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Structural Steel Frames 277
calculated by the elastic method of analysis to predict the maximum elastic working stresses
in the members of the structural frame. Beam sections are then selected so that the
maximum predicted stress does not exceed the permissible stress. In this calculation, a
factor of safety is applied to the stress in the material of the structural frame. The permissible
compressive stress depends on whether a column fails due to buckling or yielding and
is determined from the slenderness ratio of the column, Young’s modulus and the yield
stress divided by a factor of safety. The permissible stress method of design provides a safe
and reasonably economic method of design for simply connected frames and is the most
commonly used method of design for structural steel frames.
A simply connected frame is a frame in which the beams are assumed to be simply supported
by columns to the extent that while the columns support beam ends, the beam is
not fixed to the column and in consequence when the beam bends (deflects) under load,
bending is not restrained by the column. Where a beam bears on a shelf angle fixed to a
column and the top of the beam is fixed to the column by means of a small top cleat
designed to maintain the beam in a vertical position, it is reasonable to assume that the
beam is simply supported and will largely behave as if it had a pin-jointed connection to
the column.
Collapse or load factor method of design
Where beams are rigidly fixed to columns and where the horizontal or near-horizontal
members of a frame, such as the portal frame, are rigidly fixed to posts or columns, then
beams do not suffer the same bending under load that they would if simply supported by
columns or posts. The effect of the rigid connection of beam ends to columns is to restrain
simple bending, as illustrated in Figure 5.2. The fixed end beam bends in two directions,
upwards near fixed ends and downwards at the centre. The upward bending is termed
Simple
bending
Pin joint
Simply supported beam
Negative
bending
Fixed end
Positive
bending
Fixed end beam
Figure 5.2 Comparison of pin-jointed and fixed end beams.