Calculating the shear connection of a composite beam to Eurocode 4
Properly bonded steel beam and concrete slab, acting compositely, can be much stronger and stiffer, which can result in significant savings in steel and/or structural floor depth. How can we provide the necessary shear connection between the two components and how is it designed?
In conventional construction, when the concrete slab is simply rested over the steel beam, the slip between the two structural parts can occur freely and each part acts independently.
The proper connection between the steel beam and concrete slab of a composite beam, which eliminates the slip between the two components and enables to act together as a single structural member, is broadly referred to as the 'shear connection'.
The shear connection between the steel beam and the concrete is provided by shear connectors, which usually is a headed shear stud attached to the top flange of the steel beams.
The shear connectors mainly resist longitudinal shear, while tensile force can also develop in the shear connectors.
Calculating the design resistance of a headed shear stud
The design rules of the Eurocode 4 determine the resistance of headed shear studs in a solid slab.
fu is the ultimate tensile strength of the headed stud
d is the diameter of the shank of the headed stud
fck is the characteristic cylinder strength of the concrete
Ecm is the secant elastic modulus of concrete
The resistance of headed studs within profiled sheeting is determined by multiplying the design resistance for a headed stud connector in a solid concrete slab by a reduction factor.
The reduction factor depends on:
- orientation of the sheeting slab
- shape of the decking profile
- the sheet thickness
Full and partial shear connection
The maximum longitudinal shear force that is required to be transferred by the shear connectors is the lesser of the compressive force to cause concrete crushing and the force that would cause yielding of the steel section in tension.
If the shear connectors are able to transfer the maximum longitudinal shear force from the steel to the concrete, the full plastic resistance moment of the composite section can be achieved. This is known as ‘Full shear connection’.
If fewer shear connectors can be provided than reduced longitudinal shear force can only be transferred. This situation is called as ‘Partial shear connection’.
In this case, the stress block method must be modified to take into account the reduced longitudinal force that can be transferred. The deformation of the shear connectors allows slip between the concrete and the steel section. The slip is zero at the maximum bending moment and increases towards the supports. The degree of the shear connection can be defined as:
n is the number of the shear connectors provided over the part of the span between the points of zero and maximum moment
nf is the number of shear connectors required for full shear connection
Rq is the total shear force transferred by the shear connectors between the points of zero and maximum moment
Rc is the compressive force to cause concrete crushing
Rs is the force that would cause yielding of the steel section in tension
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