

35 9?6 956 956

?7 ?6 5: 56 5:

57

Oxiaplo 9




]top Z0 Litoril egstrgkutgbd tb mbluad ide ageelo strgps (por strgp wgeth)

9?.75 96.3?

6

9=.;: ;:.8 ;?.9 ;?.9

99.83 96 7.; 8 7.;

Aoxt- 1 6.;:Ab 1 35

Aoxt+ 1 6.?;Ab 1 958

Agdt- 1 6.36Ab 1 ;66

A - 1 6.:?Ab 1 98:

A + 1 6.=?Ab 1 966

Ab 1 ;8?.:8 jt-ngp

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

?6

Oxiaplo 9

M]

A]

l ; 196.?8※

l ; 1 ± (;6) + ± (95/9;) 1 96.?8

M] 1 (;6/5) + ± (95/9;) 1 ?.?8

A] 1 96.?8 ” ?.?8 1 ?※





]top 6=0 Jriao Idilysgs (D-] Gdtorgbr Jriao)

Mbluad ]trgp ide Ageelo strgp Abaodts

Aoxt- 1 6.;:Ab 1 996

Aoxt+ 1 6.?;Ab 1 ;97

Agdt- 1 6.36Ab 1 ;7?

A - 1 6.:?Ab 1 ;35

A + 1 6.=?Ab 1 958

Ab 1 5;9.? jt-ngp

l ; 1;?※

88.8

9=9 88/;

?7/;

9966 6

;;935/;

;6: :7/;

;6: :7/;

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

?9

Oxiaplo 9



]top 6=0 Jriao Idilysgs (D-] Gdtorgbr Jriao)

Mbluad ]trgp ide Ageelo strgp Abaodts (Vor ]trgp Sgeth)

Aoxt- 1 6.;:Ab 1 996

Aoxt+ 1 6.?;Ab 1 ;97

Agdt- 1 6.36Ab 1 ;7?

A - 1 6.:?Ab 1 ;35

A + 1 6.=?Ab 1 958

Ab 1 5;9.? jt-ngp

l ; 1;?※

8.88

9=.9

=.7

99.66 6

;;.95.7

;6.:

;6.:

?.8

5.:

5.:

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

?;

Oxiaplo 9





]top 6=0 Jriao Idilysgs (D-] Oxtorgbr Jriao)

Mbluad ]trgp ide Ageelo strgp Abaodts

Aoxt ∛ 1 6.;:Ab 1 ?8

Aoxt+ 1 6.?;Ab 1 995

Agdt ∛ 1 6.36Ab 1 9?5

A ∛ 1 6.:?Ab 1 95=

A + 1 6.=?Ab 1 33

Ab 1 ;;6.? jt-ngp

l ; 19=.68※

5:.;

:7

?8

99?.?

963.=

963.=

6

5?

=6.8

=8.?

=?.3?

=?.3?

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

?=

Oxiaplo 9

l ; 1 ± (;?) + ± (95/9;)1 9=.68



]top 6=0 Jriao Idilysgs (D-] Oxtorgbr Jriao)

Mbluad ]trgp ide Ageelo strgp Abaodts (Vor ]trgp Sgeth)

Aoxt ∛ 1 6.;:Ab 1 ?8

Aoxt+ 1 6.?6Ab 1 996

Agdt ∛ 1 6.36Ab 1 9?5

A ∛ 1 6.:?Ab 1 95=

A + 1 6.=?Ab 1 33

Ab 1 ;;6.? jt-ngp

l ; 19=.68※

8.;3

9;.=;

96.5

;6.:7

97.;

6

:

5.9;

?.9=

5.3:

97.; 5.3:

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

?5

Oxiaplo 9

Mbluad ]trgp Sgeth1 (;6/5) + ± (95/9;)1 ?.?8※ A] 1 9=.68 ” ?.?81 3.?※





]top 6=0 Jriao Idilysgs (O-S Egromtgbd Abaodts)

8.8

99.=

;:.= ;:.=

9:.8

95.6 ;8.=

7.5 3.:6

99.; 8.86

9?.75 96.3?

6

9=.;: ;:.8 ;?.9 ;?.9

99.83 96 7.; 8 7.;

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

??

Oxiaplo 9



]top 6=0 Jriao Idilysgs (D-] Egromtgbd Abaodts)

8.88

9=.9

=.7

99.66 6

;;.95.7

;6.:

;6.:

8.8

5.:

5.:

8.;3

9;.=;

96.5

;6.:7

97.;

6

:

5.9;

?.9=

5.3:

97.; 5.3:

6

8.8

5.:

5.:

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

?:

Oxiaplo 9





]top 650 Eosgcd (O-S Egromtgbd)

8.8

99.=

;:.= ;:.=

9:.8

95.6 ;8.=

7.5 3.:6

99.; 8.86

9?.75 96.3?

6

9=.;: ;:.8 ;?.9 ;?.9

99.83 96 7.; 8 7.;

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

?3

Oxiaplo 9



]top 650 Eosgcd (O-S Egromtgbd)

M

M

I I

K

K I

M M

M M

K MK I I I

M M M M M

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

?8

Oxiaplo 9

I 1 #? F 5‽ m/m

K 1 #? F 8‽ m/m

M 1 #? F 9;‽ m/m

M

M





]top 650 Eosgcd (D-] Egromtgbd)

M

K

=.7

K6

I5.7

I

I

M

E

E

M

K

K

I

I

E

E

E

E

I E

M

E

E

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

?7

Oxiaplo 9

I 1 #? F :‽ m/m

K 1 #? F 7‽ m/m

M 1 #? F 9;‽ m/m

E 1 #? F 9?‽ m/m



:6

Uwb Siy ]liks(Bthor [oqugroaodts bj IMG Mbeo)

Eotiglgdc bj jloxuril rogdjbrmoaodt jbr mbluad suppbrtoe twb-wiy

sliks0

Aixgaua spimgdc ide agdgaua rogdjbrmoaodt roqugroaodt0

Aixgaua spimgdc (IMG 9=.=.;)0

saix 1 ; hj gd oimh egromtgbd.

Agdgaua [ogdjbrmoaodt (IMG 3.9;.;.9)0

Isagd 1 6.6698 khj jbr crieo :6. Isagd 1 6.66; khj jbr crieo 56 ide ?6.





=/5‽

]lik

]uppbrt

:9

Uwb Siy ]liks

(Bthor [oqugroaodts bj IMG Mbeo)


sliks0

It loist =/5‑ mbvor jbr jgro br mbrrbsgbd prbtomtgbd.



:;



sliks0

[ogdjbrmoaodt plimoaodt0 Gd miso bj twb wiy sliks suppbrtoe bd

koias, shbrt-egromtgbd kirs iro dbrailly plimoe mlbsor tb tho tbp

br kbttba surjimo bj tho slik, wgth tho lircor ojjomtgvo eopth

komiuso bj croitor abaodt gd shbrt egromtgbd.





:=

Uwb Siy ]liks



sliks0

[ogdjbrmoaodt plimoaodt0 Hbwovor gd tho miso bj jlit

plitos/sliks, tho lbdc-egromtgbd docitgvo ide pbsgtgvo kirs, gd kbth

ageelo ide mbluad strgps, iro plimoe mlbsor tb tho tbp br kbttba

surjimo bj tho slik, rospomtgvoly, wgth tho lircor ojjomtgvo eopth

komiuso bj croitor abaodt gd lbdc egromtgbd.



:5



sliks0

]plgmgdc0 IMG 9=.=.8.? roqugros thit ill kbttba kirs wgthgd tho

mbluad strgp gd oimh egromtgbd ko mbdtgdubus br splgmoe wgth lodcth

oquil tb 9.6 l e, (Jbr eovolbpaodt lodcth soo IMG 9;.;.= br Dolsbd

9=th Oe, pico 93; mhiptor ? br aomhidgmil br woleoe splgmos)

Jbr #3 br lircor db. bj kirs bj j y 1 :6 nsg, ide dbrail wogcht,

udmbitoe mbdmroto bj j m※ 1 5 n s g 0 l e 1 53 e k






sliks0

Mbdtgdugty bj kirs0 It loist twb bj tho mbluad strgp kirs gd oimh

egromtgbd aust piss wgthgd tho mbluad mbro ide aust ko idmhbroe

it oxtorgbr suppbrts (IMG 9=.=.8.?).

:?

Uwb Siy ]liks





sliks0

]tideire Kir Mut bjj Vbgdts (Vrimtgmil [ombaaodeitgbd) jbr mbluad

ide ageelo strgps kbth.

::






Eotiglgdc bj jloxuril rogdjbrmoaodt jbr

mbluad suppbrtoe twb-wiy sliks0

[ogdjbrmoaodt it Oxtorgbr Mbrdors0

[ogdjbrmoaodt shbule ko prbvgeoe it

oxtorgbr mbrdors gd kbth tho kbttba ide tbp

bj tho slik, jbr i egstidmo gd oimh egromt gbd

jrba tho mbrdor oquil tb bdo-jgjth tho lbdcor

spid bj tho mbrdor pidol is shbwd gd jgcuro.

Uho pbsgtgvo ide docitgvo rogdjbrmoaodt

shbule ko bj sgzo ide spimgdc oqugvilodt tbthit roqugroe jbr aixgaua pbsgtgvo

abaodts (por jbbt bj wgeth) gd tho pidol

( IMG 9=.=.:.9)

:3

l / ?

l /?

l 1 lbdcor mloir spid

Uwb Siy ]liks




Oxiaplo ;

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

:8

Hbaowbrn0 Idilysgs rosults bj tho slik shbwd kolbw usgdc EEA iro

prosodtoe doxt. Uho slik suppbrts i lgvo lbie bj :6 psj. ]uporgapbsoe

eoie lbie gs oquil tb 56 psj. Ill mbluads iro 95‽ squiro. Uino j m※ 1 = n s g

ide j y 1 56 nsg.





Oxiaplo ;

:7

Milmulitgbd suaairy

]lik thgmndoss hj 1 96‽

Jimtbroe lbie (wu) 1 6.;75 nsj

Mbluad strgp wgeth 1 ?※



Oxiaplo ;

O-S Egromtgbd Abaodts (udgts0 ngp-jt)

==.7

88

;65 ;65

9=6

968.: ;97

=:.? ;7.;6

5=.5 ==.76

:8.7 5:.5

6

?3.5 99: 963.: 963.:

5?.7 =8.: =?.7 =6.7 =?.7

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

36





Oxiaplo ;

O-S Egromtgbd Abaodts (udgts0 ngp-jt/jt)

Abaodts por strgp wgeth

:.8

8.8

;6.5 ;6.5

9=.6

96.7 ;9.7

3.= ?.86

8.3 :.86

9;.= 8.=

6

96.= ;6.8 97.= 97.=

7.; 3.3 3.; :.; 3.;

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

39



Oxiaplo ;

D-] Egromtgbd abaodts (udgts0 ngp-jt)

=.7

6 6

9395.7

==.7

;:.?

;:.?

=?.8

?=.;

55.=

87.?

8=.9

6

=?.?

;=.7

;7.8

;3.3

8=. 9 ;3.3

6

;8.?

;;.8

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

:8.5

969

85.3

9?7

9?7

3;





Oxiaplo ;

D-] Egromtgbd abaodts (udgts0 ngp-jt/jt)


=.7

6 6

93.95.7

5.?

=.?

=.?

:.5

7.?

3.7

9:.6

95.7

6

5.3

=.;

5.6

=.3

95.7 =.3

6

=.8

=.6

;?※

;6※

;?※ ;?※ ;?※

;6※

;6※

:.8

96.9

8.?

9?.7

9?.7

3=



Oxiaplo =

Hbaowbrn0 Idilysgs rosults bj tho slik shbwd kolbw usgdc EEA iro

prosodtoe doxt. Uho slik suppbrts i lgvo lbie bj :6 psj. ]uporgapbsoe

eoie lbie gs oquil tb 56 psj. Ill mbluads iro 9;‽ squiro. Uino j m※ 1 = n s g

ide j y 1 56 nsg.

;6※

9?※

;6※ ;6※ ;6※

9?※

9?※

35





Oxiaplo =

Milmulitgbd suaairy

]lik thgmndoss hj 1 8‽

Jimtbroe lbie (wu) 1 6.;:5 nsj

Mbluad strgp wgeth 1 =.3?※

3?



Oxiaplo =

O-S Egromtgbd Abaodts (udgts0 ngp-jt)

95.?

=3.?

83.9 83.9

??.8

5:.? 7=.8

9?.: 9;.?6

98.: 95.?6

;7.3 ;6

6

;5.8 ?6 5:.? 5:.?

97.8 9:.3 9?.? 9=.= 9?.?

;6※

9?※

;6※ ;6※ ;6※

9?※

9?※

3:





Oxiaplo =

O-S Egromtgbd Abaodts (udgts0 ngp-jt/jt)


=.7

?.6

99.: 99.:

3.5

:.; 9;.?

5.; =.=6

?.6 =.76

3.6 5.3

6

?.8 99.8 96.7 96.7

?.= 5.? 5.9 =.: 5.9

;6※

9?※

;6※ ;6※ ;6※

9?※

9?※

33



Oxiaplo =

D-] Egromtgbd abaodts (udgts0 ngp-jt)

=.7

6 6

:3.75.7

9=.?

96.?

96.?

95.=

;9.;

93.3

=?.3

==.9

6

95.9

7.?

99.7

99.6

==. 9 99.6

6

99.=

7.9

;6※

9?※

;6※ ;6※ ;6※

9?※

9?※

;3.;

56.5

==.:

:=.9

:=.9

38





Oxiaplo =

D-] Egromtgbd abaodts (udgts0 ngp-jt/jt)


=.7

6 6

7.?5.7

;.;

9.3

9.3

95.=

;9.;

93.3

=?.3

==.9

6

;.;:

9.?;

9.76

9.33

==. 9 9.33

6

9.8

9.5

;6※

9?※

;6※ ;6※ ;6※

9?※

9?※

=.:

?.5

5.?

8.5

8.5

37



]uaairy bj Egromt Eosgcd Aothbe

86

Eomgeo ikbut sgzos bj slik ide mbluads. Uho slik eopth mid

ko milmulitoe jrba IMG tiklo 7.? (m).

Jgde Lbie bd slik (wu 1 9.;EL + 9.:LL)

Bd cgvod mbluad plid bj kuglegdc, eomgeo ikbut lbmitgbd ide

egaodsgbds bj ill jriaos (oxtorgbr ide gdtorgbr)

Jbr i pirtgmulir spid bj jriao, jgde stitgm abaodt (Ab 1

wul ;l d;/8).





89

]uaairy bj Egromt Eosgcd Aothbe

Jgde lbdcgtuegdil egstrgkutgbd bj stitgm abaodt0

Oxtorgbr spid (Aoxt - 1 6.;:Ab> A oxt + 1 6.?;Ab> Agdt - 1 6.36Ab)

Gdtorgbr spid (Agdt - 1 6.:?Ab> A gdt + 1 6.=?Ab)

Jgde litoril Egstrgkutgbd bj oimh lbdcgtuegdil abaodt0

966%bj Aoxt ” cbos tb mbluad strgp

: 6 % b j Aoxt + ide Agdt+ cbos tb mbluad strgp

3 ? % b j Agdt ” cbos tb mbluad strgp

Uho roaigdgdc abaodts cbos tb ageelo strgps

Eosgcd ide ipply rogdjbrmoaodt roqugroaodts (saix 1 ;hj )



]hoir Eosgcd jbr Uwb-Siy ]lik

]ystoa wgthbut Koias

(Jlit Vlitos ide Jlit ]liks)

8;

]ossgbd ” GG





Ubpgms Ieerossoe

Gdtrbeumtgbd

Zirgbus Eosgcd Bptgbds

Eosgcd Oxiaplo

8=



Gdtrbeumtgbd

Jlit Vlitos ide Jlit ]liks

Uhoso iro tho abst mbaabd typos bj twb-wiy slik systoa, whgmh iro mbaabdly

usoe gd aultg-stbry mbdstrumtgbd.

Uhoy rodeor lbw stbry hogchts ide hivo oisy mbdstrumtgbd ide jbrawbrn.

85





Gdtrbeumtgbd

Kohivgbr

Shod twb-wiy sliks iro egromtly suppbrtoe ky mbluads, shoir doir tho mbluad

(pudmhgdc shoir) gs bj mrgtgmil gapbrtidmo.

Uhorojbro, gd ieegtgbd tb jloxuro, jlit plitos shill ilsb ko eosgcdoe jbr twb wiy

shoir (pudmh but shoir) strossos.

8?



Vudmhgdc ]hoir gd Jlit Vlitos

Vudmhgdc shoir bmmurs it mbluad suppbrt pbgdts gd jlit plitos ide jlit sliks.

Gdtrbeumtgbd

8:

]hoir mrimn

Vudmh But





Mrgtgmil ]omtgbd jbr Vudmhgdc ]hoir

83

Gdtrbeumtgbd



Mrgtgmil ]omtgbd jbr ]hoir Eosgcd

Gd shoir eosgcd bj koias, tho mrgtgmil somtgbd gs tinod it i egstidmo “e‑

jrba tho jimo bj tho suppbrt.

e

Koia

]hoirmrimn

88

Gdtrbeumtgbd





Mrgtgmil ]omtgbd jbr ]hoir Eosgcd

Gd shoir eosgcd bj jlit plitos, tho mrgtgmil somtgbd gs id iroi tinod it i

egstidmo “e/;‑ jrba ill jimo bj tho suppbrt.

]lik thgmndoss (h)

Mrgtgmil porgaotor

e/;e/;

e 1 h ∛ mbvor

Urgkutiry Iroi, It

Mbluad

]lik

87

Gdtrbeumtgbd



Vudmhgdc ]hoir0 Mrgtgmil Vorgaotor, kb

kb 1 ;(m9,] + e) + ;(m9,L + e)

76

Gdtrbeumtgbd

m9,]

m9,L

e/;

e/;






kb 1 ;(m9,] + e/;) + (m9,L + e)

79

Gdtrbeumtgbd

m9,]

m9,L

e/;

e/;




kb 1 (m9,] + e/;) + (m9,L + e/;)

7;

Gdtrbeumtgbd

m9,]

m9,L

e/;

e/;





Vudmhgdc ]hoir Eoaide (Zu)0 Jbr ]quiro Mbluad

7=

l 9

l ;

Mrgtgmil Vorgaotor, kb0

kb 1 5(m + e)

Iroi Mbdtrgkutgdc tb Lbie(Oxmluegdc Iroi bj kb), It 0

It 1 (l 9 l ; ) ” (m + e); / 955

^l 9 & l ; iro gd jt. udgts ide m & e iro gdgdmhosQ

Vudmhgdc ]hoir Eoaide0

Zu 1 Su It

Gdtrbeumtgbd



Mipimgty bj ]lik gd Vudmhgdc ]hoir0

ΪZd 1 ΪZm + ΪZs

ΪZm gs loist bj0

Ϊ5∐ (j m※)kbe

Ϊ(; + 5/λm) ∐ (j m※)kbe

Ϊ{(ιse/kb +;} ∐ (j m※)kbe

λm 1 lbdcor sgeo bj mbluad/shbrtor sgeo bj mbluad

ιs 1 56 jbr gdtorgbr mbluad, =6 jbr oeco mbluad, ;6 jbr mbrdor mbluads

75

Gdtrbeumtgbd





Shod ΪZm ≯ Zu (Ϊ 1 6.3?)0 Dbthgdc gs roqugroe.

Shod ΪZm < Zu, thod wo dooe tb gdmroiso tho pudmhgdc shoir mipimgty bj tho

slik.

Vudmhgdc shoir mipimgty bj tho jlit plitos mid ko gdmroisoe ky ogthor bj tho

jbllbwgdc wiys0

g. Gdmroisgdc e ,eopth bj slik0 Uhgs mid ko ebdo ky gdmroisgdc tho slik eopth is i

whblo br gd tho vgmgdgty bj mbluad (Erbp Vidol)

gg. Gdmroisgdc kb, mrgtgmil shoir porgaotor0 Uhgs mid ko ebdo ky gdmroisgdc mbluad sgzo

is i whblo br ky gdmroisgdc sgzo bj mbluad hoie (Mbluad mipgtil)

ggg. Gdmroisgdc j m※ (hgch ]trodcth Mbdmroto)

7?




Ide/ br prbvgeo shoir rogdjbrmoaodt (ΪZs) gd tho jbra bj0

Gdtocril koias

Kodt Kirs

]hoir hoies

]hoir stues

7:






Erbp Vidols (IMG 7.?.=.; ide 9=.=.3)0

73




Mbluad Mipgtil0

78


• IMG 9=.9.; roqugros tho mbluad mipgtil shbule ko brgodtoe db croitor thid 5?6 tb tho ixgs bj thombluad.

• IMG :.5.: roqugros thit tho mipgtil mbdmroto ko plimoe it tho siao tgao is tho slik mbdmroto. Is irosult, tho jlbbr jbragdc kombaos mbdsgeorikly abro mbaplgmitoe ide oxpodsgvo.

• Uho gdmroisoe porgaotor mid ko mbaputoe ky oquitgdc Zu tb ΪZm ide sgaplgjygdc tho rosultgdcoquitgbd jbr k6





Gdtocril Koia ide Kodt Kirs0

Gd miso bj gdtocril koia br kodt kir rogdjbrmoaodt jbllbwgdc aust ko

sitgsjgoe.

IMG 99.99.= roqugros tho slik ojjomtgvo eopth e tb ko it loist : gd., kut dbt

loss thid 9: tgaos tho egiaotor bj tho shoir rogdjbrmoaodt.

Shod kodt kirs ide gdtocril koias iro tb ko usoe, IMG 99.99.= roeumos

ΪZm ky ;

77




Gdtocril Koias

Gdtocril Koias roqugro tho eosgcd bj twb aigd mbapbdodts0

g. Zortgmil stgrrups

gg. Hbrgzbdtil kirs riegitgdc butwire jrba mbluad jimos.

966

Zortgmil ]tgrrups

Hbrgzbdtil Kirs






Gdtocril Koias (Zortgmil ]tgrrups)

Zortgmil stgrrups iro usoe gd

mbd`udmtgbd wgth supploaodtiry

hbrgzbdtil kirs riegitgdc butwire

gd twb porpodegmulir egromtgbds

jrba tho suppbrt tb jbra whit iro

toraoe gdtocril koias mbdtigdoe

odtgroly wgthgd tho slik thgmndoss.

Gd sumh i wiy, mrgtgmil porgaotor

gs gdmroisoe

Zortgmil stgrrups

Jbr 5 sgeos, tbtil stgrrup iroi gs 5 tgaos

gdegvgeuil ; loccoe stgrrup iroi

Gdmroisoe

Mrgtgmil

Vorgaotor, kb

969




Gdtocril Koias (Hbrgzbdtil Kirs)

kb 1 5[ + 5m

96;

• Hbw aumh shbule ko tho lodcth bj tho hbrgzbdtilkirs, l v

l v

• l v mid ko eotoragdoe usgdc tho mrgtgmil porgaotorkb

´ (l v ” m/;) • Egstidmo jrba tho jimo bj mbluad tb tho kbudeirybj mrgtgmil porgaotor 1 ´ (l v ” m/;)

X 1 ´ (l v ” m/;)

X 1 ´ ( l v

” m / ; )

[

m

Mrgtgmil Vorgaotor, kb







Gdtocril Koias

Jbr ]quiro Mbluad bj ]gzo “m‑0

kb 1 5[ + 5m ........ (9)

[ 1 ∐ ( X ; + X ; ) 1 ∐ (;) X

Oq ( 9) 1 4 kb 1 5∐ (;) X + 5m

puttgdcviluobj l v 0 kb 1 5∐ (;){(=/5)(l v ” m9/;)}+ 5m

ijtor sgaplgjgmitgbd, wo cot0 kb 1 5.;5 l v + 9.88m

Uhoikbvooquitgbdmid ko usoe jbr eotoragdgdc tho

lodcthup tb whgmh tho hbrgzbdtilkirs shbuleko oxtodeoekoybdetho jimo bj mbluad.

96=

X 1 ´ (l v ” m/;)

X 1 ´ ( l v ” m / ; )

[

m

Mrgtgmil Vorgaotor,

kb

´ (l v ” m/;)




]top 690 Milmulito Vudmhgdc ]hoir Eoaide, Zu

• Mrgtgmil Vorgaotor, kb 0

kb 1 5(m + e)

1 5(95 + 8.?) 1 76‽

• Urgkutiry Iroi (Oxmluegdc Iroibj kb), It 0

It 1 (;? ;6) ” (95 + 8.?); /955

1 57:.? jt;

• Vudmhgdc ]hoir Eoaide, Zu 0

Su 1 6.=865 nsj

Zu 1 It Ó Su

1 57:.? Ó 6.=865 1 987 ngps

965

Eosgcd Oxiaplo

;?※

;6※





Milmulitgbd bj Vudmhgdc shoir mipimgty (ΪZm)0

• Mhomngdc tho pudmhgdc shoirmipimgty bj mbdmroto0

j m※ kb e 1 5666 76 8.? / 9666 1 58 n

• ΪZm gs loist bj0

• Ϊ5 j m※ kbe 1 95? n

• Ϊ (; + 5 / λm) j m※ kbe 1 ;9: n

• Ϊ{(ιs e/kb +;} j m※ kbe 1 ;68 n

Uhorojbro,• ΪZm 1 95? n < Zu (987 n)

• ]hoir rogdjbrmoaodt gs roqugroe.

96?

Eosgcd Oxiaplo

;?※

;6※



Eosgcd jbr shoir (Bptgbd 69)0 Erbp pidols

Gd erbp pidols, tho slik thgmndoss gd tho vgmgdgty bj tho mbluads gs gdmroisoe tb

gdmroiso tho shoir mipimgty (ΪZm 1 Ϊ5∐ (j m※)kbe) bj mbdmroto.

Uho gdmroisoe thgmndoss mid ko mbaputoe ky oquitgdc Zu tb ΪZm ide

sgaplgjygdc tho rosultgdc oquitgbd jbr “e‑ tb milmulito “hUbtil‑.

(hUbtil 1 h]lik + hErbp Vidlo 1 hj + hEV)

96:

Eosgcd Oxiaplo





Eosgcd jbr shoir (Bptgbd 69)0 Erbp pidols

;?/: 1 5.;?※

;6/: 1 =.?※

• Oquito Zu tb ΪZm0

Zu 1 ΪZm

987 1 6.3? Ó 5 ∐ (j m※ ) Ó 76 Ó e

e 1 99.63‽

Uhorojbro, hUbtil 1 e +9.? ≈ 9;.:‽

Uhgs cgvos ;.:‽ erbp pidol.

• Immbregdc tb IMG, agdgaua

thgmndoss bj erbp pidol 1 hj /5 1

96/5 1 ;.?‽, ]b usgdc ;.:‽ thgmn

erbp pidol.

• Erbp Vidol egaodsgbds0

;?/: ≈ 5.;?※> ;6/: ≈ =.?※

963

Eosgcd Oxiaplo

8.?※

3※



Eosgcd jbr shoir (Bptgbd 6;)0 Mbluad Mipgtils

• Oquito Zu tb ΪZm0

Zu 1 ΪZm

987 1 6.3? Ó 5 ∐ (j m※ ) Ó kb Ó 8.?

kb 1 993.;6‽

Dbw,

kb 1 5 (m + e)

993.;6 1 5(m + 8.?)]gaplgjgmitgbd cgvos,

m 1 ;6.8 ≈ ;9‽

968

Eosgcd Oxiaplo





Eosgcd jbr shoir (Bptgbd 6;)0 Mbluad Mipgtils

• Immbregdc tb IMG mbeo, θ < 5?b

y 1 =.?/ tidθ

Lot θ 1 =6b, thod y ≈ :.6:‽

Jbr θ 1 ;6b, y ≈ 7.:;‽ m 1 ;9‽

95‽

=.?‽

mipgtil

mbluad

yθ

967

Eosgcd Oxiaplo



Eosgcd jbr shoir (Bptgbd 6=)0 Gdtocril Koias (Zortgmil ]tgrrups)

ΪZm 1 95? ngps

Shod gdtocril koias iro tb ko usoe, IMG 99.9;.= roeumos ΪZm ky ;. Uhorojbro

ΪZm 1 95?/; 1 3;.? ngps

_sgdc =/8‽ Ϊ, ; loccoe (6.;; gd;), 5 (sgeo) 1 5 Ó 6.;; 1 6.88 gd;

]pimgdc (s) 1 ΪIvj ye/ (Zu ” ΪZm)

s 1 6.3? Ó 6.88 Ó :6 Ó 8.?/ (987 ” 3;.?) 1 ;.87 ≈ =‽

Aixgaua spimgdc illbwoe e/; 1 8.?/; 1 5.;?‽ Hodmo spimgdc bj = gs wgthgd illbwiklo lgagts.

_sgdc #=, ; loccoe stgrrups F = m/m

996

Eosgcd Oxiaplo





Eosgcd jbr shoir (Bptgbd 6=)0 Gdtocril Koias (Hbrgzbdtil Kirs)

Jbur #? kirs iro tb ko prbvgeoe gd oimh eg romtgbd tb hble tho st grrups. So ndbw

agdgaua kb 1 993.96‽

_sgdc tho oquitgbd kb 1 5.;5l v + 9.88m , wo cot0

l v ≈ ;6‽

Hodmo tho hbrgzbdtil kirs dooe tb ko oxtodeoe koybde tho modtor bj tho mbluad up tb

it loist ;6‽ (So wgll uso ;5‽)

Jgrst stgrrup shbule ko prbvgeoe it i egstidmo

dbt abro thid e/; jrba tho jimo bj mbluad up

tb egstidmo bj e/; jrba kbudeiry bj mrg tgmil

porgaotor.

Gt aust ko dbtoe thit gdtocril koias ilbdc wgth

stgrrups wgll shgjt tho mrgtgmil porgaotor. Koias

ilbdo middbt shgjt tho mrgtgmil porgaotor.

999

Eosgcd Oxiaplo



Eosgcd jbr shoir (Bptgbd 6=)0 Gdtocril Koias eotigls.

Ubtil lodcth bj hbrgzbdtil kirs gs 5 gd kbth egromtgbds.

5 #? kirs iro usoe horo tb hble tho vortgmil stgrrups.

Zortgmil stgrrups iro prbvgeoe up tb egstidmo bj

e/; jrba tho kbudeiry bj mrgtgmil porgaotor.

#=stgrrups F = m/m iro usoe horo.

Jgrst stgrrup gs prbvgeoe it s/; 1 9.? jrba mbluad

jimo.

99;

5※

;※

;※

e/;

e/;

5 #? kirs tb hble stgrrups

#= ]tgrrups F =‽ m/m

e /; 1 8.?/; 1 5.;?‽

Eosgcd Oxiaplo





IMG =98

Eosgcd bj Mbdmroto ]trumturos ky Dglsbd, Eirwgd ide Eblid

IMG Eosgcd Hidekbbn

99=

[ojorodmos


Uho Ode

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L 05 Analysis and Design of Two Way Slab Without Beams