# Shearforce and bending moments#

Calculation of the global bending moments and shear-forces in ships is an important part of checking the longitudinal or global strength of a vessel.

For this caluculation a ship is modelled as a single beam with forces acting on it. Typically these forces are cargo, self-weight, ballast and buoyancy. In DAVE the global bending moments and shear-forces can be calculated for any frame. Furthermore all loads from all nodes connected to that axis system will contribute to the shear and moment lines. This means that loads from cranes, grounding contact, trailered loads and pilelines are included.

For the calculation of the global shearforce and bending moments it is important to know at which location or over which length a force is distributed.

Example results for Billy

## Where do loads connect?#

DAVE distinguishes point loads and distributed loads.

Pointsloads are connected to the nearest point on the moment-line beam.

Distributed loads are distributed over the portion of the beam bewteen the points on the beam closest to outer points of the distributed load.

Loads from fluids (buoyancy, tanks) distributes over the area directly above/below it.

The subtle difference beteen the last two is that for normal distributed loads the imaginary line connecting the load and the beam runs perpendicular to the beam while for fluid loads it runs in vertical direction. The effect is that normal distributed loads may add an moment to the beam while fluids loads do not. The reason behind this difference is that otherwise shear and moment curves for vessels get jumps at segment intersections.

## Point loads / distributed loads#

Loads are loads resulting from forces on a point, connected frames or contact meshes.

DAVE used the concept of “footprints” to define the area over which loads are distributed. Footprints are a series of 3d points (vertices) that can be defined on any point or frame.

The projection of the footprints onto the plane in which the shearforce and moments are calculated determines the extent of the distributed load: so only the outer-most vertices in the current direction matter. Points and frame nodes for which no footprints are defined result in point loads.

## Self-weight#

Self weight of RigidBodies is applied using the same footprint.

## Connections, loads from child nodes#

Each frame applies its connection-force on its parent using its own footprint. The connection force of a frame includes the loads of all child nodes.

Footprints of nodes are only seen by the parent of a node.

## Implementation#

RigidBodies, Axis and Points have a property “footprint”. This is a list of vertices (3d).

for frame: Defined in local axis system

for point: Defined in parent axis system, relative to position of point

for RigidBody: Defined in local axis system; use for self-weight as well.

## Examples#

Example results for Billy

Various examples of bending moments

references:

DNVGL Rules for classification: Ships — DNVGL-RU-SHIP Pt.3 Ch.4. https://rules.dnvgl.com/docs/pdf/dnvgl/ru-ship/2017-01/DNVGL-RU-SHIP-Pt3Ch4.pdf