heavily loaded beam in a floor) in order that
the feasibility of a proposal can be tested or
the depth of the structural zone required for a
floor estimated. In the case of elements loaded
in bending, Table A2.3 can be used to estimate
the maximum bending moment involved.
The loading on critical elements can be
estimated from a judgement of the total area
of roof or floor which they support. These areas
are then simply multiplied by the intensity of
gravitational load to give the load on the struc-
tural element concerned.
Basic versions of element-sizing calculations
are normally based on either the permissible
stress or the load factor method of design. In the
permissible stress method the failure stress of
the material is divided by the factor of safety to
give a permissible stress and the calculations
are used to determine the sizes of cross-
sections required to ensure that the actual
stress in the structure, when the peak load is
applied, is never greater than the permissible
stress.
In the load factor method the peak load
value is multiplied by the factor of safety to
give a factored design load which is then used,
in conjunction with the actual failure stress of
the material (normally taken to be the yield
stress), to determine safe values for the sizes
of cross-sections (i.e. values which ensure that
the structure will have a margin of strength
over that which is required to resist the peak
values of the applied loads).
In some present-day final design calcula-
tions it is normal to split the factor of safety
into two or more 'partial factors of safety'
which are applied separately to load and
material strength values to take account of the
varying degrees of precision with which these
can be known. The relative advantages and
disadvantages of the different approaches to
the incorporation of the factor of safety into
structural calculations will not be discussed
here. All of the approximate sizing calculations
presented here are based on the permissible
stress method, which is the simplest to apply
in practice.A2.3.2 Elements subjected to axial tension
Elements which are subjected to axial tension
are normally constructed either of steel or of
timber. The axial tensile stress in the element
is normally considered to be uniformly distri-
buted across the cross-section and is calcu-
lated from the equation,fat = P/A (A2..1)where: fat = axial stress
P = applied axial force
A = area of cross-sectionA2.3 Element-sizing calculations
A2.3.1 Introduction
Structural elements must be of adequate
strength and must not undergo excessive
deflection under the action of load. These are
distinct requirements and either one of them
may be the critical factor which determines the
size of cross-section which must be adopted.
The calculations which are outlined here are
almost exclusively strength calculations. In the
majority of cases these are sufficient for the
purpose of determining approximately the size
of cross-section required for a structural
element. The basic principles and elementary
forms of element-sizing calculations are
outlined in this section. The modified versions
of these which are used for the principal struc-
tural materials, and which allow for the
peculiarities of different materials, are
discussed in Sections A2.4 to A2.7
Element-sizing calculations must have a
factor of safety incorporated into them to allow
for the uncertainties which are inevitably
present in the design and construction
processes. The agencies which give rise to
these inaccuracies include the imprecision
with which loads and material strengths can be
known, the inaccuracies which are present in
the calculations themselves and the discrepan-
cies which occur between the sizes and
strengths which are specified for structural
elements and those which are actually realised
in the finished structure. 249
Appendix 2