Steel Designers Manual - TheBestFriend.org

This material is copyright - all rights reserved. Reproduced under licence from The Steel Construction Institute on 12/2/2007
To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/
Steel Designers' Manual - 6th Edition (2003)
Chapter 11
Plane frame analysis
by JOHN RIGHINIOTIS
11.1 Formulae for rigid frames
11.1.1 General
The formulae given in this section are based on Professor Kleinlogel’s Rahmenformeln
and Mehrstielige Rahmen. 1 The formulae are applicable to frames which
are symmetrical about a central vertical axis, and in which each member has constant
second moment of area.
Formulae are given for the following types of frame:
Frame I Hingeless rectangular portal frame.
Frame II Two-hinged rectangular portal frame.
Frame III Hingeless gable frame with vertical legs.
Frame IV Two-hinged gable frame with vertical legs.
The loadings are so arranged that dead, snow and wind loads may be reproduced
on all the frames. For example, wind suction acting normal to the sloping rafters of
a building may be divided into horizontal and vertical components, for which appropriate
formulae are given, although all the signs must be reversed because the loadings
shown in the tables act inwards, not outwards as in the case of suction.
It should be noted that, with few exceptions, the loads between node or panel
points are uniformly distributed over the whole member. It is appreciated that it is
normal practice to impose loads on frames through purlins, siderails or beams. By
using the coefficients in Fig. 11.1, however, allowance can be made for many other
symmetrically placed loads on the cross-beams of frames I and II shown, where the
difference in effect is sufficient to warrant the corrections being made. The indeterminate
BMs in the whole frame are calculated as though the loads were uniformly
distributed over the beam being considered, and then all are adjusted by
multiplying by the appropriate coefficient in Fig. 11.1. It may be of interest to state
why these adjustments are made. In any statically indeterminate structure the indeterminate
moments vary directly with the value of the following quantity:
area of the free BM diagram
EI
Where the loaded member is of constant cross section, EI may be ignored.
342