Single span composite beams

1. INTRODUCTION

The object of this lecture is to explain the principles and rules for the design of a simply supported, i.e. single span, composite steel-concrete beam with full shear connection. Typical cross-sections of composite beams are shown in Figure 1. For simplicity, only the symmetrical steel sections 1a, 1c, and 1d are considered. The relevant symbols are given in Figure 2.

For full shear connection, the total longitudinal shear resistance of the shear connectors (R_q), distributed between the point of maximum positive bending moment and a simple end support, must be greater than (or equal to) the lesser of the resistance of the steel beam (N_pl,a  = A_af_y/γ_M0) when the plastic neutral axis is in the slab or the resistance of the concrete flange (N_c,f  = 0.85 b_eff h_c f_ck/γ_C) when the plastic neutral axis is in the steel section.

1.1 Ultimate limit state

The resistance to longitudinal shear (see Figure 3, criterion III) of a shear connection is not discussed here. An idealised load-slip behaviour of the connector, as illustrated in Figure 4, is assumed.

This lecture concentrates on the resistance of the beam to moment and vertical shear, which have maximum values at cross-sections I and II respectively, as shown in Figure 3. Between these critical cross-sections, each cross-section is subjected to a bending moment and a vertical shear. This combination is usually only of importance in the case where the loading includes point or line loads, as shown in Figure 5. Here, the maximum moment and maximum vertical shear act together at a critical cross-section adjacent to the point load or line load. Special attention must be paid to this critical cross-section.

In the case of statically determinate beams, such as simply supported single span beams, it is easy to determine the distribution of bending moments from the equilibrium conditions. To determine the stress distribution over the cross-section, plastic behaviour is assumed. The advantage of this method is that the calculation of the resistance is based on the 'maximum moment at failure' condition. This method is also easy to understand and apply.

Steel sections can be classified into 4 classes depending on the local buckling behaviour of the flange and/or web in compression. In the case of a simply supported single span, plastic design methods may be used for Class 1 and 2 sections; sections of Class 2 are only allowed when no rotation capacity is required. These classes are described as follows (see also Figure 6 and Lecture Cross-section classification):

• Class 1: plastic cross-sections which can form a plastic hinge with sufficient rotation capacity for plastic analysis
• Class 2: compact cross-sections which can develop the plastic moment of resistance but have limited rotation capacity

The steel compression flange, if properly attached to the concrete flange, may be assumed to be of Class 1.

Table 1 (part of Table 5.2 of EN 1993-1-1 [2]), classifies steel webs in compression according to their width to thickness ratios. In a composite beam, the compression part of the web, in positive bending, is always less than half the total depth for a symmetrical section. A width-to-thickness ratio less than 83ε will, therefore, always be sufficient for a symmetric steel section in positive bending. Therefore, instability of the web is not critical for the IPE-sections and the HE-sections.

Because the part in compression is always laterally restrained when the beam is in positive bending, it is not necessary to check lateral-torsional buckling. Other aspects, such as shear buckling, are discussed briefly in Section 4. Web crippling, however, is beyond the scope of this lecture - see Eurocode 3 for further information [2].

1.2 Serviceability limit state

For simply supported single spans, the concrete flange is in compression, and cracking of the concrete is not relevant. Only deflections and vibrations are important.