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

The section inertial loading in heave, i₃, is given by Equation ( 77 ) (Salvesen et al. 1970, Equation 66):

The shear force at section x₀ is calculated by integrating the loading forward of the section of interest. Thus the shear force due to the inertial forces is given by:

The bending moment at section x₀ is given by Salvesen et al. 1970, Equation 68:

where i₅ is given by:

m     section mass per unit length.

η₃     heave response.

η₅     pitch response.

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.