Grillage Analysis:Wheel Load Transfer to Nearest Joints

Grillage Analysis

      Wheel Load Transfer to nearest joints.

First Step

Cutting section along e-f

R_e x l₁ = P x b

R_e = P x b/l₁

Similarly;      

R_f = P x a/l₁

Second Step

Considering beam 1-4

R₁ = R_e x d/l₂

Thus:

R₁ = P x b x d/ (l₁ x l₂) = (b x d/l₁ x l₂) x P

Similarly:

R₄ = R_e x c/l₂

R₄ = P x b x c/ (l₁ x l₂) = (b x c/l₁ x l₂) x P

 

Considering beam 2-3

R₂ = R_f x d / l₂

R₂ = P x a x d / (l₁ x l₂) = (a x d /l₁ x l₂) x P

Also:

R₃ = R_f x c / l₂

R₃ = P x a x c / (l₁ x l₂) = (a x c / l₁ x l₂) x p

R x l₁ x l₂ = P x b x d

R₁ = (b x d / l₁ x l₂) x P

                                       Similar argument can be applied to the other nodes.

Vortex Induced Vibration-Oil Platform Riser (English Units)

CROSS FLOW VORTEX INDUCED VIBRATION ANALYSIS
Global Variables - Input
Prepared by:				Checked by:
Pipe Outside Diameter, Do =						18	in
Pipe Wall Thickness,t =						0.562	in
Concrete weight coating thickness, tc =						1.5	in
Young Modulus -Steel, E =						2.90E+07	psi
Sea current velocity for a 100 yr Return period storm, U =						3	ft/s
Specified minimum yield strength of pipe, Sy =						52000	psi
Strouhal number, St =						0.219
Kinematic viscosity of sea water at 70oC, vk						0.0000113	ft2/s
End fixity constant, C =(kπ)/2						2.55
Added mass coefficient, Cm						1
Concrete weight coating density, ρoc =						140	lbs/ft3
Density of Steel, ρos =						490	lbs/ft3
Density of Seawater, ρow =						64	lbs/ft3
Logarithm Decrement, δ						0.05
ψT =	Normal Safety Class coefficient					2
ψD =	Period transformation Factor					1
ψR =	Natural frequency Reduction Factor					1
ψU =	Extreme Current Variability factor					1
Pipe Inside Diameter, Di = Do - 2t						16.876	in
Total pipe outside diameter with concrete coating, Dtot = Do+2tc						21	in
Moment of inertia of cross section, I						1171.637829	in4
Damping ratio, ζ = δ2/(δ2+4π2)						0.007956464
Weight of displaced water, ww =(π/4)*Dtot2*ρow						153.958	lbs/ft
Weight of contents, wocn =(π/4)*Di2*ρocn						99.4266266	lbs/ft
Dry weight of pipe with concrete coating, ws
=(π/4)*((Do2-Di2)*ρos +(Dtot2-Do2))*ρoc						194.1292651	lbs/ft
Specific weight of pipe, (ρs/ρw) = (ws/ww)						1.260923532
Dynamic mass, wd =(ww + wocn + ws) / g						13.89794695	slugs/ft
Stability Parameter, Ks =π2 ζ ((ρs/ρw) -Cm)						0.020494895
Free Span Reduced Velocity, VR,ONSET CROSS FLOW
=((π3)*((ρs/ρw + Cm)/(1.5+St2+(ρs/ρw + Cm)-1.5Ks2)))^0.5						3.797567143
Limiting criteria for the onset of Cross flow Vibration,
fn ≥ (U/(VR,ONST*Dtot))*ΨT *ΨD*ΨR*ΨU						0.902833656	Hz
Maximum Allowable Free Span length, L							ft
=(((C*((EI/M)^0.5)))/fn)^0.5)						107.8787189	ft

CROSS FLOW VORTEX INDUCED VIBRATION ANALYSIS-Oil Platform Riser

CROSS FLOW VORTEX INDUCED VIBRATION ANALYSIS-Oil Platform Riser
Global Variables - Input
Pipe Outside Diameter, Do =						457.2	mm
Pipe Wall Thickness,t =						14.2748	mm
Concrete weight coating thickness, tc =						38.1	mm
Young Modulus -Steel, E =						2.00E+02	KN/mm2
Sea current velocity for a 100 yr Return period storm, U =						0.9144	m/s
Specified minimum yield strength of pipe, Sy =						52000	psi
Strouhal number, St =						0.219
Kinematic viscosity of sea water at 70oC, vk						0.0000113	ft2/s
End fixity constant, C =(kπ)/2						2.55
Added mass coefficient, Cm						1
Concrete weight coating density, ρoc =						140	lbs/ft3
Density of Steel, ρos =						490	lbs/ft3
Density of Seawater, ρow =						64	lbs/ft3
Logarithm Decrement, δ						0.05
ψT =	Normal Safety Class coefficient					2
ψD =	Period transformation Factor					1
ψR =	Natural frequency Reduction Factor					1
ψC =	Extreme Current Variability factor					1
Global Variables - Output
Pipe Inside Diameter, Di = Do - 2t						428.6504	in
Total pipe outside diameter with concrete coating, Dtot = Do+2tc						533.4	in
Moment of inertia of cross section, I						487672484	in4
Damping ratio, ζ = δ2/(δ2+4π2)						0.007956464
Weight of displaced water, ww =(π/4)*Dtot2*ρow						99327.54328	lbs/ft
Weight of contents, wocn =(π/4)*Di2*ρocn						64146.08242	lbs/ft
Dry weight of pipe with concrete coating, ws
=(π/4)*((Do2-Di2)*ρos +(Dtot2-Do2))*ρoc						125244.4367	lbs/ft
Specific weight of pipe, (ρs/ρw) = (ws/ww)						1.260923532
Dynamic mass, wd =(ww + wocn + ws) / g						8966.399452	slugs/ft
Stability Parameter, Ks =π2 ζ ((ρs/ρw) -Cm)						0.020494895
Free Span Reduced Velocity, VR,ONSET CROSS FLOW
=((π3)*((ρs/ρw + Cm)/(1.5+St2+(ρs/ρw + Cm)-1.5Ks2)))^0.5						3.797567143
Limiting criteria for the onset of Cross flow Vibration,
fn ≥ (U/(VR,ONST*Dtot))*ΨT *ΨD*ΨR*ΨC						0.010834004	Hz
Maximum Allowable Free Span length, L							ft
=(((C*((EI/M)^0.5)))/fn)^0.5)						254.3431321	ft