Continuous beams and slabs, and beams in frames - Composite Structures of Steel and Concrete - page 149

Table 4.3 Limits to redistribution of hogging moments, per cent of the initial
value of the bending moment to be reduced

Class of cross-section in hogging moment region 1 2 3 4

For 'uncracked' elastic analysis 40 30 20 10

For 'cracked' elastic analysis 25 15 10 0

the ratio of action effect to resistance is highest (usually, at the internal
supports). The effect is to increase the moments of opposite sign (usually,
in the mid-span regions).
For continuous composite beams, the ratio of action effect to resistance
is higher at internal supports, and lower at mid-span, than for most beams
of a single material, and the use of redistribution is essential for economy
in design. It is limited by the onset of local buckling of steel elements in
compression, as shown in Table 4.3, which is given for ultimate limit
states in EN 1994-1-1.
The differences between the two sets of figures show that 'uncracked'
analyses have been assumed to give hogging moments that are higher
than those from 'cracked' analyses by amounts that are respectively 12%,
13%, 9% and 10% for Classes 1 to 4 (e.g., 140/125

1.12 for Class 1).
The hogging moments referred to are the peak values at internal sup-
ports, which do not include supports of cantilevers (at which the moment
is determined by equilibrium and cannot be changed). Where the com-
posite section is in Class 3 or 4, moments due to loads on the steel
member alone are excluded. The values in Table 4.3 are based on research
(e.g., Reference 40).
The use of Table 4.3, and the need for redistribution, is illustrated in
the following example. The Eurocode also allows limited redistribution
from mid-span regions to supports, but this is rare in practice.

=

4.3.2.2 Example: redistribution of moments

A composite beam of uniform section (apart from reinforcement) is con-
tinuous over three equal spans L . The cross-sections are in Class 1. For
the ultimate limit state, the design permanent load is g per unit length, and
the variable load is q per unit length, with q 2 g . The sagging moment of

resistance, M Rd , is twice the hogging moment of resistance, M

=

′ Rd . Find the

minimum required value for M Rd :

(a) by elastic analysis without redistribution;

(b) by elastic analysis with redistribution to Table 4.3;

(c) by rigid-plastic analysis.