Shear Connection in composite beams
Transcription
Shear Connection in composite beams
ADVISORY DESK The aim of this feature is to share up-dates, design tips and answers to queries. The Steel Construction Institute provides items which, it is hoped, will prove useful to the industry. AD 266 Shear Connection in composite beams Following some recent questions on the requirements given in BS 5950-3: 1990 for the design of the shear connection in composite beams, a clarification of three major issues is given in this advisory desk article. These issues are: • Effective breadth of the concrete flange (BS 5950-3: 1990 Clause 4.6) • Partial shear connection (BS 5950-3: 1990 Clause 5.5) • Transverse reinforcement (BS 5950-3: 1990 Clause 5.6) Effective breadth of the concrete flange (BS 5950-3: 1990 Clause 4.6) In normal composite construction, a relatively thin concrete floor slab acts as the compression flange of the composite beam. The longitudinal compressive bending stresses in the slab cause shear stresses in the plane of the slab as shown in Figure 1. The effective width is defined mathematically by the following equation: Be = 2 b 0 σx σxmax dy The above equation allows the actual flange width B to be replaced by an effective width Be , such that the area GHJK equals the area ACDEF (see Figure 2). Previous research, based on elastic theory, has shown that the ratio of Be/B depends in a complex way on: • the ratio of B to the span L • the type of loading • the boundary conditions at the supports • other variables. The results of this work have been simplified and incorporated in BS 5950-3: 1990 Clause 4.6. According to this code of practice, the total effective breadth of the concrete flange Be should be taken as the sum of the effective breadths of the portions of flange be each side of the centreline of the steel beam. In the absence of any more accurate determination, the effective breadth of each portion may be taken to be: a) for a slab spanning perpendicular to the beam, be = Lz / 8 >b / b) for a slab spanning parallel to the beam be = Lz / 8 >0.8b / Figure 1. Shear stresses in a composite beam The shear stresses cause shear strains in the plane of the slab. One effect of these shear strains is that the areas of slab furthest from the steel beams are not as effective at resisting longitudinal bending stresses as the areas close to the steel beams. This effect is called shear lag. As a result, the longitudinal bending stress across the width of the slab is not constant, see Figure 2. The longitudinal stress tends to be a maximum over the web of the steel section, and reduces non-uniformly away from the centre-line of the beam. In order that simple “engineers” bending theory may be applied (i.e., plane sections remain plane in bending), the effective width concept is introduced. The section properties are calculated using the effective width, Be , which is assumed to carry a uniform stress across the width Be. The value of the stress in the concrete calculated using these effective section properties is equal to the maximum stress resulting from the effects of shear lag in the actual slab. Figure 2. Use of effective width to allow for shear lag where Lz is the distance between points of zero moment (taken as the span L for simply-supported beams) and b is the actual breadth of each portion of the concrete flange (taken as half the beam spacing or, when the beam is adjacent to a free edge, the distance between the centre-line of the web and the free edge). It should be noted that unless a reduction in composite action has been justified by tests or numerical analyses, it is not appropriate to consider a smaller effective width than given by the expressions shown above. This is because an underestimate of the effective width of the concrete flange will result in unsafe designs for the shear connectors. For this particular reason, the values of the effective breadth given in Eurocode 4 are generally higher than those in Eurocode 2 for reinforced concrete T-beams. Partial shear connection (BS 5950-3: 1990 Clause 5.5) The basic requirement for shear connectors is that they are capable of maintaining their design resistance to shear at large slips, to enable the composite beam to have sufficient rotation capacity to develop its full design bending resistance. The ductility of a shear connector is defined by its slip capacity, which is established from a standard push test, and is defined by the maximum slip that the connector can resist while still maintaining its design resistance. Provided that studs have a slip capacity greater than required in a beam design, they are considered to be “ductile”, allowing a plastic distribution of force to be assumed at the shear connection. This means that the studs may be spaced equally along the beam and assumed to be equally loaded under flexural failure of the beam. Note that the deformations of the connectors will not be equal, but will be much greater at the ends of the beam than at mid-span. From extensive numerical analyses and full-scale beam tests, it has been shown that, to enable a beam to develop its full bending resistance, the slip required increases with the beam span and the degree of shear connection. In addition, for steel sections that have a bottom flange area greater than the top flange (i.e., asymmetric sections), the slip required increases further, due to the neutral axis lying further down within the steel section. ADVISORY DESK Rather than stating slip capacities directly, the current codes of practice allow designers to assume a plastic distribution of force at the shear connection by specifying minimum degrees of shear connection in terms of the beam span and, in the case of Eurocode 4, the degree of asymmetry of the steel section. These code rules are based on numerical studies of composite beams that considered the slip capacity of the shear connection explicitly. According to BS 5950-3: 1990, for a steel beam with equal flanges, the following relationship for the degree of shear connection should be satisfied: For spans up to 10m Na / Np ≥ 0.4 For spans between 10 and 16m Na / Np ≥ (L - 6) / 10 but Na / Np ≥ 0.4 For typical internal composite beams that are equally spaced, the effective breadth of each portion of the concrete flange be is equal. In this case, the longitudinal shear force in each portion of the concrete flange is equal, and the longitudinal shear force that has to be transferred along potential shear planes such as a-a and e-e has a value of V/2. Due to the fact that it is normal to assume a plastic distribution of force at the shear connection, it is often more convenient to work in terms of a longitudinal shear force per unit length v, in which case the following equation may be used: where Na is the actual number of shear connectors provided, Np is the number of shear connectors required for full shear connection and • for full shear connection, taken as either the lesser of resistance of the concrete flange or the steel section, • for partial shear connection, taken as the resistance of the shear connection L is the beam span in metres. and s is the spacing of the shear connectors. The partial shear connection rules given in Eurocode 4 are applicable for much larger spans and additional guidance is given for steel sections with unequal flanges (provided that the bottom flange area does not exceed three times the upper flange area). In these cases, ‘ductile’ connectors are defined as those with a characteristic slip capacity of 6mm. Although BS 5950-3: 1990 and Eurocode 4 give different expressions for partial shear connection, they are identical in one respect viz. the degree of shear connection provided in a composite beam should not be less than 0.4. v = V / 2s where V is the longitudinal shear force, and is: However, for cases when composite beams are not spaced equally, or when a beam is adjacent to a free edge (such as at a hole in the slab), the longitudinal shear force per unit length along potential shear planes either side of the beam is no longer equal. This design case is illustrated in Figure 4. Transverse reinforcement (BS 5950-3: 1990 Clause 5.6) In composite beams, the longitudinal shear force that has to be transferred between the steel beam and the concrete flange is dependent on whether full shear connection or partial shear connection is provided. If the shear connectors are "ductile" (see requirements for partial shear connection above), a plastic distribution of force may be assumed at the shear connection. For full shear connection, the magnitude of this longitudinal shear force V is equal to the lesser of either the crosssectional resistance of the concrete flange or the cross-sectional resistance of the steel section. For partial shear connection, the longitudinal shear force is equal to the resistance of the shear connection (i.e., the design resistance of the stud multiplied by the number of connectors provided between the support and the critical section under consideration). For composite beams using composite or solid slabs, BS 5950-3: 1990 requires that sufficient transverse reinforcement should be provided to resist the longitudinal shear force V, to prevent longitudinal splitting of the concrete flange along the potential shear planes shown in Figure 3. Figure 4. Composite beam with an unsymmetrical concrete flange For the special case shown in Figure 4, the longitudinal shear force per unit length along shear planes f-f and g-g may be calculated from the following expressions: v v f-f g-g = Vb2 / Bes = Vb1 / Bes For further information contact: Dr Stephen Hicks, SCI. Tel: 01344 623345 E-mail: [email protected] Figure 3. Potential shear planes according to BS5950-3: 1990 A) Solid slab B) Composite slab with the sheeting spanning perpendicular to the beam C) Composite slab with the sheeting spanning parallel to the beam An Index to the Advisory Notes 1988 to 2002 The Index to the Advisory Desk Notes: 1988 to 2002: AD 001 - AD 261 is a comprehensive subject and keyword index that offers practising engineers a valuable resource for ‘offline’ searching of the first 14 years of Advisory Desk Notes. This is available to corporate members of the SCI via www.steelbiz.org