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Chapter 40
Bending of beams
Beam theory
The bending of ships can be likened to the bending of beams in many cases. This chapter shows the procedures employed with beam theory.
The problem of calculating the necessary strength of ships is made dif®cult by the many and varied forces to which the ship structure is subjected during its lifetime. These forces may be divided into two groups, namely statical forces and dynamical forces.
The statical forces are due to:
1 The weight of the structure which varies throughout the length of the ship.
2 Buoyancy forces, which vary over each unit length of the ship and are constantly varying in a seaway.
3 Direct hydrostatic pressure.
4 Concentrated local weights such as machinery, masts, derricks, winches,
etc.
The dynamical forces are due to:
1 Pitching, heaving and rolling, 2 Wind and waves.
These forces cause bending in several planes and local strains are set up due to concentrated loads. The effects are aggravated by structural discontinuities.
The purpose of the present chapter is to consider the cause of longi- tudinal bending and its effect upon structures.
Stresses
A stress is the mutual actual between the parts of a material to preserve their relative positions when external loads are applied to the material.