COMPUTERS AND STRUCTURES, INC., JUNE 2014 AUTOMATIC WAVE LOADS TECHNICAL NOTE CALCULATION O WAVE LOAD VALUES This section outlines the methoology use to calculate the wave loa an wave win loa values. Overview Wave Loa The program calculates the force exerte by a wave at a particular location on a structural object using the following steps. Steps 1 an 2 apply only if the wave water particle velocities an accelerations are calculate from wave theory (i.e., the rom Selecte Wave Theory check box was checke on the Wave Characteristics form; see Defining Wave Loas for more information). Those steps are skippe when user-efine waves are specifie. Note the wave loas are applie to only the portion of the structure that is above the mu line an below the wave surface. 1. Calculate the apparent wave perio. 2. Calculate two-imensional regular wave kinematics (water particle velocities an accelerations) using the selecte wave theory. 3. Use the specifie wave kinematics factor to moify the water particle velocities an accelerations. 4. Calculate the current profile using the specifie current stretching metho. Moify the current velocities using the specifie current blockage factor. 5. Vectorially combine moifie water particle velocities with the moifie current velocities. 6. Determine the section imensions (not incluing marine growth) base on the efine section properties or the wave overwrites. Overview Page 1 of 9
7. Determine the amount of marine growth, if any, on the consiere object base on the efine marine growth parameters or the wave overwrites. 8. Determine the rag an inertia coefficients for the consiere object base on the efine rag an inertia coefficient parameters or the wave overwrites. 9. Apply the Morison Equation to calculate the force exerte by the wave at a particular location on the object. 10. Calculate the buoyant forces acting on the object. Wave Win Loa The program calculates the force exerte by a wave win loa at a particular location on a structural object using the following steps. Note that wave win loas are applie only to the portions of the structure that are above the wave surface. 1. Calculate the esign win spee. 2. Determine the section imensions (not incluing marine growth or ice) base on the efine section properties or the wave overwrites. 3. Determine the amount of marine growth, if any, on the consiere object base on the efine marine growth parameters or the wave overwrites. 4. Determine the amount of ice, if any, on the consiere object base on the wave overwrites. Note that if both marine growth an ice is specifie at a location, only the marine growth value is use. 5. Determine the shape coefficient use for win loas for the consiere object base on the efine shape coefficient that applies to all elements or the wave overwrites. 6. Determine the win loa shieling factor, if any, on the consiere object base on the wave overwrites. The win loa on the object is multiplie by this shieling factor. 7. Calculate the win rag at a particular location on the object. Overview Page 2 of 9
Apparent Wave Perio The wave perio input in the wave efinition ata oes not inclue the effect of the current. The wave perio use when calculating the wave water particle velocities an accelerations must inclue the effect of the current component in the irection of the wave. The wave perio that inclues the effect of the current is calle the apparent wave perio, T app. The apparent wave perio is calculate by solving a system of three simultaneous nonlinear equations. Those equations, which are ocumente in Section C2.3.1b1 of the commentary of the API Recommene Practice (American Petroleum Institute 2000), are: λ = λ T T app + V I T 2 = 2πλ app g tan (2π / λ) C2.3.1b1 V I = 4π / λ + U c 0 4π ( ) ( ) cosh sinh(4π / λ) λ λ T = Wave length. = Wave perio as input by user (not consiering the current). T app = Apparent wave perio (consiers the current). V I = Effective current spee in the irection of the wave. g = Acceleration ue to gravity. = Elevation reference to the storm water level (positive above storm water level). Apparent Wave Perio Page 3 of 9
U c () = Component of steay current profile at elevation in the Wave Kinematics wave irection an not multiplie by the current blockage factor. = Storm water epth. Wave kinematics yiel the wave water particle velocities an accelerations. The velocities an accelerations are calculate from a specifie wave theory or they are user-efine. Regarless of which metho is use to obtain the wave water particle velocities an accelerations, they are then moifie by the wave kinematics factor, which is intene to account for wave irectional spreaing an irregularity in the wave profile shape. The moification consists of multiplying the horiontal velocities an accelerations by the wave kinematics factor. The vertical velocities an accelerations are not moifie. Current Profile The user specifies the current profile (velocity an irection of current as a function of height) from the mu line to the storm water level. The user specifies that either a Linear or a Nonlinear current stretching metho is use to stretch or compress the current to the wave surface at a particular location. The current velocity at a particular location etermine from applying the current stretching technique is multiplie by the current blockage factor to obtain the current velocity that is combine with the wave velocity. Linear Current Stretching Linear current stretching is base on the following equation, which is foun in Section 2.3.1b-5 of the API Recommene Practice (American Petroleum Institute 2000). The equation is solve irectly for '. ' + ) = ( + ) + η ( 2.3.1b-5 Wave Kinematics Page 4 of 9
' = Elevation of the location the water particle current velocity is esire reference to the storm water level (positive above storm water level). = Elevation of the location in the user-specifie current profile the current velocity shoul be obtaine reference to the storm water level (positive above storm water level). η = Elevation of the wave surface irectly above the water particle reference to the storm water level (positive above storm water level). = Storm water epth. Nonlinear Current Stretching Nonlinear current stretching is base on the following equation, which is foun in Section C2.3.1b-5 of the commentary of the API Recommene Practice (American Petroleum Institute 2000). The equation is solve iteratively for '. sinh ' + η sinh ( 2π ( ' + ) / λn ) ( 2π / λ ) = C2.3.1b-5 n ' = Elevation of the location the current velocity is esire reference to the storm water level (positive above storm water level). = Elevation of the location in the user-specifie current profile the current velocity shoul be obtaine reference to the storm water level (positive above storm water level). η = Elevation of the wave surface reference to the storm water level (positive above storm water level). = Storm water epth. η = Wave length. Current Profile Page 5 of 9
Morison Equation The Morison equation is use to calculate the force exerte by the wave at a particular location on an object. The equation is given in Section 2.3.1b-10 of the API Recommene Practice (American Petroleum Institute 2000). w = D + I = CD AU U + C 2g m w V g U t 2.3.1-1 = Hyroynamic force per unit length acting normal to the object longituinal axis. D = Drag force per unit length. I = Inertia force per unit length. C D = Drag coefficient. w = Weight ensity of water. g = Gravitational acceleration. A = Projecte area normal to object axis per unit length. or pipes an circles this is the effective iameter of the object, incluing marine growth. or other section types, it is the imension of the sie of the rectangle that encloses the section (incluing marine growth, if any) that is normal to the irection of the loa. V = Displace volume per unit length. or pipes an circles this is π D 2 /4 D is the effective iameter of the object, incluing marine growth. or other section types it is the prouct of the imensions of two ajacent sies of the rectangle that encloses the section (incluing marine growth, if any). U = Component of the water particle velocity acting normal to the axis of the object. Morison Equation Page 6 of 9
U = The absolute value of U. C M = Inertia coefficient. U t Buoyant orces = Component of the water particle acceleration acting normal to the axis of the object. Buoyant forces are inclue only when so inicate in the wave loa efinition. Buoyant forces are applie only to objects (or portions of objects) that lie above the mu line an below the wave surface. Buoyant forces consist of a uniform projecte Z irection loa applie to objects that are not vertical an concentrate compressive axial forces applie to the ens of all objects. Uniform Loa The magnitue of the uniform loa is calculate as: f = wv f = A uniform loa in the projecte Z irection. w V = Weight ensity of the water. = Displace volume per unit length of the object. or pipes an circles the isplace volume V is calculate as V = π 2 /4, is the iameter incluing marine growth, if any. or other sections V is calculate as V = b, b an are the with an height of a rectangle that woul enclose the section. Concentrate Compressive Loas at Object Ens The magnitue of the concentrate compressive axial loa at each en of each object is calculate as: P = wa h c Buoyant orces Page 7 of 9
P w = A concentrate compressive axial loa. = Weight ensity of the water. A c = Cross sectional area to which the loa is applie. h = Height of the water. The magnitue cross-sectional area to which the loa is applie epens on whether the object is flooe. All objects are assume to not be flooe unless the are specifically inicate to be flooe in the wave overwrites. If the object is not flooe, for pipes an circles the cross sectional area A c is calculate as A c = π 2 /4 is the iameter, incluing marine growth, if any. or other sections, A c is calculate as A c = b, b an are the with an height of a rectangle that woul enclose the section. If the object is flooe, the cross-sectional area A c is taken equal to the area specifie for the section property that is assigne to the object. Win Loas The wave win loas are calculate base on Sections 2.3.2b-1 an 2.3.2c of the API Recommene Practice (American Petroleum Institute 2000). Design Win Spee The esign win spee is calculate using the following equations that are taken irectly from the API Recommene Practice. (, t) = U ( ) 1 0.41I t ( ) ln t0 u u 2.3.2-1 the one hour mean win spee U() (ft/sec) at level (ft) is given by: ( ) = U 0 1 + C ln 32.8 U 2.3.2-2 C = 0.0573 1 + 0.0457U 0 an the turbulence intensity I u () at level is given by: Win Loas Page 8 of 9
( ) = 0.06 [ 1 + 0.0131U ] 0 32.8 0.22 I u 2.3.2-3 Win Drag orce The win rag force is calculate using the following equation that is taken irectly from the API Recommene Practice. 2 u Cs A 2 = ρ 2.3.2-8 = Win force ρ = Mass ensity of air (slugs/ft 3 ) u = Win spee (ft/sec) C s = Shape coefficient A = Are of element (ft 2 ) Win Loas Page 9 of 9