Bridge Formwork Without Anchors

Calculation examples for formwork systems y l n o e s u l a n r e t n i r o f

y l n o e s u l a n r e t n i r o f


y l n o e s u l a n r e t n i

Static department [email protected]

Static Department

26.08.2011 The formwork experts

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Calculation examples for formwork systems

Calculation example for bridge formwork without anchors............. anchors.......................... ...................... ......... 1 Overview of the structure and calculation steps ...................... .......................... ............. ......................... ............ 3 Load assumption ........................................................................................................... 4 Design of parts .............................................................................................................. 5 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Verification of plywood 3-SO 21mm ........................................................................ 5 Verification of H20 beam at the bottom formwork.................................................... 6 Verification of H20 beam for lateral panels.............................................................. 7 Verificati Verification on of WS10 ................................. .................................................. .................................. .................................. ............................ ........... 8 Verification of spindle strut T7 (S1) ....................................................................... 10 Verification of vertical WS10 ................................................................................. 11 Verification of spindle strut T7 (S2) ....................................................................... 13 Verificati Verification on of WS10 ................................. .................................................. .................................. .................................. .......................... ......... 14 Verification of spindle strut T7 (S3) ....................................................................... 16 Verification of vertical WS10 ................................................................................. 17 Verification of spindle strut T7 (S4) ....................................................................... 18 Verification of horizontal profile WS10 .................................................................. 19

Annex A ........................... .............. ......................... .......................... ........................... .......................... .......................... .......................... .......................... ............... 21 A.1 A.2 A.3 A.4 A.5 A.6 A.7

Verification of of H20 beam at the bottom bottom formwork ................... ......... ................... .................. ................... ............. ... 21 Verification of of H20 beam for lateral lateral panels .................. ........ ................... .................. ................... ................... .............. ..... 23 Verification of of WS10 ................... .......... .................. ................... ................... ................... ................... .................. .................. ................... .......... 25 Verification of of vertical WS10 .................. ......... .................. ................... ................... ................... ................... .................. ................. ........ 27 Verification of of WS10 ................... .......... .................. ................... ................... ................... ................... .................. .................. ................... .......... 29 Verification of of vertical WS10 .................. ......... .................. ................... ................... ................... ................... .................. ................. ........ 31 Verification of of horizontal profile profile WS10 ................... ......... ................... .................. ................... ................... .................. ........... .. 33





Remark: This calculation example example doesn´t contain the verification of the scaffolding scaffolding beneath the superstructure.

Anmerkung: Bei diesem Berechnungsbeispiel Berechnungsbeispiel erfolgt kein Nachweis Nachweis des Traggerüstes unter dem Oberbau.

Static Department


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Calculation examples for formwork systems Bridge formwork

y l n o l n e o s u e l s a u n l r a e n t r n i e t r n i o f r o f

Overview of the structure and calculation steps

4


8 6 10

5

11 1

7


9

3

12

2

y l n o l n e o s u e l s a u n l r a e n t r n i e t r n i o f r o f y l n o l n e o s u e l s a u n l r a e n t r n i e t r n i o f r o f

Static Department


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Load assumption

Permanent actions (self-weight): Formwork Top 50:

0,65

[kN/m²]

(plywood, (plywood, wooden parts, steel parts)

Posts and steel parts:

0,50

[kN/m²]

Handrail post and planks:

0,50

[kN/m]


Variable imposed actions (variable loads): Concrete weight:

25

[kN/m³]

Concrete pressure:

50

[kN/m²]

Live load while pouring:

1,50 [kN/m²] < 10% < 10% of the concrete weight

(acc. EN 12812):

+ 0,75 [kN/m²] for construction operations loading 2,50 [kN/m²]

Live load on platform (acc. EN12812):

1,50 [kN/m²]

Wind load (acc. DIN1055 part 4):

1,04 [kN/m²] (max. wind, height above ground <20m)




Static Department


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Calculation examples for formwork systems Design of parts


1. Verification Verification of plyw ood 3-SO 3-SO 21mm 21mm (Nachweis (Nachweis Schalhaut im Betonbalkenbereich)



concrete pressure: max. 50 [kN/m²]



max.M

< perm. M max.Def. < perm. Def. =l/500 The 3-SO 21mm has to be checked in all significant situations! (Nachweis (Nachweis der Schalhaut ist in den maßgebenden Lastfällen zu führen!)

Static Department

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Calculation examples for formwork systems 2. Verification Verification of H20 beam at the bottom bott om form wo rk


(Nachweis (Nachweis H20 im B etonbalkenbereich, Schalung der Balkenunterseite) Balkenunterseite)

Load assumption for influence e= 0,24m (Lastannahme für 0,24m Einflussbreite) Einflussbreite)

Live load while pouring (Nutzlast während Betonage):

Ll  2,5kN / m² x 0,24m  0,60kN / m

r o f

Concrete weight (Betongewicht):

C w

 1,60m x 25kN / m³ x

0,24m  9,60kN / m y l n o e s u l a n r e t n i

Dead load (Eigengewicht):

Dl  0,65kN / m² x 0,24m  0,16kN / m

r o f



System:

Cw=9.60kN/m Ll=0.60kN/m Dl=0.16kN/m 675mm

1500mm 14.76 kN

max.Shear

<

perm. Shear

675mm 14.76 kN

Pv =max. reaction force for the WS10 (max. Auflagerreaktion WS10)

max.M

< perm. Moment max.Def. < perm. Deformation For detailed calculation see Annex A, A.1

Static Department


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Calculation examples for formwork systems 3. Verificatio n of H20 beam fo r lateral lateral panels

y y l l n n o o e e s s u u l l a a n n r r e e t t n n i i r r o o f f

(Nachweis (Nachweis H20 im B etonbalkenbereich, etonbalkenbereich, seitliche Schalung )

Load assumption for influence e= 0,284m (Lastannahme für 0,284m Einflussbreite) Einflussbreite)

Concrete pressure (Betondruck):

C p



25kN / m³ x 1,31m x 0,284m  9,31kN / m

y l y l n n o o e e s s u u l l a a n n r r e e t t n n i i r r o o f f y y l l n n o o e e s s u u l l a a n n r r e e t t n n i i r r o o f f

System:

Cp=9.31kN/m

675mm

1500mm 13.27 kN

max.Shear

<

675mm 13.27 kN

perm. Shear

y y l l n n o o e e s s u u l l a a

max.M

< perm. M max.Def. < perm. Def. The H20 has to be checked in all determining situations! (Nachweis (Nachweis des H20 ist in den ausschlaggebenden Lastfällen zu führen!)

n r e t n i r o f

For detailed calculation see Annex A, A.2 A. 2

Static Department


y l y l n n o o e e s s u u l l a a n n r r e e t t n n i i r r o o f f

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Calculation examples for formwork systems 4. Verific ation of WS10 WS10 (Nachweis WS10)

The worst condition for WS10 before.

 see

tipbeam calculation no. 2. H20 (concrete beam – bottom formwork)

( WS10 WS10 erhält den größten Lasteinfluss  wie in der vorherigen Tipbeam Berechnung Nr. 2. H20 (Schalung der Balkenunterseite) Balkenunterseite) ersichtlich). ersichtlich).

r o f

max. influence of the WS10: (max. Einfluss von WS10) 

max. reaction of H20 divided by max. linear load of H20.



( max. max. Auflagerreaktion dividieren durch die gesamte Linienlast).

:  Ll

emax

 Pv

 C w 

emax

 14,76kN :



Dl 

0,60kN / m  9,60kN / m  0,16kN / m  1,42m

r o f




Load assumption assumption for WS10: e= 1,42m (Lastannahme für WS10: e = 1,42m)

Live load while casting (Nutzlast während Betonage):

Ll  (0,20m + 0,28m)/2 x 25kN/m³ x 0,10 + 0,75kN/m² = 1,35kN/m² < 1,5kN/m² Ll  1,50kN / m² x 1,42m  2,13kN / m Static Department


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Calculation examples for formwork systems Live load and dead load platform (Nutzlast und Eigengewicht Arbeitsbühne):

Ll p




1,50kN / m²  0,50kN / m² x 1,42m  2,84kN / m

Concrete weight 1 (Betongewicht 1) (0,20m):

C w1

0,20m x 25kN / m³ x 1,42m  7,10kN / m




C w 2

r o f

0,282m x 25kN / m³ x 1,42m  10,01kN / m





Dl  0,65kN / m² x 1,42m  0,92kN / m Hand rail (Schutzgeländer):

H R



0,50kN / m x 1,42m  0,71kN

r o f

Bending moment from wind (Moment aus Windlast):

M W



1,04kN / m² x 0,50 x1,922m x1,42m x

1,922m 2



1,36kNm

System: Cw2=10.01kN/m

Cw1=7.10kN/m

HR=0.71kN

Llp=2.84kN/m Ll=2.13kN/m

Dl=0.92kN/m

MW=1.36kNm 780mm

113mm

1171mm

11.33 kN vertical load of spindle strut S1

max. Shear

<

5.50 kN vertical load of WS10 = Pv1

max. M



the serviceability is given

For detailed calculation see Annex A, A.3

Static Department


r o f



perm. Shear

< perm. M max.Def. < perm. Def.


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Calculation examples for formwork systems 5. Verification of spin dle stru t T7 (S1) (S1) (Nachweis d er Spind elstrebe T7 (S1)) (S1))

The inclined position of the W S10 is not considered. (Die Neigung des WS10 wird nicht berücksichtigt).

S 1v S 1h

S 1

 11,33kN x



11,33kN

tan1,4  0,28kN

 11,33kN : cos cos 1,4  11,33kN

Spindle strut S1(T7): Length: L=1,61m





max. Pspindle strut T7

11,33kN

Static Department

< <

perm. Pspindle strut T7

70kN


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Calculation examples for formwork systems 6. Verific ation of vertical WS10 WS10 (Nachweis des verti kalen WS10)

The inclined position of the W S10 is not considered. The spindle S2 is used as the second bearing of the WS10. (Die Neigung des WS10 wird nicht berücksichtigt. berücksichtigt. Die Spindelstrebe Spindelstrebe S2 dient als zweites Auflager des WS10.)





S h



0,28kN = the horizontal component of the spindle strut T7 (S1)

see

the calculation of T7

before.(= die horizontale Komponente aus der Spindelstrebe T7 (S1)  wie in der Berechnung von T7 ersichtlich). Concrete pressure (Betondruck):

C p



25kN / m³ x 1,65m x 1,42m  58,58kN / m


Static Department


Seite 11 von 35

Calculation examples for formwork systems Force resulting from wind on the hand rail (Kraft aus Windlast auf das Schutzgeländer):

RW

 1,04kN / m² x 0,50 x 1,497m x 1,42m 


1,11kN

Wind load on the formwork (Windlast auf die Schalung):

W L

 1,04kN / m² x 1,0 x 1,42m 

1,48kN / m

r o f

System: Cp=58.58kN/m

RW=1.11kN Sh=0.28kN

W L=1. 48kN/m


558mm

320mm 43.56 kN

1175mm 9.67 kN

horizontal load of spindle strut S2

max. Shear

<


perm. Shear

max. M




r o f


Static Department


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Calculation examples for formwork systems 7. Verification of spin dle stru t T7 (S2) (S2) (Nachweis d er Spind elstrebe T7 (S2)) (S2))

Horizontal force resulting from the calculation of vertical WS10. (Horizontale Kraft aus der Berechnung von WS10 vertikal ersichtlich).

S 2 h S 2





43,56kN

43,56kN : cos cos 43,6  60,15kN Spindle strut S2 (T7): Length: L=1,58m





60,15kN

< <


70kN

Vertical load on the horizontal WS10 (Vertikallast (Vertikallast auf den WS10):

S 2v



60,15kN x cos cos 42,0  44,70kN



Static Department


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Calculation examples for formwork systems y l n o e s u l a n r e t n i

8. Verific ation of WS10 WS10 (Nachweis WS10)

r o f




Load assumption assumption for WS10: e= 1,42m (Lastannahme für WS10: e = 1,42m)

Live load while pouring (Nutzlast Betonage):

Ll  (0,25m + 0,275m)/2 x 25kN/m³ x 0,10 + 0,75kN/m² = 1,41kN/m² < 1,5kN/m² Ll  1,50kN / m² x 1,42m  2,13kN / m



C w3



0,275m x 25kN / m³ x 1,42m  9,76kN / m

r o f

Static Department


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Calculation examples for formwork systems Concrete weight 4 (Betongewicht 2) (0,25m):

C w 4




0,25m x 25kN / m³ x 1,42m  8,88kN / m


Dl  0,65kN / m² x 1,42m  0,92kN / m

r o f

System: Cp=58.58kN/m Cw4=8.88kN/m

Cw4=8.88kN/m Cw3=9.76kN/m

r o f

Ll=2.13kN/m

Dl=0.92kN/m

1148mm 5.54 kN

598mm 15.42 kN

0.00 kN

vertical load of WS10 = Pv3

<

5.54 kN


perm. Shear


max. M




vertical load of spindle strut S3

max. Shear


r o f

the serviceability is given


Static Department



Seite 15 von 35


9. Verificatio n of spi nd le strut T7 (S3) (S3) (Nachweis der Spindelstreb e T7 (S3))

The inclined position of the W S10 is not considered. (Die Neigung des WS10 wird nicht berücksichtigt).

S 3v S 3h

S 3

 15,42kN x



15,42kN

tan 2,4  0,65kN

 15,42kN : cos cos 2,4  15,43kN

r o f




Spindle strut S3 (T7): Length: L=1,47m

r o f


max. Pspindle strut T7 < perm. Pspindle strut T7

15,43kN

<

70kN

Static Department


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Calculation examples for formwork systems 10. Verification of vertic al WS10 (Nachweis des verti kalen WS10)

The inclined position of WS10 is not considered. The spindle strut S4 and the horiz. WS10 are bearings of this vertical WS10 (because of the symmetry of the cross-section). (Die Neigung des WS10 wird nicht berücksichtigt. Die Spindelstrebe S4 und der horizontale WS10 sind Auflager dieses vertikalen WS10. (aufgrund der Symmetrie des Querschnitts)) Querschnitts))

S 3h



0,65kN = the horizontal component of spindle strut T7 (S3)

see

the calculation of T7

before.(= die horizontale Komponente aus der Spindelstrebe T7 (S3)  wie in der Berechnung von T7 ersichtlich). Concrete pressure (Betondruck):

C p1



25kN / m³ x 0,275m x 1,42m  9,76kN / m

C p 2



25kN / m³ x 1,61m x 1,42m  57,16kN / m

System: Cp2=57.16kN/m

S3h=0.65kN/m Cp1=9.76kN/m

523mm

501mm 3.86 kN

34.45 kN

583mm

409mm


5.61 kN


Static Department


Seite 17 von 35

y l n l o n e o s u e l s a u n l r a e t n r n i e t r n o i f r o f y l n l o n e o s u e l s a u n l r a e t n r n i e t r n o i f r o f y l n l o n e o s u e l s a u n l r a e t n r n i e t r n o i f r o f y l n l o n e o s u e l s a u n l r a e t n r n i e t r n o i f r o f y l n l o n e o s u e l s a u n l r a e t n r n i e t r n o i f r o f

Calculation examples for formwork systems 11. Verification of s pin dle s trut T7 (S4) (S4) (Nachweis der Spindelstreb e T7 (S4))

Horizontal force see calculation of vertical WS10 before. (Horizontale Kraft aus der Berechnung von WS10 vertikal ersichtlich).

S 4h S 4





34,45kN

34,45kN : cos cos 40,2  45,10kN Spindle strut S2 (T7): Length: L=1,43m





45,10kN

< <


70kN

Vertical load on the horizontal WS10 (Vertikallast (Vertikallast auf den WS10):

S 4v



45,10kN x cos cos 46,3  31,16kN



Static Department


Seite 18 von 35

Calculation examples for formwork systems 12. Verification of h orizo ntal p rofi le WS10


(Nachweis (Nachweis des ho rizontalen rizontalen WS10WS10- Profils)

r o f



Load assumption assumption for continuous continuous WS10 profile: e= 1,42m (Lastannahme für WS10 Profil: e = 1,42m)

Hand rail (Schutzgeländer):

H R



0,50kN / m x 1,42m  0,71kN


Vertical load spindle strut S1 (Vertikallast Spindelstrebe S1):

S 1v



11,33kN


S 2v



44,70kN


S 3v



15,42kN


S 4v



31,16kN

Reaction of the WS10 at the cantilever (Auflagerreaktion (Auflagerreaktion aus dem Nachweis WS10 im Kragarmbereich):

P v1  5,50kN (Auflagerre aktion aus dem Nachweis horizontaler horizontale r Reaction of the horizontal WS10 at the center of the bridge (Auflagerreaktion WS10 in der Mitte des Brückenquerschnitts):

P v3



5,54kN

Static Department


Seite 19 von 35


Calculation examples for formwork systems Concrete weight 1 (Betongewicht 1):

C w1



25kN / m³ x 0,282m x1,42m 10,01kN / m


Concrete weight 2 (Betongewicht 2):

C w2



25kN / m³ x 0,30m x 1,42m 10,65kN / m


C w3



25kN / m³ x1,60m x 1,42m  56,80kN / m


C w4



25kN / m³ x 0,275m x 1,42m  9,76kN / m

Live load 1 while pouring (Nutzlast Betonage 1):


Ll 1 1,50kN / m² x 1,42m  2,13kN / m Live load 2 while pouring (Nutzlast Betonage 2):

Ll 2

  3,55kN / m  2,50kN / m² x 1,42m

(Eigengewicht 1 geneigte Schalung): Dead load 1 inclined formwork (Eigengewicht

Dl 1

 0,65kN / m² x1,32m x1,44m 1,24kN

(Eigengewicht 2 geneigte Schalung): Dead load 2 inclined formwork (Eigengewicht

Dl 2

 0,65kN / m² x 1,29m x 1,42m 1,19kN


Dead load formwork (Eigengewicht (Eigengewicht Schalung):

Dl  0,65kN / m² x 1,42m  0,92kN / m Dead load (Eigengewicht):

Dl  0,50kN / m² x 1,42m  0,71kN / m System:


For detailed calculation see Annex A, A.7 A. 7 Remark: The supporting reactions of this system are the loads per leg for the scaffolding beneath, which is not considered in t his calculation example. (Anmerkung: Die Auflagerreaktionen dieses Systems sind die Stiellasten für die darunterliegende Tragkonstruktion, die in diesem Beispiel nicht berechnet wird.)

Static Department


Seite 20 von 35


Calculation examples for formwork systems Annex A A A.1 .1


Verification Verification of H20 beam at the botto m form wo rk

r o f





L l= Cw= Dl=

Static Department


Seite 21 von 35


Pv =max. reaction force for the WS10 (max. Auflagerreaktion WS10)

r o f





Static Department


Seite 22 von 35

Calculation examples for formwork systems A.2


Verification of H20 beam for lateral panels





Static Department


Seite 23 von 35






Static Department


Seite 24 von 35


Verification of WS10





HR = MW =

LL LLP Cw1 DL

= = = =

r o f


Cw2=

r o f

Static Department


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Static Department


Seite 26 von 35


Verification of vertic al WS10





from spindle strut S1: S h= Rw=


CP= W L=

r o f

Static Department


Seite 27 von 35








Static Department


Seite 28 von 35


Verification of WS10




LL Cw3 Cw4 DL


= = = =


Static Department


Seite 29 von 35









Static Department


Seite 30 von 35


Verification of vertic al WS10 y l n o e s u l a n r e t n i r o f





Static Department


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r o f





Static Department


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Calculation examples for formwork systems A A.7 .7

Verification Verification of hor izontal prof profile ile WS10 WS1 0 l n o e s u l a n r e t n i r o f

l n o e s u l a n r e t n i r o f




Static Department


Seite 33 von 35




HR S1V S2V PV1 DL1 DL2 PV3 S4V S3V

DL DL DL Cw1 Cw2 Cw3 Cw3 Cw2 LL1 LL2 LL1


= = = = = = = = =


= = = = = = = = = = =

r o f


Static Department


Seite 34 von 35






max. Shear

< perm. Shear max. Moment < perm. Moment max.Def. < perm. Def.  the serviceability is given Remark: The supporting reactions of this system are the loads per leg for the scaffolding beneath, which is not considered in this calculation example. (Anmerkung: Die Auflagerreaktionen dieses Systems sind die Stiellasten für die darunterliegende Tragkonstruktion, die in diesem Beispiel nicht berechnet wird.)


Static Department


Seite 35 von 35

Bridge Formwork Without Anchors

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