This module calculates the vertical shear forces and bending moment components due to hydrodynamic forces.

The section hydrodynamic loading in heave, d3, is given by (Salvesen et al. 1970, Equation 79):

On differentiating the heave and pitch accelerations and velocities, Equation ( 89 ) may be expressed in terms of the heave and pitch amplitudes:

The shear force at section x₀ is then given by:

The bending moment at section x0 is given by (Salvesen et al. 1970, Equation 81):

,with d₅:

where:

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.