Figure 6.1 shows typical examples of beams for buildings within the scope of EN 1994-1-1. The details include web encasement, and profiled sheeting with spans at right angles to the span of the beam, and continuous or discontinuous over the beam. The top right-hand diagram represents a longitudinal haunch. Not shown (and not excluded) is the common situation in which profiled sheeting spans are parallel to the span of the beam. A re-entrant trough is shown in the bottom right-hand diagram. Sheeting with trapezoidal troughs is also within the scope of the code.
The steel cross-section may be a rolled I- or H-section or may be a doubly-symmetrical or mono-symmetrical plate girder. Other possible types include any of those shown in sheet 1 of Table 5.2 of EN 1993-1-1; for example, rectangular hollow sections. Channel and angle sections should not be used unless the shear connection is designed to provide torsional restraint. Stub girders are not within the scope of EN 1994-1-1. There is an extensive literature on their design.41
Shear connection
Clause 6.1.1(4)P
In buildings, composite cross-sections are usually in Class 1 or 2, and the bending resistance is determined by plastic theory. At the plastic moment of resistance, the longitudinal force in a concrete flange is easily found, so design of shear connection for buildings is often based on the change in this force between two cross-sections where the force is known. This led to the concepts of critical cross-sections (clause 6.1.1(4)P to clause 6.1.1(6)) and critical lengths (clause 6.1.1(6)). These concepts are not used in bridge design. Cross-sections in Class 3 or 4 are common in bridges, and elastic methods are used. Longitudinal shear flows are therefore found from the well-known result from elastic theory, vL= .
Points of contraflexure are not critical cross-sections, partly because their location is different for each arrangement of variable load. A critical length in a continuous beam may therefore include both a sagging and a hogging region. Where connectors are uniformly spaced over this length, the number in the hogging region may not correspond to the force that has to be transferred from the longitudinal slab reinforcement. This does not matter, provided that the reinforcing bars are long enough to be anchored beyond the relevant connectors. The need for consistency between the spacing of connectors and curtailment of reinforcement is treated in clause 6.6.1.3(2)P.
Clause 6.1.1(5)
A sudden change in the cross-section of a member changes the longitudinal force in the concrete flange, even where the vertical shear is zero. In theory, shear connection to provide this change is needed. Clause 6.1.1(5) gives a criterion for deciding whether the change is sudden enough to be allowed for, and will normally show that changes in reinforcement can be ignored. Where the clause is applied, the new critical section has different forces in the flange on each side of it. It may not be clear which one to use.
One method is to use the result that gives the greater change of force over the critical length being considered. An alternative is to locate critical cross-sections on both sides of the change point, not more than about two beam depths apart. The shear connection in the short
Fig. 6.1. Typical cross-sections of composite beams
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critical length between these two sections, based on the longitudinal forces at those sections, needs to take account of the change of section.
The application of clause 6.1.1(5) is clearer for a beam that is composite for only part of its length. The end of the composite region is then a critical section.
A tapering member has a gradually changing cross-section. This can occur from variation in the thickness or effective width of the concrete flange, as well as from non-uniformity in the steel section. Where elastic theory is used, the equation vL, Ed= VEdA /I should be
replaced by
(D6.1)
Clause 6.1.1(6)
where x is the coordinate along the member. For buildings, where resistances may be based on plastic theory, clause 6.1.1(6) enables the effect to be allowed for by using additional critical sections. It is applicable, for example, where the steel beam is haunched. The treatment of vertical shear then requires care, as part of it is resisted by the sloping steel flange.
Clause 6.1.1(7)
Provisions for composite floor slabs, using profiled steel sheeting, are given only for buildings. The space within the troughs available for the shear connection is often insufficient for the connectors needed to develop the ultimate compressive force in the concrete flange, and the resistance moment corresponding to that force is often more than is required, because of other constraints on design. This has led to the use of partial shear connection, which is defined in clause 6.1.1(7). It is applicable only where the critical cross-sections are in Class 1 or 2. Thus, in buildings, bending resistances are often limited to what is needed, i.e. to
MEd, with shear connection based on bending resistances; see clause 6.6.2.2.
Where bending resistances of cross-sections are based on an elastic model and limiting stresses, longitudinal shear flows can be found from vL, Ed= VEdA /I. They are related to
action effects, not to resistances. Shear connection designed in this way, which is usual in bridges, is ‘partial’ according to the definition in clause 6.1.1(7)P, because increasing it would increase the bending resistances in the vicinity – though not in a way that is easily calculated, because inelastic behaviour and partial interaction are involved.
For these reasons, the concept ‘partial shear connection’ is confusing in bridge design and not relevant. Clauses in EN 1994-1-1 that refer to it are therefore labelled ‘for buildings’.
Effective cross-section of a beam with a composite slab
Where the span of a composite slab is at right angles to that of the beam, as in the lower half of Fig. 6.1, the effective area of concrete does not include that within the ribs. Where the spans are parallel (θ = 0), the effective area includes the area within the depth of the ribs, but usually this is neglected. For ribs that run at an angle θ to the beam, the effective area of concrete within an effective width of flange may be taken as the full area above the ribs plus cos2θ times the area of concrete within the ribs. Where θ > 60°, cos2θ should be taken as zero.
Service ducts in slabs can cause a significant loss of effective cross-section.