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Calculation examples for formwork systems
Static Department 26.08.2011
The formwork experts Seite 1 von 35
Calculation example for bridge formwork
without anchors
Static department [email protected]
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Calculation examples for formwork systems
Static Department 26.08.2011
The formwork experts Seite 2 von 35
List of contents Calculation example for bridge formwork without anchors ................................... 1 Overview of the structure and calculation steps ............................................................ 3
Load assumption ........................................................................................................... 4 Design of parts .............................................................................................................. 5
1. Verification of plywood 3-SO 21mm ........................................................................ 5 2. Verification of H20 beam at the bottom formwork.................................................... 6 3. Verification of H20 beam for lateral panels.............................................................. 7 4. Verification of WS10 ............................................................................................... 8 5. Verification of spindle strut T7 (S1) ....................................................................... 10 6. Verification of vertical WS10 ................................................................................. 11 7. Verification of spindle strut T7 (S2) ....................................................................... 13 8. Verification of WS10 ............................................................................................. 14 9. Verification of spindle strut T7 (S3) ....................................................................... 16 10. Verification of vertical WS10 ................................................................................. 17 11. Verification of spindle strut T7 (S4) ....................................................................... 18 12. Verification of horizontal profile WS10 .................................................................. 19
Annex A ....................................................................................................................... 21 A.1 Verification of H20 beam at the bottom formwork .................................................. 21 A.2 Verification of H20 beam for lateral panels ............................................................ 23 A.3 Verification of WS10 .............................................................................................. 25 A.4 Verification of vertical WS10 .................................................................................. 27 A.5 Verification of WS10 .............................................................................................. 29 A.6 Verification of vertical WS10 .................................................................................. 31 A.7 Verification of horizontal profile WS10 ................................................................... 33
Remark: This calculation example doesn´t contain the verification of the scaffolding beneath the superstructure. Anmerkung: Bei diesem Berechnungsbeispiel erfolgt kein Nachweis des Traggerüstes unter dem Oberbau.
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Calculation examples for formwork systems
Static Department 26.08.2011
The formwork experts Seite 3 von 35
Bridge formwork
Overview of the structure and calculation steps
12
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Calculation examples for formwork systems
Static Department 26.08.2011
The formwork experts Seite 4 von 35
Load assumption
Permanent actions (self-weight):
Formwork Top 50: 0,65 [kN/m²] (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% of the concrete weight
(acc. EN 12812): + 0,75 [kN/m²] for construction operations loading
O 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)
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Calculation examples for formwork systems
Static Department 26.08.2011
The formwork experts Seite 5 von 35
Design of parts
1. Verification of plywood 3-SO 21mm
(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 der Schalhaut ist in den maßgebenden Lastfällen zu führen!)
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Calculation examples for formwork systems
Static Department 26.08.2011
The formwork experts Seite 6 von 35
2. Verification of H20 beam at the bottom formwork (Nachweis H20 im Betonbalkenbereich, Schalung der Balkenunterseite)
Load assumption for influence e= 0,24m (Lastannahme für 0,24m Einflussbreite)
Live load while pouring (Nutzlast während Betonage):
Concrete weight (Betongewicht):
mkNmxmkNxmCw /60,924,0³/2560,1
Dead load (Eigengewicht):
mkNmxmkNDl /16,024,0²/65,0
System:
max.Shear < perm. Shear max.M < perm. Moment max.Def. < perm. Deformation For detailed calculation see Annex A, A.1
Pv =max. reaction force for the WS10 (max. Auflagerreaktion WS10)
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mkNmxmkNLl /60,024,0²/5,2
Cw=9.60kN/m
Ll=0.60kN/m
Dl=0.16kN/m
14.76 kN 14.76 kN
675mm 1500mm 675mm
Calculation examples for formwork systems
Static Department 26.08.2011
The formwork experts Seite 7 von 35
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3. Verification of H20 beam for lateral panels (Nachweis H20 im Betonbalkenbereich, seitliche Schalung)
Load assumption for influence e= 0,284m (Lastannahme für 0,284m Einflussbreite)
Concrete pressure (Betondruck):
mkNmxmxmkNCp /31,9284,031,1³/25
System:
max.Shear < perm. Shear max.M < perm. M max.Def. < perm. Def.
The H20 has to be checked in all determining situations! (Nachweis des H20 ist in den ausschlaggebenden Lastfällen zu führen!)
For detailed calculation see Annex A, A.2
Cp=9.31kN/m
13.27 kN 13.27 kN
675mm 1500mm 675mm
Calculation examples for formwork systems
Static Department 26.08.2011
The formwork experts Seite 8 von 35
4. Verification of WS10 (Nachweis WS10)
The worst condition for WS10 see tipbeam calculation no. 2. H20 (concrete beam – bottom formwork) before. (WS10 erhält den größten Lasteinfluss wie in der vorherigen Tipbeam Berechnung Nr. 2. H20 (Schalung der
Balkenunterseite) ersichtlich). max. influence of the WS10: (max. Einfluss von WS10) max. reaction of H20 divided by max. linear load of H20. (max. Auflagerreaktion dividieren durch die gesamte Linienlast).
lwl DCLPve :max
mmkNmkNmkNkNe 42,1/16,0/60,9/60,0:76,14max
Load assumption for WS10: e= 1,42m (Lastannahme für WS10: e = 1,42m)
Live load while casting (Nutzlast während Betonage):
1,5kN/m² < 1,35kN/m² = 0,75kN/m² + 0,10 x 25kN/m³ x 0,28m)/2+(0,20mlL
mkNmxmkNLl /13,242,1²/50,1
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Calculation examples for formwork systems
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The formwork experts Seite 9 von 35
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Live load and dead load platform (Nutzlast und Eigengewicht Arbeitsbühne):
mkNmxmkNmkNLpl /84,242,1²/50,0²/50,1
Concrete weight 1 (Betongewicht 1) (0,20m):
mkNmxmkNxmCw /10,742,1³/2520,01
Concrete weight 2 (Betongewicht 2) (0,282m):
mkNmxmkNxmCw /01,1042,1³/25282,02
Dead load (Eigengewicht):
mkNmxmkNDl /92,042,1²/65,0
Hand rail (Schutzgeländer):
kNmxmkNHR 71,042,1/50,0
Bending moment from wind (Moment aus Windlast):
kNmm
xmxmxxmkNMW 36,12
922,142,1922,150,0²/04,1
System:
max. Shear < perm. Shear max. M < perm. M max.Def. < perm. Def. the serviceability is given
For detailed calculation see Annex A, A.3
vertical load of spindle strut S1
vertical load of WS10 = Pv1
Llp=2.84kN/m
11.33 kN 5.50 kN
780mm 113mm 1171mm
Cw1=7.10kN/m Cw2=10.01kN/m
Ll=2.13kN/m Dl=0.92kN/m HR=0.71kN
MW=1.36kNm
Calculation examples for formwork systems
Static Department 26.08.2011
The formwork experts Seite 10 von 35
5. Verification of spindle strut T7 (S1)
(Nachweis der Spindelstrebe T7 (S1))
The inclined position of the WS10 is not considered. (Die Neigung des WS10 wird nicht berücksichtigt).
kNS
v33,111
kNxkNS
h28,04,1tan33,111
kNkNS 33,114,1cos:33,111
Spindle strut S1(T7):
Length: L=1,61m
max. Pspindle strut T7 < perm. Pspindle strut T7 11,33kN < 70kN
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Calculation examples for formwork systems
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6. Verification of vertical WS10
(Nachweis des vertikalen WS10)
The inclined position of the WS10 is not considered. The spindle S2 is used as the
second bearing of the WS10. (Die Neigung des WS10 wird nicht berücksichtigt. Die Spindelstrebe S2 dient als zweites Auflager des WS10.)
kNSh 28,0 = 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):
mkNmxmxmkNCp /58,5842,165,1³/25 fo
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Calculation examples for formwork systems
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Force resulting from wind on the hand rail (Kraft aus Windlast auf das Schutzgeländer):
kNmxmxxmkNRW 11,142,1497,150,0²/04,1
Wind load on the formwork (Windlast auf die Schalung):
mkNmxxmkNWL /48,142,10,1²/04,1
System:
max. Shear < perm. Shear max. M < perm. M max.Def. < perm. Def.
For detailed calculation see Annex A, A.4
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horizontal load of spindle strut S2
horizontal load of spindle strut S2
WL=1. 48kN/m
43.56 kN
558mm 320mm 1175mm
RW=1.11kN
Cp=58.58kN/m
Sh=0.28kN
9.67 kN
Calculation examples for formwork systems
Static Department 26.08.2011
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7. Verification of spindle strut T7 (S2) (Nachweis der Spindelstrebe T7 (S2))
Horizontal force resulting from the calculation of vertical WS10. (Horizontale Kraft aus der Berechnung von WS10
vertikal ersichtlich).
kNS h 56,432
kNkNS 15,606,43cos:56,432
Spindle strut S2 (T7):
Length: L=1,58m
max. Pspindle strut T7 < perm. Pspindle strut T7
60,15kN < 70kN
Vertical load on the horizontal WS10 (Vertikallast auf den WS10):
kNxkNS v 70,440,42cos15,602
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Calculation examples for formwork systems
Static Department 26.08.2011
The formwork experts Seite 14 von 35
8. Verification of WS10 (Nachweis WS10)
Load assumption for WS10: e= 1,42m (Lastannahme für WS10: e = 1,42m)
Live load while pouring (Nutzlast Betonage):
1,5kN/m² < 1,41kN/m² = 0,75kN/m² + 0,10 x 25kN/m³ x 0,275m)/2+(0,25mlL
mkNmxmkNLl /13,242,1²/50,1
Concrete weight 3 (Betongewicht 3) (0,275m):
mkNmxmkNxmCw /76,942,1³/25275,03
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Calculation examples for formwork systems
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Concrete weight 4 (Betongewicht 2) (0,25m):
mkNmxmkNxmCw /88,842,1³/2525,04
Dead load (Eigengewicht):
mkNmxmkNDl /92,042,1²/65,0
System:
5.54 kN
max. Shear < perm. Shear max. M < perm. M max.Def. < perm. Def. the serviceability is given
For detailed calculation see Annex A, A.5
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vertical load of WS10 = Pv3
Cw4=8.88kN/m
5.54 kN
1148mm 598mm
Cw3=9.76kN/m
15.42 kN
vertical load of spindle strut S3
0.00 kN
Ll=2.13kN/m Dl=0.92kN/m
Cw4=8.88kN/m
Cp=58.58kN/m
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Static Department 26.08.2011
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9. Verification of spindle strut T7 (S3) (Nachweis der Spindelstrebe T7 (S3)) The inclined position of the WS10 is not considered. (Die Neigung des WS10 wird nicht berücksichtigt).
kNS
v42,153
kNxkNS h 65,04,2tan42,153
kNkNS 43,154,2cos:42,153
Spindle strut S3 (T7):
Length: L=1,47m max. Pspindle strut T7 < perm. Pspindle strut T7 15,43kN < 70kN
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Calculation examples for formwork systems
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10. Verification of vertical WS10 (Nachweis des vertikalen 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))
kNS h 65,03 = 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):
mkNmxmxmkNCp /76,942,1275,0³/251
mkNmxmxmkNCp /16,5742,161,1³/252
System:
For detailed calculation see Annex A, A.6
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horizontal load of spindle strut S4
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Cp2=57.16kN/m
3.86 kN
501mm 583mm
Cp1=9.76kN/m
34.45 kN 5.61 kN
523mm 409mm
S3h=0.65kN/m
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11. Verification of spindle strut T7 (S4) (Nachweis der Spindelstrebe T7 (S4)) Horizontal force see calculation of vertical WS10 before. (Horizontale Kraft aus der Berechnung von WS10 vertikal
ersichtlich).
kNS h 45,344
kNkNS 10,452,40cos:45,344
Spindle strut S2 (T7):
Length: L=1,43m
max. Pspindle strut T7 < perm. Pspindle strut T7
45,10kN < 70kN
Vertical load on the horizontal WS10 (Vertikallast auf den WS10):
kNxkNS v 16,313,46cos10,454
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12. Verification of horizontal profile WS10 (Nachweis des horizontalen WS10- Profils)
Load assumption for continuous WS10 profile: e= 1,42m (Lastannahme für WS10 Profil: e = 1,42m)
Hand rail (Schutzgeländer):
kNmxmkNHR 71,042,1/50,0
Vertical load spindle strut S1 (Vertikallast Spindelstrebe S1): kNS v 33,111
Vertical load spindle strut S2 (Vertikallast Spindelstrebe S2): kNS v 70,442
Vertical load spindle strut S3 (Vertikallast Spindelstrebe S3): kNS v 42,153
Vertical load spindle strut S4 (Vertikallast Spindelstrebe S4): kNS v 16,314
Reaction of the WS10 at the cantilever (Auflagerreaktion aus dem Nachweis WS10 im Kragarmbereich):
kNPv 50,51
Reaction of the horizontal WS10 at the center of the bridge (Auflagerreaktion aus dem Nachweis horizontaler
WS10 in der Mitte des Brückenquerschnitts): kNPv 54,53
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Concrete weight 1 (Betongewicht 1): mkNmxmxmkNCw /01,1042,1282,0³/251
Concrete weight 2 (Betongewicht 2): mkNmxmxmkNCw /65,1042,130,0³/252
Concrete weight 3 (Betongewicht 3): mkNmxmxmkNCw /80,5642,160,1³/253
Concrete weight 4 (Betongewicht 4): mkNmxmxmkNCw /76,942,1275,0³/254
Live load 1 while pouring (Nutzlast Betonage 1): mkNmxmkNLl /13,242,1²/50,11
Live load 2 while pouring (Nutzlast Betonage 2): mkNmxmkNLl /55,342,1²/50,22
Dead load 1 inclined formwork (Eigengewicht 1 geneigte Schalung): kNmxmxmkNDl 24,144,132,1²/65,01
Dead load 2 inclined formwork (Eigengewicht 2 geneigte Schalung): kNmxmxmkNDl 19,142,129,1²/65,02
Dead load formwork (Eigengewicht Schalung): mkNmxmkNDl /92,042,1²/65,0
Dead load (Eigengewicht): mkNmxmkNDl /71,042,1²/50,0
System:
For detailed calculation see Annex A, A.7
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.)
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Calculation examples for formwork systems
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Annex A
A.1 Verification of H20 beam at the bottom formwork
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Ll= Cw= Dl=
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Pv =max. reaction force for the WS10 (max. Auflagerreaktion WS10)
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A.2 Verification of H20 beam for lateral panels
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A.3 Verification of WS10
HR =
MW =
LL = LLP = Cw1 = DL =
Cw2=
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vertical load of spindle strut S1
vertical load of WS10 = Pv1
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A.4 Verification of vertical WS10
from spindle strut S1: Sh=
Rw=
CP=
WL=
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horizontal load of spindle strut S2
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A.5 Verification of WS10
LL = Cw3 = Cw4 = DL =
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vertical load of WS10 = Pv3
vertical load of spindle strut S3
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A.6 Verification of vertical WS10
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horizontal load of spindle strut S4
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A.7 Verification of horizontal profile WS10
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HR =
S1V = S2V =
PV1 = DL1 =
DL2 = PV3 =
S4V = S3V =
DL = DL = DL =
Cw1 = Cw2 = Cw3 = Cw3 = Cw2 = LL1 = LL2 = LL1 =
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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.)
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