Bow String Calculation

8/10/2019 Bow String Calculation

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BOW STRING CALCULATION

PROJECT:

1.0 Scope

This worksheet is designed to estimate the forces in bow string and shackle elevations for different stages of startup

analysis.

Following are the main steps used for the analysis:1) Run the OFFPIPE using assumed shackle elevation for particular number of joints off the Barge Stern.

2) Revise other OFFPIPE inputs if necessary to achieve desired stress level.

3) Run the MathCAD worksheet using cable angle, tension and elevation from OFFPIPE Output.

θ

θ

α

α α

kN 103

N⋅≡ ORIGIN 1≡

2.0 Inputs:

L 60.96 m⋅:= _bow string length

EL1 4.572 m⋅:= _elevation of top attachment point

File : bow string.xmcd Page 1 of 5 Date: 18/12/2013



EL2 30.00− m⋅:= _elevation of bottom attachment point

B 10:= _jacket leg batter (1 in ......)

Elevation, cable angle and tension at tie-off shackle (Extracted from OFFPIPE Output)

n 5:= i 1 n..:= _no of steps

Stepi

1

2

3

4

5

:= Nodei

84

108

133

157

181

:= ELi

18.50− m⋅

24.30− m⋅

27.60− m⋅

27.40− m⋅

28.07− m⋅

:= αi

7.30 deg⋅

17.17 deg⋅

23.29 deg⋅

22.84 deg⋅

24.29 deg⋅

:= Ts

i

178.23 kN⋅

212.60 kN⋅

251.25 kN⋅

340.48 kN⋅

339.31 kN⋅

:=

3.0 Calculations

h1

EL1 EL2−

B:= h1 3.457 m= _horizontal dist. between EL1 and EL2

3.1 Calculation of Horizontal Distance between EL1 and EL

hL

2

:= h 30.480 m= _horizontal distance between EL1 and EL (initial assumed value for solving equation)

L1i

EL1 ELi−( )2

h2

+:= _length of upper portion of bow string

L2i

ELi EL2−( )2

h h1−( )2

+:= _length of lower portion of bow string

L1i

1

1

2

3

4

5

38.228

41.984

44.318

44.173

44.660

m

= L2i

1

1

2

3

4

5

29.368

27.617

27.129

27.148

27.092

m

=

Equation for solving "h" from L = L1 + L2

hsoli

root EL1 ELi−( )2

h2

+ ELi EL2−( )2

h h1−( )2

++ L− h, :=






θ bi

atan

∆y bi

∆x bi

:= θ bi

1

1

2

3

4

5

26.480

14.627

6.636

7.154

5.398

deg⋅

= _angle made by bottom bow string w.r.t. horizontal

αti

π αi+ θti

− ELi EL1<if

π αi− θti

+ otherwise

:= _angle made by top bow string w.r.t. cable

α bi

π αi− θ bi

+ ELi EL2<if

π αi− θ bi

− otherwise

:= _angle made by bottom bow string w.r.t. cable

αti

1

1

2

3

4

5

146.3

148.4

150.1

149.9

150.5

deg⋅

= α bi

1

1

2

3

4

5

146.2

148.2

150.1

150.0

150.3

deg⋅

=

Values of ααααt & ααααb should be almost equal for force equilibrium at shackle tie-off location.

If not, then revise the assumed bow string length and / or assumed shackle node and re-run the worksheet

3.3 Calculation of Forces in Bow String

θi θti

θ bi

− ELi EL2<if

θti

θ bi

+ otherwise

:= _angle between top and bottom bow string

T bowi

Tsi

sin αti

sin θi( )⋅:= _tension in bow string

Hti

T bowi

cos θ

ti

⋅:= _horizontal force at EL1




H bi

T bowi

cos θ bi

⋅:= _horizontal force at EL2

θi

1

1

2

3

4

5

67.478

63.401

59.813

60.062

59.209

deg⋅

= T bowi

1

1

2

3

4

5

107.050

124.601

144.838

196.859

194.625

kN⋅

= Hti

1

1

2

3

4

5

80.794

82.115

86.808

118.724

114.918

kN⋅

= H bi

1

1

2

3

4

5

95.819

120.563

143.868

195.327

193.762

kN⋅

=


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Bow String Calculation