Design a Beams by Eurocode
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Transcript of Design a Beams by Eurocode
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8/9/2019 Design a Beams by Eurocode
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1
REF
Φ
Dimension:
Span , L 8000width, B 3000
Slab Thicness 110
Beam si!e ""# #00 mm
$ha%acte%istic loads
Finishes etc 1
'a%iable, ( 3
)ate%ials:
*nit wei+ht o conc%ete "#
$ha%acte%istic st%en+th o conc%ete, c "#
$ha%acte%istic st%en+th osteel, - #00
$ha%acte%istic st%en+th o lin, - #00
Nominal concrete cover 30mm
.ss/med :
Φba%1 = "0 mm
Φba%" = 1" mm
Φlin = mm
#&3&"&1
Distributed load 33&32m
)oment "42m
2m"
2m"
2))3
2mm"
2mm"
2mm"
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"
REF $.L$*L.T562S
L7 8000 mm
L7 8000 mm
L7 8000 mmspan 1" span"3 span39
""# mm ""# mm ""#
110 mm 110 mm 110
h 7 #00 mm #00 mm #00
1900 mm 1900 mm 1900
1900 mm 1900 mm 1900
.ct/al an+e with
b =7 30"# mm
Span 1-2
E;ecti = L #00
140# 140#
890 890
890 890
Span 4-5
b = 7 30"# mm
0&8# = L 800
"19# "19#
40 40
Bw
7
h
7
b1
7
b"
7
b1
+ b 2
+ bw
L6
7
bef ,
= bef , I
+ bw
< b
be; , 1
i
+ 0.1l 0
< 0.2l o
be; , 1
i
+ 0.1l 0
< 0.2l o
b1
+ b 2
+ bw
L6
7
bef ,
= bef , I
+ bw
< b
be; , 1
i
+ 0.1l 0
< 0.2l o
be; , 1
i
+ 0.1l 0
< 0.2l o
b1
+ b 2
+ bw
L6
7
bef ,
= bef , I
+ bw
< b
be; , 1
i
+ 0.1l 0
< 0.2l o
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3
40 40
ACTIONS
Actions on slab:
Selwei+ht 7 "&>#
Finishes 1
9&"#
3
Actions of beamCA-!
Dist%ib/tion o action %om slabs to beam a%e as ollows
?anel 11a.D:
ly/lx = "&> @ "
one wa-
0
be; , 1
i
+ 0.1l 0
< 0.2l o
2m"
2m"
$ha%acte%istic pe%manent load, + 2m"
cha%acte%istic
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9
MAIN REINFORCEMENT
Span 1-2
9#9 mm
Benin+ moment,
) 7 143&8 2m
1339&94140882m
M @
2e/t%al ais within an+e
k =
7 0&01>#""841"
7 0&489301"9> 0&4#
.%ea o tension %eino%cement
7 103"&3"90883
4&"&1&1 )inim/m and maim/m %eino%cement a%ea
7 13#&48"08 13#&48"08
9#00
s"ppo#t 2
E;ecti! ck bh! "d#$%h!&
M!
M/! ck
bd2
' = d ( #$% " #$2% k / 1$1)*&1/2
s
= M/#$-. !yk'
mm"
.s,min 7 C0&"C! ctm /! yk &bdmm"
.s, ma
7 0&09.c
mm"
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#
999 mm
) 7 "3> 2m
k =
7 0&"13>">"908
Redist%ib/tion 7
7 0&1838>"
comp%ession %eino%cement is %e(/i%ed
d 7
7 9
7 0&8"0>081> 0&8"0>08"
7 39&3499"1
7Cd!0&9
7 144&013439
d 7 0&"31134#438 0&"31134
.%ea o comp%ession steel
7 300&1#>801#
.%ea o tension steel
7 19>&9>>9>08
13"&4888 13"&4888 mm
E;ecti
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7 9#00 mm
span 2-4
9#9
) 7 1#1 2m
Benin+ moment,) 7 1#0&92m
7 118#&1>81"88
M
2e/t%al ais within an+e
k =
7 0&01#39#4991
7 0&48">41 0&4#
.%ea o tension %eino%cement
7 80"&418>3#34
7 13#&48"08 13#&48"08 0&0013bd
9#00
s"ppo#t 4
999 mm
E;ecti!
ck bh
! "d#$%h!&
M!
M/! ck
bd2
' = d ( #$% " #$2% k / 1$1)*&1/2
s
= M/#$-. ! yk '
mm"
.s,min 7 C0&"C! ctm /! yk &bd
.s, ma
7 0&09.c
mm"
E;ecti
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>
) 7 "3> 2m
k =
7 0&"13>">"908
Redist%ib/tion 7
7 0&1838>"
comp%ession %eino%cement is %e(/i%ed
d 7 7 9
7 0&8"0>081> 0&8"0>08"
7 39&3499"1
7Cd!0&9
7 144&013439
d 7 0&"31134#438 0&"31134
.%ea o comp%ession steel
7 300&1#>801#
.%ea o tension steel
7 19>&9>>9>08
13"&4888 13"&4888 mm
7 9#00 mm
M/! ck
bd2
bal
7 0&9#9CG1
" 0&18"HCG
1
"I"
bal
c J Φlin
J 0Φba%
' = d ( #$% " #$2% k bal
/ 1$1)*&1/2
.s
7 C bal
! ck
bd2 /"#$-.! yk
"dd&
s = k bal ! ck bd2
/#$-. !yk' + s
.s,min
7 C0&"C! ctm
/! yk &bd
.s, ma
7 0&09.c
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8
span4-5
9#9
) 7 1#1 2m
Benin+ moment,) 7 143&82m
7 1339&9414088
M
2e/t%al ais within an+e
k =
7 0&01>#""841"
7 0&489301"9> 0&4#
.%ea o tension %eino%cement
7 103"&3"90889
7 13#&48"08 13#&48"08
9#00
S$%A& &%IN'O&C%(%NT
&"&3 $onc%ete st%/t capacit-
7 "8#&3" 2
913&>12
E;ecti!
ck bh
! "d#$%h!&
M!
M/! ck
bd2
' = d ( #$% " #$2% k / 1$1)*&1/2
s
= M/#$-. ! yk '
mm"
.s,min 7 C0&"C! ctm /! yk &bd
.s, ma
7 0&09.c
mm"
'Rd, ma 7 0&3bwd ! ck " 1! ck /2%#&/"cot K + tan K &
cot K 7
cot K 7
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4
S"ppo#t 1
0&9# F7 0&9#"4
7 1"1&0# 2
Shea% lins
7 0&"818808""
t%- lin : M
#"
Spacin+ , s 7 "00">4 0&># d
4&"&"C 390
&"&3C>
.dditioinal lon+it/dinal %eino%cement
additional tensile o%ce,
7 1#0&10" 2
994&004>893> 2 @
7 39#&0"084
S"ppo#t 2
0&0 F
7 0&0"4
7 11&9 2
0 ed =
v d, max
cot K =2$%
v d, max
cot K =1$#
The%eo%e an+le K ""N
.sw
s 7 0 ed / #$.-!
ykdcot Φ
.SO
7 mm"
PFtd
7 0'ed
cot Φ
)ed , ma
! 7
PFtd
.s,%e(
7 PFtd
0&8> -
mm"
0 ed
=
v d, max
cot K =2$%
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10
Shea% lins
7 0&3>#891101
t%- lin : M
#"
Spacin+ , s 7 1#0&38">004> @ 0&># d
4&"&"C 1#0&38">
&"&3C>
.dditioinal lon+it/dinal %eino%cement
additional tensile o%ce,
7 "00&13 2
994&004>893> 2 @
7 90&08">#8"1
S"ppo#t 2
0# F
7 0#"4
7 19>&4# 2
Shea% lins
7 0&399#"10048
t%- lin : M
#"
v d, max
cot K =1$#
The%eo%e an+le K ""N
.sw
s 7 0 ed / #$.-!
yk cot Φ
.SO
7 mm"
PFtd
7 0'ed
cot Φ
)ed , ma
! 7
PFtd
.s,%e(
7 PFtd
0&8> -
mm"
0 ed
=
v d, max
cot K =2$%
v d, max
cot K =1$#
The%eo%e an+le K ""N
.sw
s 7 0 ed / #$.-!
yk cot Φ
.SO
7 mm"
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11
Spacin+ , s 7 19&0#38## @ 0&># d
4&"&"C 19&0#38
&"&3C>
.dditioinal lon+it/dinal %eino%cement
additional tensile o%ce,
7 183&9#8 2
994&004>893> 2 @
7 9"1&>9"#"8>3
S"ppo#t 4
0# F
7 0#"4
7 19>&4# 2
Shea% lins
7 0&399#"10048
t%- lin : M
#"
Spacin+ , s 7 19&0#38## @ 0&># d
4&"&"C 19&0#38
&"&3C>
.dditioinal lon+it/dinal %eino%cement
additional tensile o%ce,
7 183&9#8 2
PFtd 7 0' ed cot Φ
)ed , ma
! 7
PFtd
.s,%e(
7 PFtd
0&8> -
mm"
0 ed
=
v d, max
cot K =2$%
v d, max
cot K =1$#
The%eo%e an+le K ""N
.sw
s 7 0 ed / #$.-!
yk cot Φ
.SO
7 mm"
PFtd
7 0'ed
cot Φ
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1"
994&004>893> 2 @
7 9"1&>9"#"8>3
S"ppo#t 4
0& F
7 0&"4
7 11&9 2
Shea% lins
7 0&3>#891101
t%- lin : M
#"
Spacin+ , s 7 1#0&38">004> @ 0&># d
4&"&"C 1#0&38">
&"&3C>
.dditioinal lon+it/dinal %eino%cement
additional tensile o%ce,
7 "00&13 2
994&004>893> 2 @
7 90&08">#8"1
S"ppo#t 4
0&9#F
7 0&9#"4
7 1"1&0# 2
)ed , ma
! 7
PFtd
.s,%e(
7 PFtd
0&8> -
mm"
0 ed
=
v d, max
cot K =2$%
v d, max
cot K =1$#
The%eo%e an+le K ""N
.sw
s 7 0 ed / #$.-!
yk cot Φ
.SO
7 mm"
PFtd
7 0'ed
cot Φ
)ed , ma
! 7
PFtd
.s,%e( 7 PFtd 0&8> -
mm"
0 ed
=
v d, max
cot K =2$%
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13
Shea% lins
7 0&"818808""
t%- lin : M
#"
Spacin+ , s 7 "00">4 @ 0&># d
4&"&"C "00">
&"&3C>
.dditioinal lon+it/dinal %eino%cement
additional tensile o%ce,
7 1#0&10" 2
994&004>893> 2 @
7 39#&0"084
4&"&"C#
minim/m lins
7 0&18
t%- lin : M #"
4&"&"C Spacin+ , s 319 0&>#d
shea% %esistance o minim/m lins
7 >4&>> 2
v d, max
cot K =1$#
The%eo%e an+le K ""N
.sw
s 7 0 ed / #$.-!
yk cot Φ
.SO
7 mm"
PFtd
7 0'ed
cot Φ
)ed , ma
! 7
PFtd
.s,%e(
7 PFtd
0&8> -
mm"
.sw
s 7 0&08! ck
1/2 bw/! yk
.SO
7
'min
7 C.sw
sC0&>8 -
cotΦ
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19
)in* a##an+ement
118&100>14m
1#4&01100>14m
19#100>14m
118&100>14m
&"&9 T%ans310 2
Lon+it/dinal shea% st%ess
7 1&1#"0>"80>
&"&9C 0&98
T%ans4#"
9
"N
K 7
7 >&91403994 N
/se : K 7 " 0&948#81
"&00
t%ans !
ykcot K
cccccc
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1#
7 0&19#""8414
T%- : M 10 >8
#90&8004"3>mm
4&"&1&1 )inim/m t%ans1#43""#
>&9 !%')%CTIOIN
Percentage of required tension of reinforcement
= 0.0101059627
Reference reinforcement ratio,
0.005
Percentage of required compression reinforcement,
0
Q > ρo !"#$%
1.&
1.5
l/d =
'"()$*
#odification factor for span +ess tan 7m 1
#odification factor for stee+ area pro-ided,
/'0*
erefore a++oa3+e span effecti-e dept ratio,
.s
7
Spacin+ , s
7
.s,min
7 C0&"C! ctm
/! yk &bh
!
mm"m
Q = A s,required / bd
Qo = 4 fck)1/2 x 10-3 =
ρ = A s' ,required
/ bd =
11 81.5! ck o /3 +)$24! ck "o /3 1&)/2 "1&11 81.5!
ck"
o /33 & +1/124!
ck4
"3 /3o & "2&
end s+a3
=
interior s+a3
=
11 81.5! ck
o /3 +)$24!
ck"
o /3 1&)/2 "1&
" pro-
"s,required
=
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1
'"()$*
'"()$* '"()$*
(l/d) allowable
=
4l/d)actual
= (l/d)allowable
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1>
6*T?*T
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18
6*T?*T
mm
mm
mm
mm
mm
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14
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"0
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"1
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""
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"3
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"9
"
1
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"#
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"
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">
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"8
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"4
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30
Estimate
"&00#84>
1
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31
/se M10
mm"
1#>mm"m
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3"