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278 Barry’s Advanced Construction of Buildings
negative bending and the downward positive bending. It will be seen that bending at the
ends of the beam is prevented by the rigid connections that take some of the stress due to
loading and transfer it to the supporting columns. Just as the rigid connection of beam to
column causes negative or upward bending of the beam at the ends, so a comparable, but
smaller, deformation of the column will occur.
Using the elastic method of analysis to determine working stress in a fixed end beam,
to select a beam section adequate for the permissible stress, the design method produces
a section greater than is needed to provide a reasonable factor of safety against collapse,
because in practice the permissible stress is not reached and in consequence the beam could
safely support a greater load.
The collapse or load factor method of design seeks to provide a load factor, that is, a
safety factor, against collapse applied to particular types of structural frame for economy
in the use of materials by using the load factor which is applied to the loads instead of
stress in materials. The load factor method was developed principally for use in the design
of reinforced concrete and welded connection steel frames with rigid connections as an
alternative to the permissible stress method, as a means to economy in the selection of
structural sections. In the use of the load factor method of design, plastic analysis is used.
In this method of analysis of the forces acting in members, it is presumed that extreme
fibre stress will reach or exceed yield stress and the fibres behave plastically. This is a valid
assumption as in practice the fibres of the whole section play a part in sustaining stress,
and under working loads extreme fibre stress would not reach yield point.
Limit state method of design
The purpose of structural analysis is to predict the conditions applicable to a structure that
would cause it to become either unserviceable in use or unable to support loads to the
extent that members might fail.
In the permissible stress method, a limit is set on the predicted working stress in the
members of the frame by the use of a factor of safety applied to the predicted yield stress
of the materials used. In the load factor method of design, a limit is set on the working
loads to ensure that they do not exceed a limit determined by the application of a factor
of safety to the loads that would cause collapse of the structure. The limit state method of
design seeks to determine the limiting states of both materials and loads that would cause
a particular structure to become unserviceable in use or unsafe due to excessive load. The
limiting conditions that are considered are serviceability during the useful life of the building
and the ultimate limit state of strength.
Serviceability limit states set limits to the behaviour of the structure to limit excessive
deflection, excessive vibration and irreparable damage due to material fatigue or corrosion that
would otherwise make the building unserviceable in use. Ultimate limit states of strength set
limits to strength in resisting yielding, rupture, buckling and transformation into a mechanism,
and stability against overturning and fracture due to fatigue or low-temperature brittleness.
In use the limit state method of design sets characteristic loads and characteristic
strengths, which are those loads and strengths that have an acceptable chance of not being
exceeded during the life of the building. To take account of the variability of loads and
strength of materials in actual use, a number of partial safety factors may be applied to the
characteristic loads and strengths to determine safe working loads and strengths.