When calculating the shear Force and the bending moment diagrams for more complex loading
across discontinuities such as concentrated loads and moments. Simple methods are
not enough. For the more complicated cases the use of singularity functions provide
a convenient method.

A singularity function is expressed as

Where

n = any integer (positive or negative) including zero

a = distance on x axis along the beam,from the selected origin, identifying the location of the discontinuity.

If n >0 and the expression inside the angular brackets is positive then
f_{n}(x) = (x-a)^{n} the expression is a normal algbraic formula |

If n > 0 and the expression inside the angular brackets is negative then f_{n}(x) = 0 |

If n < 0 then f_{n} = 1 for x = a and f_{n}(x) = 0 otherwise |

If n = 0 then f_{n} = 1 for x >= a and f_{n}(x) = 0 otherwise |

Unit Singularity Function | Singularity Function as used |

The requirement is to obtain the Shear load, moment, slope and deflection anywhere along the beam as shown

The equations above can be used to determine the shear load, moment, slope and deflection
for the beam from x = 0 to x = L

**Sites Providing Relevant Information **

- Beam deflection usingDiscontinuity Functions...pdf download - Very informative paper
- Deflection of Beams...Berkely U. Useful download on beam deflection including use of singularity functions
- Singularity functions-Notes from office hours... Concise information with comments