Design a Beams by Eurocode

8/9/2019 Design a Beams by Eurocode

1/32

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"


2/32

"

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


3/32

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


4/32

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"


5/32

#

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


6/32

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


k =

7 0&01#39#4991

7 0&48">41 0&4#


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


7/32

>

) 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


8/32

8

span4-5

9#9

) 7 1#1 2m

Benin+ moment,) 7 143&82m

7 1339&9414088

M


k =

7 0&01>#""841"

7 0&489301"9> 0&4#


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


9/32

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$%


10/32

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>



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$#


.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$#


.sw

s 7 0 ed / #$.-!

yk cot Φ

.SO

7 mm"


11/32

11

Spacin+ , s 7 19&0#38## @ 0&># d

4&"&"C 19&0#38

&"&3C>



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>



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$#


.sw

s 7 0 ed / #$.-!

yk cot Φ

.SO

7 mm"

PFtd

7 0'ed

cot Φ


12/32

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>



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$#


.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$%


13/32

13

Shea% lins

7 0&"818808""

t%- lin : M

#"

Spacin+ , s 7 "00">4 @ 0&># d

4&"&"C "00">

&"&3C>



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$#


.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


14/32

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


15/32

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

=


16/32

1

'"()$*

'"()$* '"()$*

(l/d) allowable

=

4l/d)actual

= (l/d)allowable


17/32

1>

6*T?*T


18/32

18

6*T?*T

mm

mm

mm

mm

mm


19/32

14


20/32

"0


21/32

"1


22/32

""


23/32

"3


24/32

"9

"

1


25/32

"#


26/32

"


27/32

">


28/32

"8


29/32

"4


30/32

30

Estimate

"&00#84>

1


31/32

31

/se M10

mm"

1#>mm"m


32/32

3"

Design a Beams by Eurocode

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