Post on 18-Feb-2018
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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)
;
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 2/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Jloxuril Idilysgs ide Eosgcd bj Uwb-
Siy ]lik ]ystoa wgthbut Koias
(Egromt Eosgcd Aothbe)
=
]ossgbd ” G
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
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 3/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Gd provgbus lomturos, i 76※ :6※ Hill wis idilyzoe is i
bdo-wiy slik systoa is shbwd kolbw.
Kimncrbude
?
Bptgbd 69 Bptgbd 6;
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Kimncrbude
:
Ilsb, gd provgbus lomturo, tho slik bj 966※ :6※
mbaaormgil kuglegdc wis idilyzoe is slik wgth koias
usgdc Abaodt mbojjgmgodt aothbe.
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 4/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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.
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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.
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 5/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Gd EEA, jriaos rithor thid pidols iro idilyzoe.
7
Gdtorgbr Jriao
Oxtorgbr Jriao
Gdtorgbr Jriao
Oxtorgbr Jriao
Gdtrbeumtgbd tb EEA
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
96
O-S Jriaos
Gdtrbeumtgbd tb EEA
Jbr mbaploto idilysgs bj slik systoa jriaos, iro
idilyzoe gd O-S ide D-] egromtgbds.
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 6/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Jbr mbaploto idilysgs bj slik systoa jriaos, iro
idilyzoe gd O-S ide D-] egromtgbds.
99
D-] Jriaos
Gdtrbeumtgbd tb EEA
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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.
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
_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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
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 8/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6;0 Lbies
Uho slik lbie gs milmulitoe gd usuil aiddor.
9?
]tops Gd EEA
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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.
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 9/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6=0 Idilysgs
93
Oxtorgbr Jriao
l 9
l ; 1 Vidol wgeth/; +h;/;
l ;Hilj wgeth bj pidolbd bdo sgeo
h;/;
• ]top G0 k) Airngdc O-S Jriao (Oxtorgbr Jriao)
]tops Gd EEA
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
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 10/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6=0 Idilysgs
97
M]/; 1 Loist bj l 9/5 br l ;/5
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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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/;
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 11/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
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 12/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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"
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 13/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6=0 Idilysgs
]top Z0 Litoril Egstrgkutgbd tb mbluad ide ageelo strgps.
Aoxt- 1 6.;:Ab
A oxt+ 1 6.?;Ab
Agdt- 1 6.36Ab
6.:6Aoxt
+
9.66Aoxt∛ 6.3?Agdt∛
;:
]tops Gd EEA
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 14/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6=0 Idilysgs
]top Z0 Litoril Egstrgkutgbd tb mbluad ide ageelo strgps.
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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
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 15/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6=0 Jriao Idilysgs (O-S Gdtorgbr Jriao)
]top G0 Airngdc O-S Gdtorgbr Jriao.
=;
Gdtorgbr Jriao
l 9
l ;Hilj wgeth bj pidolbd bdo sgeo
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"
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 17/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6=0 Jriao Idilysgs (O-S Gdtorgbr Jriao)
]top GG0 Airngdc mbluad ide ageelo strgps.
==
M]/; 1 Loist bj l 9/5 br l ;/5
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"
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6=0 Jriao Idilysgs (O-S Gdtorgbr Jriao)
]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
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 18/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6=0 Jriao Idilysgs (O-S Gdtorgbr Jriao)
]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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6=0 Jriao Idilysgs (O-S Gdtorgbr Jriao)
]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
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 19/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6=0 Jriao Idilysgs (O-S Gdtorgbr Jriao)
]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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6=0 Jriao Idilysgs (O-S Gdtorgbr Jriao)
]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
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
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 20/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6=0 Jriao Idilysgs (O-S Gdtorgbr Jriao)
]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 % 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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6=0 Jriao Idilysgs (O-S Gdtorgbr Jriao)
]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
3? % bj Agdt- cbos tbmbluad strgp ideroaigdgdc tb ageelo strgp
;?※
;6※
;?※ ;?※ ;?※
;6※
;6※
99=
;:= ;:=
9:8
956 ;85
56
Oxiaplo 9
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 21/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6=0 Jriao Idilysgs (O-S Gdtorgbr Jriao)
]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※
99=
;:= ;:=
9:8
956 ;8=
99;/; 75/; 88/; 3:/;6 88/;
99;/; 75/; 88/; 3:/;6 88/;
59
Oxiaplo 9
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
;?※
;6※
;?※ ;?※ ;?※
;6※
;6※
]top 6=0 Jriao Idilysgs (O-S Gdtorgbr Jriao)
]top Z0 Litoril egstrgkutgbd tb mbluad ide ageelo strgps.
;:= ;:=
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
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 22/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6=0 Jriao Idilysgs (O-S Oxtorgbr Jriao)
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/;
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 23/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
;?※
;6※
;?※ ;?※ ;?※
;6※
;6※
]top 6=0 Jriao Idilysgs (O-S Oxtorgbr Jriao)
]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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
;?※
;6※
;?※ ;?※ ;?※
;6※
;6※
]top 6=0 Jriao Idilysgs (O-S Oxtorgbr Jriao)
]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 ∛
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 24/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
;?※
;6※
;?※ ;?※ ;?※
;6※
;6※
]top 6=0 Jriao Idilysgs (O-S Oxtorgbr Jriao)
]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:
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
;?※
;6※
;?※ ;?※ ;?※
;6※
;6※
]top 6=0 Jriao Idilysgs (O-S Oxtorgbr Jriao)
]top Z0 Litoril 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※
58
Oxiaplo 9
6.:6A+6.3?A ∛
6.3?A ∛
6.:6Aoxt+
9.66Aoxt ∛6.3?Agdt∛
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 25/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
;?※
;6※
;?※ ;?※ ;?※
;6※
;6※
]top 6=0 Jriao Idilysgs (O-S Oxtorgbr Jriao)
]top Z0 Litoril 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
87Ab 1 ;8?.:8 jt-ngp
l ; 196.?8※
:6
6
35 9?6 956 956
?7 ?6 5: 56 5:
57
Oxiaplo 9
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]top 6=0 Jriao Idilysgs (O-S Oxtorgbr Jriao)
]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 ?※
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 26/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
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 27/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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.?※
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 28/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
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 29/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
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 30/57
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
: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.
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
=/5‽
]lik
]uppbrt
:9
Uwb Siy ]liks
(Bthor [oqugroaodts bj IMG Mbeo)
Eotiglgdc bj jloxuril rogdjbrmoaodt jbr mbluad suppbrtoe twb-wiy
sliks0
It loist =/5‑ mbvor jbr jgro br mbrrbsgbd prbtomtgbd.
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
:;
Uwb Siy ]liks(Bthor [oqugroaodts bj IMG Mbeo)
Eotiglgdc bj jloxuril rogdjbrmoaodt jbr mbluad suppbrtoe twb-wiy
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.
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
:=
Uwb Siy ]liks
(Bthor [oqugroaodts bj IMG Mbeo)
Eotiglgdc bj jloxuril rogdjbrmoaodt jbr mbluad suppbrtoe twb-wiy
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.
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
:5
Uwb Siy ]liks(Bthor [oqugroaodts bj IMG Mbeo)
Eotiglgdc bj jloxuril rogdjbrmoaodt jbr mbluad suppbrtoe twb-wiy
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
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Eotiglgdc bj jloxuril rogdjbrmoaodt jbr mbluad suppbrtoe twb-wiy
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
(Bthor [oqugroaodts bj IMG Mbeo)
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Eotiglgdc bj jloxuril rogdjbrmoaodt jbr mbluad suppbrtoe twb-wiy
sliks0
]tideire Kir Mut bjj Vbgdts (Vrimtgmil [ombaaodeitgbd) jbr mbluad
ide ageelo strgps kbth.
::
Uwb Siy ]liks(Bthor [oqugroaodts bj IMG Mbeo)
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
(Bthor [oqugroaodts bj IMG Mbeo)
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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.
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Oxiaplo ;
:7
Milmulitgbd suaairy
]lik thgmndoss hj 1 96‽
Jimtbroe lbie (wu) 1 6.;75 nsj
Mbluad strgp wgeth 1 ?※
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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;
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Oxiaplo ;
D-] Egromtgbd abaodts (udgts0 ngp-jt/jt)
Abaodts por strgp wgeth
=.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=
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Oxiaplo =
Milmulitgbd suaairy
]lik thgmndoss hj 1 8‽
Jimtbroe lbie (wu) 1 6.;:5 nsj
Mbluad strgp wgeth 1 =.3?※
3?
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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:
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Oxiaplo =
O-S Egromtgbd Abaodts (udgts0 ngp-jt/jt)
Abaodts por strgp wgeth
=.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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Oxiaplo =
D-] Egromtgbd abaodts (udgts0 ngp-jt/jt)
Abaodts por strgp wgeth
=.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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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).
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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 )
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]hoir Eosgcd jbr Uwb-Siy ]lik
]ystoa wgthbut Koias
(Jlit Vlitos ide Jlit ]liks)
8;
]ossgbd ” GG
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Ubpgms Ieerossoe
Gdtrbeumtgbd
Zirgbus Eosgcd Bptgbds
Eosgcd Oxiaplo
8=
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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?
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Vudmhgdc ]hoir gd Jlit Vlitos
Vudmhgdc shoir bmmurs it mbluad suppbrt pbgdts gd jlit plitos ide jlit sliks.
Gdtrbeumtgbd
8:
]hoir mrimn
Vudmh But
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Mrgtgmil ]omtgbd jbr Vudmhgdc ]hoir
83
Gdtrbeumtgbd
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Vudmhgdc ]hoir0 Mrgtgmil Vorgaotor, kb
kb 1 ;(m9,] + e) + ;(m9,L + e)
76
Gdtrbeumtgbd
m9,]
m9,L
e/;
e/;
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Vudmhgdc ]hoir0 Mrgtgmil Vorgaotor, kb
kb 1 ;(m9,] + e/;) + (m9,L + e)
79
Gdtrbeumtgbd
m9,]
m9,L
e/;
e/;
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Vudmhgdc ]hoir0 Mrgtgmil Vorgaotor, kb
kb 1 (m9,] + e/;) + (m9,L + e/;)
7;
Gdtrbeumtgbd
m9,]
m9,L
e/;
e/;
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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?
Zirgbus Eosgcd Bptgbds
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Ide/ br prbvgeo shoir rogdjbrmoaodt (ΪZs) gd tho jbra bj0
Gdtocril koias
Kodt Kirs
]hoir hoies
]hoir stues
7:
Zirgbus Eosgcd Bptgbds
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Erbp Vidols (IMG 7.?.=.; ide 9=.=.3)0
73
Zirgbus Eosgcd Bptgbds
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Mbluad Mipgtil0
78
Zirgbus Eosgcd Bptgbds
• 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
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
Zirgbus Eosgcd Bptgbds
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
Zirgbus Eosgcd Bptgbds
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
Zirgbus Eosgcd Bptgbds
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
Zirgbus Eosgcd Bptgbds
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Zirgbus Eosgcd Bptgbds
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/;)
Zirgbus Eosgcd Bptgbds
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
]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※
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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※
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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※
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
7/23/2019 L 05 Analysis and Design of Two Way Slab Without Beams
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
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
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Vrbj. Er. Yigsir Ilg [ogdjbrmoe Mbdmroto Eosgcd ” GG
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
IMG =98
Eosgcd bj Mbdmroto ]trumturos ky Dglsbd, Eirwgd ide Eblid
IMG Eosgcd Hidekbbn
99=
[ojorodmos
Eopirtaodt bj Mgvgl Odcgdoorgdc, _dgvorsgty bj Odcgdoorgdc ide Uomhdblbcy Voshiwir
Uho Ode