Design of Cantilever Beam

7/23/2019 Design of Cantilever Beam

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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

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Design of Cantilever Beam