Design of Corbel for Precast Girder, G1
ENGR. THOMAS OHN D. AGRA!"O
Design Specifications ( f c’ = = 28 MPa, f MPa, f y = 276 MPa) Design a bracket that projects from a 5 mm s!"are co#"mn to s"pport $ea$ an$ #i%e #oa$s of V u
6&8 k' an$ &75 ', respecti%e#*& +ss"ming a horionta# force of &
$"e to creep, shrinkage an$
φ
temperat" temperat"re re effects& effects& 'ote-
sha## be taken e!"a# to &75 in a## $esign ca#c"#ations accor$ing to 'S.P
/00&0&&0 1.
#act #actor oreed $oad $oadss V u =
1actore$ shear,
0&2(6&8) 0&6(&75) = 026&0 k' N uc =
3orionta# force, %.
&(026&0) &(026&0 ) = 7&8 k' 4 (&2" = 2&7 k')
('S.P /00&0&&/)
Prel Preli& i&in inar ar' ' brac( brac(et et si)e si)e& he shear span a is $epen$ent on the bearing #ength re!"ire$ to s"pport the
reaction on the concrete& V u
= φ (&85 f c9 A plat e = φ (&85 f c9 bw L
earing strength, L =
V u
φ &85 f c9 bw
=
0260 &65(&85)(28)(5 5 )
= 06&
:ength of bearing p#ate,
mm
*se + && -late lengt as te -ractical &ini&/& a v = 25 +
2
(;.D,
(75) = 75
Shear span,
mm
25 mm ma>im"m c#earance at the beam en$& eam reaction is ass"me$ at thir$ point of bearing p#ate to sim"#ate sim"#ate rotation of s"pporte$ gir$er gir$er an$ triang"#ar triang"#ar $istrib"tion $istrib"tion of stress "n$er bearing p#ate (Simp#ifie$ ;.D, ?i##esania) 0.
De-t De-t of of bra brac( c(et et for for se sear ar
V n
=
V u
φ
026 &0 = 026 = 068 068 &0 &75
k' V n
1or norma# @eight concrete,
sha## not e>cee$ the sma##est of-
('S.P /00&0&&0)
V n = &2 fc 9 bw d = &2( 28)bw d = 5&6bw d V n = (& + &8 fc 9 )bw d = [ & + &8( 28)]bw d = 5&5/bw d V n = 00bw d ?o%ernsA V n
= 5&5/bw d
0680
d =
d
6&7 mm .
= 5&5/(5 )d
minim"m
base$ on shear re!"irements
De-t of brac(et for fle2/re
M u
= V u av + N uc (h − d ) = 026 &0(&75 ) + 7&8(&5 ) = 00&5 k'Bm
('S.P Section /00&0&)
(h − d ) = 5
Cstimating
mm
sing Minim"m reinforcement ratio,
('S.P Section /00&0&5)
f c9 = &/( 28 ) = &/6 f y 276
min ρ = &/
Strength ;atio, m
=
(;.D,
&85 fc 9
=
276 &85(28)
= 00&6
.oefficient of resistance, Ru
(;.D,
ρ m &/6 (00&6) = 0&/ = ρ fy 0 − = &/6 ( 276)0 − 2 2
MPa ;e!"ire$ effecti%e $epth,
d reqd =
M u φ Ru b
(;.D,
=
00&5 × 0
6
&75(0&/ )(5 )
= 066 & mm a E d
5&
Select brac(et de-t & Since the pro%isions of 'S.P for brackets an$ corbe# $esign app#* on#* @hen
$oes not e>cee$ 0&, ( a E d = &/5) < 0&
F
('S.P Section /00&0&0)
d = a
= 75
min
mm d ≈ 5
h = 5
r*
− 25 − 8 = 07
mm ,
mm Avf
6&
Deter&ine sear3friction reinforce&ent
Avf =
V u
φ fy µ
=
0260 &75( 276 )(0&/)
= /5 &0 mm2
('S.P /00&8&/&0)
µ = 0&/λ = 0&/(0) = 0&/
µ = 0&/
A f
7&
(+.GB00&&&)
Deter&ine te fle2/re reinforce&ent
.oefficient of resistance,
Ru
=
M u
φ bd 2
=
(;.D,
&75(5 )(07 ) 2
= &0 MPa
Stee# ratio,
ρ =
/
A f
2 R m 0 0 2(&0)(00&6) 0 − 0 − u = 0 − 0 − = &08 < ( ρ min = &/6 ) 276 m fy 00&6
ρ =
/
(&08 ) = &0/6/
= ρ bd = &0/6/ (5)(07 ) = 22&/ mm2 An
4.
Deter&ine additional reinforce&ent for a2ial tension
An
=
N uc φ fy
=
78 &75(276)
= 082 &75 mm2
('S.P /00&8&/&0)
A sc &
('S.P /00&0&)
Total &ain tension reinforce&ent A sc
+rea of primar* reinforcement tension reinforcement
sha## not be #ess than the
#arger of A sc
= A f + An = 22 &/ + 082 &7 = /0/ &7/ mm2
A sc
=
2
Avf + An
=
2
(/5 &0) + 082 &75 = /72 &8/
mm2 Ab =
?o%ernsA
π (06) 2 = 20 /
sing 06 mm φ barsn=
/72 &8/ 20
= 2&5 , sa' 0315 &&
bars
0& Deter&ine closed stirr/- re6/ire&ents Ah
('S.P /00&0&/)
= &5( A sc − An ) = &5(/72 &8/ − 082 &75) = 0/5 &5
min Ab =
π (0) 2 (2) = 057 / mm2
sing 0 mm φ tiesn=
0/5 &5 057
= &2 , sa' %317 &&
s =
2
closed oo-s
(07 ) E 2 = 06
Spacing-
mm, /se 177 && s-acing
00& O8erall brac(et di&ension& +ss"ming that a 25 mm thick bearing p#ate is to be @e#$e$ to the main tension reinforcement, the o%era## $epth is h = bearing p#ate thickness bar ra$i"s effecti%e $epth, d = 25 8 07 = 5 mm 0 5
2
:ength of bracket projection 9 mm bearing p#ate shear span, = 5 H(75) 75 = 062&5 mm, sa* 2 mm
av
= 062&5 mm, sa* 075 mm
16 mm bars welded to underside of Steel plate
Welded
0 2
Minim"m Depth of o"ter face of bracket =
h=
0 2
(5 ) = 075
mm
C#astomeric bearing pa$s @ith minim"m thickness 0 mm p#ate is "se$ in the $esign (P.G 6&5&8&0)& earing pa$s are "se$ to $istrib"te concentrate$ #oa$s an$ reactions o%er the bearing area an$ to a##o@ #imite$ horionta# an$ rotationa# mo%ements to pro%i$e stress re#ief& 1%. Details
