# # Thin Walled Sections

The effect of shear deformation on the results of a structural analysis
is usually negligible. Where it is more significant, it will usually
suffice to make a simple approximation to the shear deformation area of
members with a cross-section such as those shown in Fig 1. The usual
approximation is, by analogy with a simple rectangular beam, to take

For those rare structures where the shear deformation is very important
it may be necessary to use a more exact value for the area. This Note
gives formulae for

These were derived from the virtual work formula, shear deflection per
unit length =

To see what the formulae mean in practice, they were applied to steel
sections taken from the handbook with the results shown in the table
below. In a web or flange with varying thickness,

It can be seen that, for sections with top and bottom flanges bending,
as nature intended, in their strong direction, the usual approximation
is satisfactory (although it should be noted that d is the distance
between flange centres, not overall depth). For the more bizarre
sections used in bending, values of

Section | F |
---|---|

Bending in strong direction | |

UB | 5.72 to 5.81 |

Joist | 5.17 to 5.78 |

UBP | 5.25 to 5.28 |

UC | 5.28 to 5.53 |

SHS | 5.0 |

RHS | 5.0 to 5.49 |

Channel | 5.06 to 5.60 |

Angle | 3.68 to 4.62 |

Tee from UB | 4.78 to 4.97 |

Tee from UC | 4.11 to 4.35 |

Cruciform | 5 |

Bending in weak direction | |

Channel | 2.12 to 3.78 |

RHS | 4.02 to 5.0 |

Angle | 2.55 to 3.68 (for |

I’s, T’s, & cruciform | 5.0 |

With regard to calculating shear stresses, the exact distribution is not
normally required, or even usable, because Codes of Practice base the
shear strength on an allowable average shear stress calculated on the
total net area

is the shear flow in the web at the junction with the flange, and

is the maximum shear flow in the web, in which

For circular annuli, assuming that the stress is constant across the
wall thickness

## # Formulae

Shear deformation area

Type A1

Types A2 & A3

Special case of A3 with constant wall thickness so that

Type B1

Special case of B1 with constant

Types B2 & B3

Special case of B3 with constant thickness

Type C

## # Stress Factors

Type A1, A2 & A3

Type B1, B2 & B3