Annex

Deflection formulae for simply supported tapered and double tapered beams subjected to a point load at mid-span or to a uniformly distributed load.

The equations for deflection due to bending moment and to shear at mid-span in simply supported tapered and double tapered beams when subjected to a mid-span point load or a uniformly distributed load along the length of each beam type are based on the equations in the Timber Designers' Manual and are given in Table A6.1. Although the maximum deflection in a tapered beam when subjected to a point load at mid-span will be marginally off centre, the use of the central deflection value is good enough for design purposes.

A graphical representation of the equations in Table A6.1 is given in Figures A6.1 and A6.2.

Table A6.1 Deflection formulae for simply supported tapered and double tapered beams subjected to a point load at mid span or a uniformly distributed load along the beam length

Beam type and loading condition

Bending deflection at mid span

Shear deflection at mid span

Tapered beam with a point load at mid span, FdL

Tapered beam with a uniformly distributed load qjxmii length along the qdL2

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