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Steel Designers' Manual - 6th Edition (2003)
Analysis of composite section 611
(1) the unfactored imposed load does not exceed twice the unfactored dead load;
(2) the load is uniformly distributed;
(3) end spans do not exceed 115% of the length of the adjacent span;
(4) adjacent spans do not differ in length by more than 25% of the longer span.
An alternative to the elastic approach is plastic hinge analysis of plastic sections.
Conditions on the use of plastic hinge analysis are presented in BS 5950: Part 3 1 and
Eurocode 4 (draft). 8 However, large redistributions of moment may adversely affect
serviceability behaviour (see section 21.7.8).
The ultimate load resistance of a continuous beam under positive (sagging)
moment is determined as for a simply-supported beam. The effective breadth of the
slab is based on the effective span of the beam under positive moment (see section
21.7.1).The number of shear-connectors contributing to the positive moment capacity
is ascertained knowing the point of contraflexure.
The negative (hogging) moment resistance of a continuous beam or cantilever
should be based on the steel section together with any properly anchored tension
reinforcement within the effective breadth of the slab. This poses problems at edge
columns, where it may be prudent to neglect the effect of the reinforcement unless
particular measures are taken to provide this anchorage. The behaviour of a continuous
beam is represented in Fig. 21.5.
The negative moment resistance is evaluated from plastic analysis of the section:
Case 1: Rr < Rw (plastic neutral axis lies in web):
(21.9)
where Rr is the tensile resistance of the reinforcement over width Be, Rq is the capacity
of the shear-connectors between the point of contraflexure and the point of
maximum negative moment (see section 21.7.3), and Dr is the height of the reinforcement
above the top of the beam.
Case 2: Rr > Rw (plastic neutral axis lies in flange):
M R (21.10)
NB the last term in this expression is generally small.
The formulae assume that the web and lower flange are compact i.e. not subject
to the effects of local buckling. The limiting depth of the web in compression is 78te
(where e is defined in Chapter 2) and the limiting breath : thickness ratio of the
flange is defined in Table 11 of BS 5950: Part 1.
If these limiting slendernesses are exceeded then the section is designed elastically
– often the situation in bridge design.The appropriate effective breadth of slab
is used because of the sensitivity of the position of the elastic neutral axis and hence
the zone of the web in compression to the tensile force transferred by the reinforcement.The
elastic section properties are determined on the assumption that the
concrete is cracked and does not contribute to the resistance of the section.
D M M R
2
( Rs - Rr)
T
nc = s + RD r r -
2 Rf
4
D Rq
D
nc s s Dr
R
2
Ê ˆ
= + +
Ë ¯ w
-
2 4