R.V. R.V. COLLEGE OF ENGINEERING, ENGINEER ING, BANGALORE-560059 (Autonomous Institution Affiliat! to V"#, Bl$aum%
&E'IGN OF OR"AL OR"AL FRA)E' REOR"
Submitted by
A&AR'* A&AR' * +A"NOOR +A"NOOR RANAV RAB*AAR 'AN"O'* ) NAI
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'u2mitt! to ROF. RA&*ARI'*NA &EAR")EN" OF CIVIL ENGINEERING
R V COLLEGE OF ENGINEERING
R.V. COLLEGE OF ENGINEERING, BANGALORE - 560059 (Autonomous Institution Affiliat! to V"#, Bl$aum% &EAR")EN" OF CIVIL ENGINEERING.
CER"IFICA"E
Certif Certified ied that the Self Study Study work titled titled &E'IGNN OF OR"AL FRA)E' is carried out byA&AR'* A&AR'* +A"NOOR NOOR (RV (RVCV0 CV00%, 0%, RANA RANAV V RAB*A RAB*AAR AR (RV (RVCV CV0/% 0/% 3 who are are a bona bonafi fide de stud studen ents ts of R.V R.V Coll Colleg egee of 'AN"O 'AN"O'* '* ) NAI NAI (RV (RVCV CV051% 051%,, who Engi Engine neer erin ing, g, Bang Bangal alor ore, e, in part partia iall fulf fulfil illm lmen entt for for the the awar awardd of degr degree ee of Ba4lo Ba4lo of Visvesvarayaa echnolog echnological ical !niversity !niversity,, Belgaum Belgaum En$inin$ in Ci7il Ci7il En$in En$inin$ in$ of the Visvesvaray during the year 05-06 . "t is certified that all corrections#suggestions indicated for the internal $ssessment have been incorporated in the report deposited in the departmental library. he Self Study report has been approved as it satisfies the academic re%uirements in respect of Self Study work prescribed by the institution for the said degree. &arks awarded ' (Evaluation) ' *+
'i$natu of staff in 4a$
1
'i$natu of *a! of t &8atmnt
R.V. COLLEGE OF ENGINEERING, BANGALORE - 560059 (Autonomous Institution Affiliat! to V"#, Bl$aum% &EAR")EN" OF CIVIL ENGINEERING.
CER"IFICA"E
Certif Certified ied that the Self Study Study work titled titled &E'IGNN OF OR"AL FRA)E' is carried out byA&AR'* A&AR'* +A"NOOR NOOR (RV (RVCV0 CV00%, 0%, RANA RANAV V RAB*A RAB*AAR AR (RV (RVCV CV0/% 0/% 3 who are are a bona bonafi fide de stud studen ents ts of R.V R.V Coll Colleg egee of 'AN"O 'AN"O'* '* ) NAI NAI (RV (RVCV CV051% 051%,, who Engi Engine neer erin ing, g, Bang Bangal alor ore, e, in part partia iall fulf fulfil illm lmen entt for for the the awar awardd of degr degree ee of Ba4lo Ba4lo of Visvesvarayaa echnolog echnological ical !niversity !niversity,, Belgaum Belgaum En$inin$ in Ci7il Ci7il En$in En$inin$ in$ of the Visvesvaray during the year 05-06 . "t is certified that all corrections#suggestions indicated for the internal $ssessment have been incorporated in the report deposited in the departmental library. he Self Study report has been approved as it satisfies the academic re%uirements in respect of Self Study work prescribed by the institution for the said degree. &arks awarded ' (Evaluation) ' *+
'i$natu of staff in 4a$
1
'i$natu of *a! of t &8atmnt
S -
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*
"ntroduction
0
/roc /roced edur uree for for $naly nalysi siss and and desi design gn of /ort ortal fram frames es11
2
/ortal frame de design with hinge
3
/ortal frame de design without hinge
CON"EN"'
Design of Portal Frames Into!u4tion
$ portal frame consists of vertical member called Columns and top member which may be hori4ontal, curved or pitched. he vertical and top members built monolithically are considered as rigidly connected. hey are used in the construction of large sheds, bridges and viaducts. he base of portal frame may be hinged or fi5ed. he portal frames are spaced at suitable distance and it supports the slab above the top members. Various forms ofRCC portal frames used in practice is shown in 6ig.
he portal frames have high stability against lateral forces such as wind and earth%uake and the moments in the top beam are also reduced. But at the same time, large moments are induced in the columns which become more costly. $ portal frame is a statically indeterminate structure. "n the case of buildings, the portal frames are generally spaced at intervals of 2 to 3m with a reinforced concrete slab cast monolithically between the frames. 6rames used for ware house sheds and workshop structures are provided with sloping of purlins and asbestos sheet roofing between the portal frames. he base of the columns of the portal frames are either fi5ed or hinged. 7enerally the columns having raft or piles are considered as fi5ed for analysis purpose. $nalysis of frames can be done by any standard methods like i) Slope deflection method, ii) &oment distribution method iii) Strain energy method iv) 8ani9s method. Columns are designed for a5ial force and bending moment, whereas beam isdesigned for bending moment and shear force. hese forces are obtained from the analysis carried out on the frame. imit state method of design is used for design of members. ables given in S/*: may be used for design.
o4!u fo Anal:sis an! !si$n of otal fams
Step*1 Design of slabs Slabs are supported on beams and are designed as continuous. 7enerally these slabs are designed as one way slabs. &a5imum bending moments and shear forces arecomputed using the coefficients given in tables *0 and *2 respectively of "S3;:<0+++. 6or the assumed depth the re%uired steel is computed from table * to3 or ; to 33 of S/*:. $rea of distribution steel are computed based on the minimum steel re%uirement ie., +.*0= of gross area. Step01 Preliminary design of beams and columns >epth of the beam is generally decided on the basis of span to depth ratio. 6or lightly loaded beams it is taken as 0+ and *0 to *; for heavily loaded beams. he width of the beam depends on the architectural re%uirements. 7enerally the width of the beam kept e%ual to the width of the wall or column. he si4e of the column is decided based on a5ial load calculated as reaction of beam or by e5perience. Step21 Analysis he forces on beams and at ?oints if any are first calculated and then forces in columns and beams are calculated using any standard methods of analysis like slope deflection method, moment distribution method etc., or tables given in S/32 can also be used for finding the shear force and bending moment. Step31 Design of beams !sing the end moments and superposing simple support bending moment diagram, the design moments at mid span and at ends are computed. he mid span section of intermediate frame is designed as
otal Fam &si$n ;it *in$ ROBLE) &si$n 't8s
*. >esign of slabs 0. /reliminary design of beams and columns$nalysis 2. >esign of beams 3. >esign of Columns ;. >esign of footings o2lm
$ portal frame hinged at base has following data1 Spacing of portal frames ' 2m eight of columns ' 3m >istance between column centers ' :m ive load on roof ' *.; k-#m0 RCC slab continuous over portal frames. Safe bearing capacity of soil'0++ k-#m0 $dopt &<0+ grade concrete and 6e<3*; steel. >esign the slab, portal frame and foundations and sketch the details of reinforcements. Solution1 >ata given1 •
Spacing of frames ' 2m
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Span of portal frame ' :m
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eight of columns ' 3m
•
ive load on roof ' *.; k-#m0
•
Concrete1 &0+ grade
•
Steel1 6e 3*;
't8 &si$n of sla2 •
$ssume over all depth of slab as **+mm and effective depth as A+mm
•
Self weight of slab ' +.** 5 03
' 0.:3 k-#m0
•
Deight of roof finish
' +.;+ k-#m0 (assumed)
•
Ceiling finish
' +.0; k-#m0 (assumed)
•
otal dead load wd
' 2.2A k-#m0
•
ive load w
' *.;+ k-#m0 (7iven in the data)
•
&a5imum service load moment at interior support '
•
&u'*.; 5 .; ' :.@; k-
•
&ulim'lim bd0 , where (lim'0.@:)
' 3.;; k-
' 0.@: 5 *+++ 5 A+0 # * 5 *+: '002;: k-
6rom table 0 of S/*: pt'+.003G $st'(+.03 5 *+++ 5 **+)#*++' 0@0. mm0
•
Spacing of *+ mm dia bars ' (@.;3 5 *+++)#23' 0+ mm c#c
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/rovide H*+ I 0+ c#c
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$rea of distribution steel $dist'+.*0 5 *+++ 5 **+ # *++ ' *20 mm 0
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Spacing of mm dia bars ' (;+.0: 5 *+++)#*20' 2+ mm c#c
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/rovide J I 2+ c#c. &ain and dist. reinforcement in the slab is shown in 6ig
't8 limina: !si$n of 2ams an! 4olumns •
Bam
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Effective span ' :m
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Effective depth based on deflection criteria ' :+++#*0 ' ;++mm
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$ssume over all depth as ;;+ mm with effective depth ' ;++mm, breadth b ' 3++mm and column section e%ual to 3++ mm 5 ;++ mm.
't8 Anal:sis Loa! on fam
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i) oad from slab ' (2.2AK*.;) 5 2 ' *3.:@ k-#m
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ii) Self weight of rib of beam ' +.35+.;;503' ;.0+ k-#m
•
otal L *A.A; k-#m
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eight of beam above hinge ' 3K+.*<(+.;;#0 )'2.0; m
•
he portal frame sub?ected to the udl considered for analysis is shown in 6ig. :.*+
•
•
•
•
•
he moments in the portal frame hinged at the base and loaded as shown in 6ig. is analised by moment distribution "$B ' 3++ 5 ;++2#*0 ' 3*.: 5 *+ mm3, "BC' 3++ 5 ;++2#*0 ' 3*.: 5 *+ mm3 Stiffness 6actor1 8B$' "$B # $B ' *+.3 5 *+; 8BC' "BC # BC ' *2. 5 *+; &isti2ution Fa4tos
>B$ ' (8 B$# (8 B$K8 BC)) ' +.32 >BC ' (8 BC# (8 B$K8 BC)) ' +.;@ Fi<! En! )omnts •
&6$B' &6B$' &6C>' &6>C '+
•
&6BC' <'<;A. k-
=oint )m2s &F FE) BALANC E CO BALANC E CO BALANC E CO
A
$B 0 -
B
C
BA 0./ 0 5.1/
BC 0.51 -59.> /.0>
CB 0.51 59.> -/.0>
1.
-1.0/ 9.1
1.0/ -9.1
.0>
-/.>5 .16
/.>5 -.16
-.>
.>
& C& 0./ 0 -5.1/
&C 0 -
-1.
-
-.0>
-
BALANC E "O"AL
-
0.59
0.1>
-0.1>
-0.59
-
-
5.1
-5.1
5.1
-5.1
-
&si$n momnts •
Service load end moments1 &B'2;.@ k-
•
>esign end moments &uB'*.; 5 2;.@ ' ;2.;; k-
•
Service load mid span moment in beam' *A.A;5:0# M ;2.;; '2:.00; k-
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>esign mid span moment &uK'*.; 5 2:.00; ' ;3.22 k-
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&a5imum Dorking shear force (at B or C) in beam ' +.; 5 *A.A0 5 : ' ;A.@:k-
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>esign shear force Vu ' *.; 5 ;A.@: ' A.:3 k-
't8/ &si$n of 2ams •
he beam of an intermediate portal frame is designed. he mid span section of this beam is designed as a
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>esign of
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>esign moment &u';3.22 k-
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6lange width bf'
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ere o'+.@ 5 ' +.@ 5 : '3.0m
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bf' 3.0#:K+.3K:5+.**'*.@:m
Step31 >esign of
•
•
•
bf #bw'3.3 and >f #d '+.00 Referring to table ; of S/*:, the moment resistance factor is given by 8 '+.3*, &ulim'8 bwd0fck ' (+.3* 5 3++ 5 ;;+0 5 0+)#*5*+: ' AA0.0 k-
•
•
$st'+.*32 5 3++5;;+#*++ ' 2*3.: mm0 !sing S/ *: ence 0 -os. of *:mm at bottom in the mid span
&si$n of R4tan$ula 2am •
•
•
&u#bd0 ' ;3.22 5 *+:#(3++5;;+0) for this pt'+.*32 $st'+.*32 5 3++5;;+#*++ ' 2*3.: mm0 ence 0 -os. of J*: at the top near the ends for a distance of o.0; ' *.;m from face of the column as shown in 6ig
C4? fo 'a •
-ominal shear stress ' v'Vu# (bd) ' +.3+@
•
•
pt'*++5 2*3.:#(3++5;;+)'+.*32L+.*; /ermissible stress for pt'+.3 from table *A tc'+.22 Ntv ence shear reinforcement is re%uired to be designed
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Strength of concrete Vuc'+.22 5 3++ 5 :++#*+++ ' @A.0 k-
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Shear to be carried by steel Vus'A.:3<@A.0 ' *+.33 k-
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-ominal shear stress ' '8a4in$ l$$! > mm !ia stiu8
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s7@(0.>1f :As7!%Vus@0.>1/5505500.//@/0.>>
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wo legged H stirrups are provided at 2++ mm c#c (e%ual to ma5imum spacing)
't85 &si$n of Columns •
Cross
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!ltimate a5ial load /u'*.; 5 ;A.@: ' A.:3 k- ($5ial load ' shear force in beam)
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!ltimate moment &u' *.; 5 2:.00; ' ;3.22 k-
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$ssuming effective cover d9 ' ;+ mmG d9#> O+.*
&u#(f ck b>0)' ;3.22P*+:#0+P3++P;++0 ' +.+0@ /u#(f ck b>) ' A.:3P*+2#0+P3++P;++' +.+00 •
Referring to chart 20 of S/*:, p#fck'+.+3G p'0+ 5 +.+3 ' +. =
•
E%ual to &inimum percentage stipulated by "S3;:<0+++ (+. = )
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$st'+.53++5;++#*++ ' *:++ mm0
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-o. of bars re%uired ' *:++#2*3 ' ;.+A
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/rovide : bars of dia 0+mm.
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mm diameter tie shall have pitch least of the following
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east lateral dimension ' 3++ mm
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*: times diameter of main bar ' 20+ mm
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3 times diameter of tie bar ' 23
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2++mm
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/rovide mm tie I 2++ mm c#c
't86 &si$n of *in$s •
$t the hinge portion, concrete is under tria5ial stress and can withstand higher permissible stress.
•
/ermissible compressive stress in concrete at hinge' 05+.3f ck '*: &/a
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6actored thrust '/u'A.3k-
•
•
Cross sectional area of hinge re%uired ' A.3+5*+2#*:' ;;@.; mm0 /rovide concrete area of 0++ 5*++ ($rea '0++++mm0) for the hinge
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Shear force at hinge ' otal moment in column#height ' 2;.@#2.0'A.23
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!ltimate shear force ' *.;5A.23'*3.+* k-
•
•
"nclination of bar with vertical ' % ' tan<*(2+#;+) '2*o !ltimate shear force ' +.@ f y$stsin%
$st ' *3.+* P *+2 #+.@P3*;Psin2* '@;.22 •
o7i! /-6 !ia (Aa@>0/ mm %
't81 &si$n of Footin$s •
Loa!$5ial Dorking load on column
' ;A.@: k-
Self weight of column ' +.3 5 +.; 52.@05 03 ' *@.; Self weight of footing I*+= •
•
•
•
•
•
•
' *: k-otal load ' A2.:* k-
Dorking moment at base ' 30 5 * '30 k-
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6actored moment &uL0:.2* k-
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ver all depth shall be assumed as 2++ mm and effective depth as 0;+ mm,
&u#bd0' 0:.2*P*+:#*+++P0;+0' +.30* •
Corresponding percentage of steel from able 0 of S/*: is pt' +.*2= F &inimum pt'+.*0=
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$rea of steel per meter width of footing is $st'+.*05*+++50;+#*++'2++ mm0
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Spacing of *0 mm diameter bar ' **25*+++#2++ ' 2@: mm c#c
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/rovide J*0 I 2++ c#c both ways
•
•
ength of punching influence plane ' ao' ;++K0;+ ' @;+ mm Didth of punching influence plane ' bo' 3++K0;+ ' :;+ mm
•
•
•
/unching shear 6orce ' V punch 'A2.:<3:.@A5(+.@;5+.:;)'@+.@ k/unching shear stress t punch 'V punch#(05(aoKbo)d) '@+.+ 5*+2#(05(@;+K:;+)0;+) ' +.*+2 &/a /ermissible shear stress ' +.0;fck'*.* &/a Ft punch Safe Check for ne Day Shear
•
Shear force at a distance Td9 from face of column
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V' 3:.@A5*5+.3+ ' *.@* k-
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Shear stress tv'*.@* 5*+2#(*+++50;+)'+.++@ &/a
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6or pt'+.*; , the permissible stress tc ' +.0 (6rom table *A of "S3;:<0+++)
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this stress is very small and hence safe
Problem 2 Design Steps:
Design of slabs Preliminary design of beams and columns Analysis Design of beams Design of Columns Design of footings Problem:
A portal frame hinged at base has following data: Spacing of portal frames = 4m Height of columns = 4m Distance between column centers = 1m !i"e load on roof = 1#$ %&'m( )CC slab continuous o"er portal frames# Safe bearing capacity of soil=( %&'m(
Adopt *+( grade concrete and ,e+41$ steel# Design the slab- portal frame and foundations and s%etch the details of reinforcements# Solution: Data gi"en: •
Spacing of frames = 4m
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Span of portal frame = 1m
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Height of columns = 4m
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!i"e load on roof = 1#$ %&'m (
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Concrete: *( grade
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Steel: ,e 41$
Step1: Design of slab •
Assume o"er all depth of slab as 1(mm and effecti"e depth as 1mm
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Self weight of slab = #1( . (4 = (#// %&'m(
•
0eight of roof finish
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Ceiling finish
= #($ %&'m( assumed2
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3otal dead load wd
= #5 %&'m(
•
!i"e load w!
= 1#$ %&'m( 6i"en in the data2
•
*a.imum ser"ice load moment at interior support =
•
*ulim=7limbd( - where 7 lim=(#852
= #$ %&'m( assumed2
/#$ %&+m
= (#85 . 1 . 1( ' 1 . 15 = (8#5 %&+m 9 1(#8$ %&+m
•
,rom table ( of SP15 pt=#/4 Ast=#/4 . 1 . 12'1= /4 mm(
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Spacing of 1 mm dia bars = 8/#$4 . 12'/4= (4#$ mm c'c
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Pro"ide ;1 < ( c'c
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Area of distribution steel Adist=#1( . 1 . 1( ' 1 = 144 mm (
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Spacing of / mm dia bars = $#(5 . 12'144= 4 mm c'c
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Pro"ide >/ < 4 c'c# *ain and dist# reinforcement in the slab is shown in ,ig
Step2: Preliminary design of beams and columns •
Beam:
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?ffecti"e span = 1m
•
•
?ffecti"e depth based on deflection criteria = 1'1 = 85#(mm Assume o"er all depth as 8$ mm with effecti"e depth = 8mmbreadth b = 4$mm and column section e@ual to 4$ mm . 5 mm#
Step3: Analysis Load on frame •
i2 !oad from slab = #51#$2 . 4 = (#$( %&'m
•
ii2 Self weight of rib of beam = #4$.#5.(4= 5#/ %&'m
•
3otal B (/# %&'m
•
Height of beam abo"e hinge = 4#1+8$'( 2=#8( m
•
•
•
•
•
•
3he portal frame subected to the udl considered for analysis is shown in ,ig# 5#1
3he moments in the portal frame hinged at the base and loaded as shown in ,ig# is analised by moment distribution AE = 4$ . 5 '1( = /1 . 1 / mm4EC= 4$ . 8$ '1( = 1$/#( . 1 / mm4 Stiffness ,actor: FEA= AE ' !AE = (1#88 . 1 $ FEC= EC ' !EC = 1$#/ . 1 $ Distribution Factors:
Fixed nd !oments:
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*,AE= *,EA= *,CD= *,DC
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*,EC= +=+( %&+m and *,CE= =( %&+m
Fig: !oment Distribution "able
Design moments: •
Ser"ice load end moments: * E=1$5 %&+m-
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Design end moments * uE=1#$ . 1$5 = (4 %&+m-
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Ser"ice load mid span moment in beam= (/.1 ( '/ G 1( =14 %&+m
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Design mid span moment *u=1#$ . 14 = (1 %&+m
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*a.imum 0or%ing shear force at E or C2 in beam = #$ . (/ . 1 = 14%&
•
Design shear force u = 1#$ . 14 = (1 %&
Step#: Design of beams: •
3he beam of an intermediate portal frame is designed# 3he mid span section of this beam is designed as a 3+beam and the beam section at the ends are designed as rectangular section#
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Design of 3+section for *id Span :
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Design moment *u=(1 %&+m
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,lange width bf=
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Here !o=#8 . ! = #8 . 1 =8m
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bf= 8'5#4$5.#1(=(#m
Step4: Design of 3+beam: •
•
b 'b f w=$#( and D f 'd =#18 )eferring to table $/ of SP15- the moment resistance factor is gi"en by F 3=#4*ulim=F3 bwd( fc% = #4 . 4$ . 8 ( . ('1.1 5 = 1/5# %&+m 9 *u Safe
•
3he reinforcement is computed using table ( of SP15
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*u'bd( = (1 . 1 5 '4$.8(2B1# for this p t=#(
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Ast=#( . 4$.8'1 = 1(4#/ mm (
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&o of ( mm dia bar = 1(4#/'p.( ( '42 =#
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Hence 4 &os# of >( at bottom in the mid span
Design of $ectangular beam: •
Design moment *uE=(4 %&+m
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*uE 'bd(= (4.15'4$.8 ( B1#1 ,rom table ( of SP15 p t=#(8
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Ast=#(8 . 4$ . 8 ' 1 = 1
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&o of ( mm dia bar = 1'p.( ( '42 =#(
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Hence 4 &os# of >( at the top near the ends for a distance of o#($ ! = (#$m from face of the column as shown in ,ig
Fig: Long Section of Beam
Fig: %ross Section %&ec' for S&ear:
•
&ominal shear stress =
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pt=1. 1($5'4$.82=#B#4
•
•
Permissible stress for pt=#4 from table 1 tc=#4( I t" Hence shear reinforcement is re@uired to be designed Strength of concrete uc=#4( . 4$ . 8'1 = 15 %&
•
Shear to be carried by steel us=(1+15 = 84 %&
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&ominal shear stress = pt=1. 4('4.52=#B#4
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Permissible stress for pt=#4 from table 1 t c=#4( I t " Hence shear reinforcement is re@uired to be designed
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Strength of concrete uc=#4( . 4 . 5'1 = 1 %&
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Shear to be carried by steel us=15(+1 = $ %& Spacing 2 legged ( mm dia stirrup
•
•
s)*
3wo legged ;/ stirrups are pro"ided at mm c'c e@ual to ma.imum spacing2
Step$: Design of Columns: •
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Cross+section of column = 4$ mm . 5 mm Jltimate a.ial load Pu=1#$ . 14 = (1 %& A.ial load = shear force in beam2
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Jltimate moment *u= 1#$ . 1$5 = (4 %&+m *a.imum2
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Assuming effecti"e co"er dK = $ mm dK'D L#1
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)eferring to chart ( of SP15- p'fc%=#4 p=( . #4 = #/ M
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?@ual to *inimum percentage stipulated by S4$5+( #/ M 2
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Ast=#/.4$.5'1 = (15 mm(
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&o# of bars re@uired = (15'14 = 5#/
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Pro"ide / bars of dia (mm#
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/mm diameter tie shall ha"e pitch least of the following
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!east lateral dimension = 4$ mm
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15 times diameter of main bar = ( mm
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4/ times diameter of tie bar = /4
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mm
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Pro"ide / mm tie < mm c'c
Step+: Design of ,inges: •
At the hinge portion- concrete is under tria.ial stress and can withstand higher permissible stress#
•
Permissible compressi"e stress in concrete at hinge= (.#4f c% =15 *Pa
•
,actored thrust =P u=(1%&
•
Cross sectional area of hinge re@uired = (1.1 '15=11($ mm(
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Pro"ide concrete area of ( .1 Area =(mm (2 for the hinge
•
Shear force at hinge = 3otal moment in column'height = 1$5'#8(=4(
•
Jltimate shear force = 1#$.4(=5 %&
•
•
nclination of bar with "ertical = @ = tan+1'$2 =1 o Jltimate shear force = #/8 f y Ast sin@
•
Pro)ide #-1+ dia .Area*(/# mm 20 Step: Design of Footings:
•
Load:
A.ial 0or%ing load on column
= 14 %&
Self weight of column = #4$ . #5 .#8(. (4 = (4 Self weight of footing <1M
= 15 %&
3otal load = 1/ %& •
•
•
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0or%ing moment at base = 4( . 1 =4( %&+m Appro.imate area footing re@uired = !oad on column'SEC= 1/'( =# m ( Howe"er the area pro"ided shall be more than re@uired to ta%e care of effect of moment# 3he footing siNe shall be assumed to be 1m.(m Area=( m (2
*a.imum pressure @ma.=P'A*'O = 1/'(5.4('1.(( = 1$ %&'m (
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•
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*inimum pressure @min =P'A+*'O = 1/'(+5.4('1.( ( = (8 %&'m ( A"erage pressure @ = 1$(82'( = %&'m ( Eending moment at + = . 1 . #8('( = (( %&+m
•
,actored moment *uB %&+m
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Q"er all depth shall be assumed as mm and effecti"e depth as ($ mm-
•
•
Corresponding percentage of steel from 3able ( of SP15 is pt= #1$M 9 *inimum pt=#1(M Area of steel per meter width of footing is A st=#1(.1.($'1= mm(
•
Spacing of 1( mm diameter bar = 11.1' = 85 mm c'c
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Pro"ide >1( < c'c both ways
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!ength of punching influence plane = ao= 5($ = /$ mm 0idth of punching influence plane = bo= 4$($ = 8 mm Punching shear ,orce = punch =1/+.#/$.#82=1(5#$ %& Punching shear stress t punch =punch '(.aobo2d2 =1(5#$.1'(./$82($2 = #15 *Pa Permissible shear stress = #($Rfc%=1#1/ *Pa 9 t punch Safe Chec% for Qne 0ay Shear
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Shear force at a distance dK from face of column
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= .1.#4$ = 4#$ %&
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Shear stress t"=4#$.1'1.($2=#15( *Pa
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,or pt=#1$ - the permissible stress t c = #(/ ,rom table 1 of S4$5+(2
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Details of reinforcement pro"ided in footing is shown in ,ig#
otal Fam &si$n ;itout *in$ ROBLE) &si$n 't8s
>esign of slabs /reliminary design of beams and columns $nalysis >esign of beams
>esign of Columns >esign of footings o2lm
$ portal frame hinged at base has following data1 Spacing of portal frames ' 3m eight of columns ' :.;m >istance between column centers ' *+m ive load on roof ' *.; k-#m0 RCC slab continuous over portal frames. Safe bearing capacity of soil'*0+ k-#m0 $dopt &<0+ grade concrete and 6e<3*; steel. >esign the slab, portal frame and foundations and sketch the details of reinforcements. Solution1 >ata given1 •
Spacing of frames ' 3m
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Span of portal frame ' *+m
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eight of columns ' :.:m
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ive load on roof ' *.; k-#m0
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Concrete1 &0+ grade
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Steel1 6e 3*;
't8 &si$n of sla2 •
$ssume over all depth of slab as *++mm and effective depth as ;mm
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Self weight of slab ' +.** 5 03
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ive load w
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&a5imum service load moment at interior support '
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&u'*.; 5 ;.: ' .3 k-
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&ulim'lim bd0 , where (lim'0.@:)
' 0.3 k-#m0
' *.;+ k-#m0 (7iven in the data)
' 0.@: 5 *+++ 5 ;0 # * 5 *+: '*AA3* k-
' ;.: k-
(&u#bd0)' +.2 •
6rom table 0 of S/*: pt'+.003G $st'(+.03 5 *+++ 5 *++)#*++' 03 mm0
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Spacing of *+ mm dia bars ' (@.;3 5 *+++)#23' 0@+ mm c#c
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/rovide H*+ I 0+ c#c
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$rea of distribution steel $dist'+.*0 5 *+++ 5 *++ # *++ ' *0+ mm0
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Spacing of mm dia bars ' (;+.0: 5 *+++)#*0+' 3*+ mm c#c
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/rovide J I 3*+ c#c. &ain and dist. reinforcement in the slab is shown in 6ig
't8 limina: !si$n of 2ams an! 4olumns •
Bam
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Effective span ' *+m
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Effective depth based on deflection criteria ' *++++#*; ' @++mm
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$ssume over all depth as :++ mm with effective depth ' :;+mm, breadth b ' 2++mm and column section e%ual to 2++ mm 5 ;++ mm.
't8 Anal:sis Loa! on fam •
i) oad from slab ' (0.;0K*.;) 5 3 ' *:.+@ k-#m
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ii) Self weight of rib of beam ' +.35+.;;503' ;.0+ k-#m
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otal L 0+.2: k-#m
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eight of beam above hinge ' 3K+.*<(+.;;#0 )'2.0; m
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he portal frame sub?ected to the udl considered for analysis is shown in 6ig. :.*+
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he moments in the portal frame hinged at the base and loaded as shown in 6ig. is analised by moment distribution "$B ' 2++ 5 @++2#*0 ' ;.@; 5 *+ mm3, "BC' 2++ 5 ;++2#*0 ' 2*.0; 5 *+ mm3
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Stiffness 6actor1 8B$' "$B # $B ' *+.3 5 *+; 8BC' "BC # BC ' *2. 5 *+; &isti2ution Fa4tos
>B$ ' (8 B$# (8 B$K8 BC)) ' +.2: >BC ' (8 BC# (8 B$K8 BC)) ' +.:3 Fi<! En! )omnts •
&6$B' &6B$' &6C>' &6>C '+
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&6BC' <'<*:A.@k-
=oint )m2s &F FE) BALANC E CO BALANC E CO BALANC E CO BALANC E "O"AL
A
$B
B
C
BA 0.6 0 6.
BC 0.6/ -69.1 0>.6
CB 0.6/ 69.1 -0>.6
9.5/
-5/. /.16
5/. -/.16
6.6
-1.> .
1.> -.
. -
0.59
-5.56 0.1>
//.11
>9.5/
->9.5/
0 0.55 9.11 -
& C& 0.6 0 -6.
&C 0 -
-9.5/
-0.55 -
-6.6
-9.11 -
5.56 -0.1>
-0.59
-. -
>9.5/
-//.11
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&si$n momnts •
Service load end moments1 &B'0;3;+ k-
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Service load mid span moment in beam' 0;3.;<A.; '*:3.A: k-
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&a5imum Dorking shear force (at B or C) in beam ' +.; 5 0+.2: 5 *+ ' *+*. P *+U2
't8/ &si$n of 2ams
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he beam of an intermediate portal frame is designed. he mid span section of this beam is designed as a
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>esign of
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>esign moment &u'*:3.A: k-
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6lange width bf'
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ere o'+.@ 5 ' +.@ 5 *+ '@m
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bf' @#:K+.3K:5+.**'0.:3m
't85 &si$n of "-2am 1 •
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bf #bw';.0 and >f #d '+.0 Referring to table ; of S/*:, the moment resistance factor is given by 8 '+.3@, &ulim'8 bwd0fck ' (+.3@ 5 2++ 5 @++0 5 0+)#*5*+: ' *3A0.0 k-
&si$n of R4tan$ula 2am •
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&u#bd0 ' A.;3 5 *+:#(2++5@++0) for this pt'+.*: $st'+.*: 5 3++5;;+#*++ ' *0;+ mm0 ence 3 -os. of J0+ at the top near the ends for a distance of o.0; ' *.;m from face of the column as shown in 6ig
C4? fo 'a •
-ominal shear stress ' v'Vu# (bd) ' +.3+@
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pt'*++5 2*3.:#(2++5@+++)'+.*32L+.*;
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/ermissible stress for pt'+.3 from table *A tc'+.22 Ntv ence shear reinforcement is re%uired to be designed Shear to be carried by steel Vus' @+.@3 k -ominal shear stress ' '8a4in$ l$$! > mm !ia stiu8
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'7@(0.>1f :As7!%Vus@0.>1/55010010.1/@0
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wo legged H stirrups are provided at **+ mm c#c (e%ual to ma5imum spacing)
't85 &si$n of Columns •
Cross
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!ltimate a5ial load /u'*.; 5 ;A.@: ' A.:3 k- ($5ial load ' shear force in beam)
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!ltimate moment &u' *.; 5 2:.00; ' ;3.22 k-
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$ssuming effective cover d9 ' ;+ mmG d9#> O+.*
&u#(f ck b>0)' *:3.22P*+:#0+P2++P@++0 ' +.+0@ /u#(f ck b>) ' *+.P*+2#0+P3++P;++' +.+00 •
Referring to chart 20 of S/*:, p#fck'+.+3G p'0+ 5 +.+3 ' +. =
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E%ual to &inimum percentage stipulated by "S3;:<0+++ (+. = )
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$st'+.52++5@++#*++ ' *; mm0
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-o. of bars re%uired ' *:++#2*3 ' ;.+A
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/rovide : bars of dia 0+mm.
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mm diameter tie shall have pitch least of the following
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east lateral dimension ' 2++ mm
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*: times diameter of main bar ' 20+ mm
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3 times diameter of tie bar ' 23
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2++mm
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/rovide mm tie I 2++ mm c#c
't86 &si$n of Footin$s
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Loa!
$5ial Dorking load on column
' *+ k-
Self weight of column ' +.2 5 +.: 5;.@05 03 ' 03.@* Self weight of footing I*+=
' *: k-
otal load ' *3 k•
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Dorking moment at base ' 3 5 * '3 k-
&a5imum pressure %ma5'/#$K&#Q ' *22.; k-#m0 &inimum pressure %min '/#$<&#Q ' ' :;.3 k-#m0 $verage pressure % ' A@.:@ k-#m0 Bending moment at < ' ' 0@.;3 k-
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6actored moment &uL2:.0* k-
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ver all depth shall be assumed as 2++ mm and effective depth as 0;+ mm, &u#bd0' +.;:2
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Corresponding percentage of steel from able 0 of S/*: is pt' +.*2= F &inimum pt'+.*0=
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$rea of steel per meter width of footing is $st'+.*05*+++50;+#*++'2++ mm0
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Spacing of *0 mm diameter bar ' **25*+++#2++ ' 2@: mm c#c
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/rovide J*0 I 2++ c#c both ways
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ength of punching influence plane ' ao' @++K0;+ ' A;+ mm
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Didth of punching influence plane ' bo' 2++K0;+ ' ;;+ mm /unching shear 6orce ' V punch '*2+.@ k/unching shear stress t punch 'V punch#(05(aoKbo)d) '*2+.+ 5*+2#(05(A;+K;;+)0;+) ' +.**2 &/a /ermissible shear stress ' +.0;fck'*.* &/a Ft punch Safe Check for ne Day Shear
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Shear force at a distance Td9 from face of column
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V' ;.* k-
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Shear stress tv'+.+*A &/a
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6or pt'+.*; , the permissible stress tc ' +.0 (6rom table *A of "S3;:<0+++)
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this stress is very small and hence safe.
/RBE& 3 he roof of a m wide hall is supported on a portal frame spaced at 3m intervals. he height of the portal frame is 3m. he continuous slab is *0+ mm thick. ive load on roof ' *.; k-#m0, SBC of soil ' *;+ k-#m0. he columns are connected with a plinth beam and the base of the column may be assumed as fi5ed. >esign he slab, column, beam members and suitable footing for the columns of the portal frame. $dopt &0+ grade concrete and 6e 3*; steel. $lso prepare the detailed structural drawing. Solution1 >ata given1 Spacing of frames ' 3m Span of portal frame ' m eight of columns ' 3m ive load on roof ' *.; k-#m0 hickness of slab ' *0+mm Concrete1 &0+ grade Steel1 6e 3*; 't8&si$n of sla2
Self weight of slab ' +.*0 5 03 ' 0. k-#m0 Deight of roof finish ' +.;+ k-#m0 (assumed) Ceiling finish ' +.0; k-#m0 (assumed) otal dead load wd ' 2.:2 k-#m0 ive load w ' *.;+ k-#m0 (7iven in the data)
6rom table 0 of S/*: pt'+.23G $st'(+.23 5 *+++ 5 *++)#*++' 23 mm0 Spacing of *+ mm dia bars ' (@.;3 5 *+++)#23' 0+3.; mm c#c o7i! 0 D 00 44
$rea of distribution steel $dist'+.*0 5 *+++ 5 *0+ # *++ ' *33 mm0 Spacing of mm dia bars ' (;+.0: 5 *+++)#*33' 23A mm c#c o7i! > D /0 44. 't8 limina: !si$n of 2ams an! 4olumns Beam:
Effective span ' m Effective depth based on deflection criteria ' +++#*0 ' :::.:@mm $ssume over all depth as @++ mm with effective depth ' :;+mm, breadth b ' 3++mm and column section e%ual to 3++ mm 5 :++ mm. 't8 Anal:sis Load on frame
i) oad from slab ' (2.:2K*.;) 5 3 '0+.;0 k-#m ii) Self weight of rib of beam ' +.35+.;503 ' ;.;: k-#m otal ≈ 0@.++ k-#m he moments in the portal frame fi5ed at the base and loaded as shown in 6ig. :.3 are analysed by moment distribution "$B ' 3++ 5 :++2#*0 ' @0 5 *+ mm3, "BC' 3++ 5 @++2#*0 ' **3.22 5 *+ mm3 Stiffness Factor:
8 B$' "$B # $B ' * 5 *+; 8 BC' "BC # BC ' *3.2 5 *+;
Design moments:
Service load end moments1 &B'*+0 k-esign end moments &uB'*.; 5 *+0 ' *;2 k-esign mid span moment &u K'*.; 5 **3 ' *@* k-esign shear force Vu ' *.; 5 *+ ' *:0 k't8/&si$n of 2ams
he beam of an intermediate portal frame is designed. he mid span section of this beam is designed as a
>esign moment &u'*@* k- : + + , ere o'+.@ 5 ' +.@ 5 ';.:m bf ' ;.:#:K+.3K:5+.*0'0m bf #bw'; and >f #d '+.0 Referring to table ; of S/*:, the moment resistance factor is given by 8 '+.3;A, &ulim'8 bwd0 f ck ' +.3;A 5 3++ 5 :++0 5 0+#*5*+: ' *20*.A0 k-
ence 2 -os. of J0+ at bottom in the mid span Design of Rectangular-section for End Span :
>esign moment &uB'*;2 k-
't85&si$n of 4olumns
Cross ≈+.*
Referring to chart 20 of S/*:, p#f ck '+.+2G p'0+ 5 +.+2 ' +.: &inimum steel in column should be +. =, ence min steel percentage shall be adopted $st'+.53++5:++#*++ ' *A0+ mm0 -o. of bars re%uired ' *A0+#2*3 ' :.* o7i! > 2as of 0
mm diameter tie shall have pitch least of the following i) east lateral dimension ' 3++ mm ii) *: times diameter of main bar ' 20+ mm iii) 3 times diameter of tie bar ' 23 iv) 2++mm o7i! > mm ti D 00 mm 44
