This module calculates the vertical shear forces and bending moment components due to the incident wave excitation forces.

The section wave excitation loading in heave, e₃, is given by (Salvesen et al. 1970, Equation 73):

Here the Froude-Krilov force, f₃, and the wave diffraction force, h₃, as calculated in the hydrodynamics module, include the wave amplitude and water density factor zr.

The shear force at section x₀ is calculated by integrating the loading forward of the section of interest and adding a speed dependent term. Thus the shear force due to the wave excitation is given by:

The bending moment at section x0 is given by (Salvesen et al. 1970, Equation 74):

where e₅ is given by:

f₃      2D section Froude-Krilov wave force in heave.

h₃     2D section diffraction wave force in heave.

ω     encounter frequency.

ξ      longitudinal distance from LCG.

x₀     longitudinal position of section of interest.

The functions in this module are set up to calculate the value of the integrands at all sections and then integrate over the appropriate sections to obtain the shear force and bending moments; integrations are evaluated using the trapezium rule.

The bending moment integrands are dependent on the section, x₀, at which the bending moment is being evaluated and hence need to be re-evaluated for each section.