Structural Design for Architecture
element's cross-section. The permissible stress
values which are used in practice are not based
on the Euler formula, however. For some
materials they are derived from equations
which are similar to, but more sophisticated
than, the Euler formula while in others they
are based almost entirely on experimental
data. The practising designer is not normally
concerned with the derivation of permissible
levels of stress, however, as recommended
values can normally be found in codes of
practice. They are usually presented in the
form of tables or graphs giving permissible
values of average compressive stress for differ-
ent values of slenderness ratio.
The procedures which are used to assess
slenderness ratio and effective length tend also
to be different for different materials.A2.4 Steel structures
A2.4.1 Introduction
Steel is used principally in skeleton-frame-type
structures so the principal types of element are
columns, beams and triangulated girders. The
structures are normally hinge-jointed which
makes approximate analysis straightforward.
Permissible stresses for steel are given in Table
A2.4.^2A2.4.2 Beams^3
The most common types of these are floor
beams in multi-storey frames, for which the
I-section is suitable, or secondary elements,
such as purlins or cladding rails, for which
smaller sections such as the channel are
normally used.
A good approximation to the size required
for a beam is given by the equation:Zreq =M/fpb (A2.11)2 These should only be used for preliminary sizing of
elements to test the feasibility of a proposed structure.
They should not be used for final element-sizing calcu-
258 lations.Zreq is the required modulus of section and
provides the basis for selecting a suitable size
of cross-section from the available ranges
specified in Table 3.2. If a suitable section size
cannot be found from Table 3.2 another type of
section will be required (refer to manufactur-
ers' tables). It is normal to select the lightest
cross-section which will provide the required
section modulus.
M is the maximum applied bending moment
determined from the structural analysis.This is
determined either from first principles, using
the 'imaginary cut' technique, or from the
relevant formula in Table A2.3. The load
pattern is determined from the area of floor or
roof which the beam supports or by estimating
the point loads which will be applied to it from
other skeleton elements which it supports.
fpb is the appropriate value of permissible
bending stress selected from Table A2.4.^3
The above procedure will give a reasonably
accurate prediction of the size required for an
element which is subjected to bending
moment. A more accurate prediction is
obtained if the shear stress and deflection are
also checked and the section size adjusted if
necessary.
The average shear stress is given by:Vav = V/Aavvav should not be greater than the relevant
value given in Table A2.3. V is the maximum
value of the shear force in the beam. This will
normally occur close to the supports. Aav is the
area of the cross-section which resists shear. In
the case of steel sections this is the area of the
web (the total depth of the section multiplied
by the web thickness).3 No allowance is made in this procedure for secondary
effects such as the compression instability of thin
flanges or webs - see Draycott, Structural Elements Design
Manual (Butterworth-Heinemann, Oxford, 1990). It must
therefore be used only for preliminary element sizing.
In most architectural structures the parts of elements
which are likely to buckle due to local compression are
adequately restrained laterally. The estimates obtained
from the procedure are therefore likely to be reasonably
accurate in most cases.