design of cantilever beam
TRANSCRIPT
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DESIGN OF CANTILEVER BEAM (L.S.M)
1) Design a cantileve !ea" #$ s%an &" s'!ecte t# '..l #$ 1*+N,".
'seM-* gae c#ncete an /SD !as. Design as %e L.S.M.
Data:
For M20 grade concrete, fck = 20N/mm.
For HYSD bars, fy = !"N/mm.
S#$er %m$osed &oad = !0'N/m.
S$an = (m.
)# ma). = 0.*d.
+readt and de$t of te beam:-ss#me de$t, d = / = (000/ = 2*mm.
&et #s ado$t oera&& de$t of te beam, D = "00mm.
at te f%)ed end. 1e de$t can be red#ced to 200mm m%n. %s !"0mm3 at te free
end. 4ere te +.M 5%&& be 6ero. 7ro%de, b= D/2 = "00/2= 2"0mm.
te effect%e s$an = c&ear s$an for cant%&eers = (m.
eff. 8oer = 0mm.
d, eff. De$t = "0090 =0mm.
oads and +.M:
Se&f 5e%gt of beam = 0.";0.23/2
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1%s acts at = (/(0.";2
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8eck for def&ect%on:
-ct#a& &/d = (000/0 =."2
-&&o5ab&e &/d = bas%c &/d3
+as%c &/d= for cant%&eers c&a#se 2(.2.!3
-&&o5ab&e &/d=
Factored ma). Sear force at te f%)ed end = !."!0
= 0.(( N/mm
For 0."2J stee& and M20 grade concrete
c , $erm%ss%b&e sear stress = 0.? N/mm L
1ere fore $ro%de m%n%m#m sear re%nforcement.
s%ng *mm d%a 29&egged ert%ca& st%rr#$s
S$ac%ng = -s< 0.*fy3/0.b3 = 2
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= P = "2mm.
8eck for crack%ng:
8&ear d%stance bet5een bars = 2"092
8#rta%&ment of &ong%t#d%na& re%nforcement:
1e re%nforcement can be c#rta%&ed to5ards te free end of te cant%&eer as bend%ng
moment decreases ery ra$%d&y.et #s c#rta%& !9!P bar at ) d%stance from free end 5ere t%s %s not reC#%red to res%st
bend%ng moment.
Rffect%e de$t of te beam at d%stance ) =20090 ; 09!03/(000>
= !!"!??2*;!"!.2)
) = 22!( mm. d = (*!.( mm
Hence, !9!P can be c#rta%&ed at (000922!(3 *mm from te f%)ed end.
Ho5eer as $er c&a#se 2.2.(.! , te re%nforcement sa&& e)tend beyond te $o%nt at
5%c %t %s no &onger reC#%red. 1o res%st f&e)#re for a d%stance eC#a& to te effect%e de$t
of te member or !2 P 5%c eer %s greater.
Here d= (*!.(mm
!2P = !2
2"0mm
"00mm
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Treater %s (*!.( mm.
R)tend te for a &engt of (*!.(mm from te teoret%ca& c#toff $o%nt.
7ract%ca& c#toff $o%nt = *;(*!.(
= !!*.( say !!0mm.
M%n.d%stance at 5%c any bar can be c#rta%&ed from te f%)ed end %s d = "2mmB
!!0mmo.k.3
F#rter ,te rema%n%ng 29!P bars m#st be cont%n#ed #$to a &engt d beyond te
-ct#a& c#toff $o%nt %n order to dee&o$ te%r f#&& tens%&e strengt at tat sect%on.
LINTEL C0M S0NSADE
() Design t2e lintel an s'n s2ae #ve an #%ening -" 3ie in a 3all &**""
t2ic4ness. T2e lengt2 #$ t2e s'n s2ae is 56*"".t2e live l#a #n s'ns2ae is
6**N,"7 an t2e ensit8 #$ "as#n8 is 19+N,":.T2e 2eig2t #$ #%ening is -" 3it2
t2e 2eig2t #$ t2e $l## !eing &.-".0se M-* c#ncete an Fe;16 steel.
Design #$ s'ns2ae** "" ee% s'!ecte t# a BM #$1** 4N=" s2ea $#ce #$ -6 4N an t3isting "#"ent #$ ;* 4N=". 0se M-* gae
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c#ncete an /SD !as.Design as %e LSD "et2#.
A).
M# = *0 kN9m #= 0 kN 1#= 0 kN9m
-ss#me effect%e coer = "0mm
effect%e de$t = d = 00 E "0 = ""0m
RC#%a&ent sear e = #; !.1#/b = 0 ; !. < 0/0.( = 2*(.( kN.
eeC#%a&ent nom%na& sear stress = 2(
/2.!"0
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L#ngit'inal steel
RC#%a&ent +.M = Me!= M# ; Mt.
4ere, ..:.0.!
(00/:00!0
.!
/mkN
bDlTM ut =
+=
+=
Me!= *0 ;0. = !"0. kN Em.
MtB M#No stee& %s reC#%red on com$ress%on face. c&.: !..2.!3
C2ec4 e%t2
Me!= 0.( fck b )#ma)d90.2 )#ma)3
\#ma)= 0.*d
!"0.
S%nce d aa%&ab&e%s greater tan dreC#%redfor a ba&anced sect%on,te sect%on 5%&& be des%gned as
.@.+eam.
=
2
!:.!!".0
fckbd
M
fy
fckbdA est
=
2
:
""0
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b! = b E 2 2"3 ; 2 !/23>
= (00 E = 2(
d! = 00 E "03 < 2 = "00
!"
0*.!"
(: SvSv
+=
= 0.? S ; 0.!"" S.
!".0* = !.!0S
S = !2 mm
23.fy
Asv*/.0
Sbc39e =
!"
1ranserse re%nforcement as $er 8&. 2.".!. of KS "
(3. S$ac%ng , S = )!
)! = 2( ; ! ; !0 = 20 mm
y! = 00 E 2 "03 ; 2!/23 ; 2!0/23
= "2 mm.
3 ".!?:
"2:2:0
!! =+
=+ yx
"3 (00 mm.
7ro%de st%rr#$s at !0 c/c
-s te de$t %s greater tan "0mm $ro%de s%de face re%nforcement O 0.!J of
8.S area 8&.2".".!.b33= 2!*0:00
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@e%nforcement deta%&s