Structural Engineering & Statics
where the load goes
Concept

Shear connector — where it appears

A stud, channel or bar welded to a steel beam and cast into the slab above it, carrying the interface shear that makes the two act as one section. Its spacing follows the shear force rather than the moment, so connectors crowd at the supports and thin out at midspan.

Named by 5 essays across one field — each of them below, with the objects they name alongside it.

Between two beams and one, and much nearer one. How composite a beam is, against the one dimensionless group that decides it: αL, where α² = K·EI∞/(EA*·EI₀). At αL = 0 the layers slide freely and the beam is two beams; past about 20 the connection is stiff enough that the last per cent is unbuyable. The beam drawn sits at αL = 15.8 and is 96% composite, deflecting 36.7 mm against 33.9 for full interaction and 110 for none. The curve is steep where a real design sits, which is why halving the number of studs does not halve anything.

Half the studs, and most of the beam

Bonding two layers together quadruples the stiffness of the pair. A real connection is a row of studs that deform, so the layers slide a little and the beam sits between the two answers — but not halfway between, and the number that decides where is a single dimensionless group.

internal-forces · Partial interaction The studs are evenly spaced and the demand is not. The force per unit length the shear connection carries along half of a 12 m composite beam, from Newmark's solution. It is largest at the support — 282 N/mm — falls to nothing at mid-span, and averages 156: the end studs are asked for 1.81 times the mean. Studs are nevertheless placed at a uniform spacing, and the justification is the one the variable-angle truss uses for its stirrups — a ductile connector sheds what it cannot carry to its neighbours, so the uniform distribution is a plastic redistribution and not a description of the elastic state.

The connection is busiest where the beam is not

A composite beam's studs are spaced evenly along it and the demand on them is not even at all. It peaks at the supports, where the bending stress is nothing, and falls to zero at mid-span, where the section is working hardest — so the connection is designed from a diagram nobody looks at.

internal-forces · Composite action Six millimetres of slip draw the Eurocode's line. The least degree of shear connection at which a 457 × 191 × 67 UB in S355 under a 130 mm slab of C30/37 2.5 m wide, with 19 mm studs of 80 kN can reach 95 per cent of its plastic moment without its end studs slipping more than 6 mm, against the span (solid), and EN 1994-1-1's minimum for ductile studs in a beam with equal steel flanges, 1 − (355/fy)(0.75 − 0.03L), not less than 0.4 (dashed). 6 m: 0.24 against 0.43; 8 m: 0.51 against 0.49; 10 m: 0.61 against 0.55; 12 m: 0.69 against 0.61; 14 m: 0.75 against 0.67; 16 m: 0.77 against 0.73; 18 m: 0.80 against 0.79; 20 m: 0.88 against 0.85. From 8 m up the two differ by at most 0.08: a stud model and a slip capacity reproduce the rule's slope as well as its level. At 6 m the slip alone would allow 0.24, and the rule asks for 0.43.

The slip the plastic moment asks of the studs

A composite beam with half the studs that full interaction needs still has 85 per cent of the full plastic moment, because the slab's compression block simply gets thinner and the steel finds its own neutral axis. That is the stress-block answer, and it assumes every stud slips as far as the beam asks. Follow the slip along the beam and the end studs of a 12 m beam need 6.6 mm to reach nine tenths of that moment and 9 mm to reach 95 per cent — past the 6 mm a stud is trusted to give. Require 6 mm and the Eurocode's minimum degree of shear connection comes out of the arithmetic, slope and all.

internal-forces · Composite action The same studs moved toward the supports slip less. Half of a 12.0 m composite beam, a 457 × 191 × 67 UB in S355 under a 130 mm C30/37 slab, with 50 per cent shear connection, 19 studs from the support (left) to mid-span (right): spaced evenly, and graded so that they crowd toward the support. Below, the slip along the half-span with the mid-span moment at 95 per cent of the beam's plastic moment: evenly spaced, the end studs must slip 8.8 mm; graded, 4.4 mm. The dashed line is the 6 mm a ductile stud is trusted to give. The plastic moment is the same for both, because the studs are the same in number and each reaches its capacity.

The same studs, moved to where the slip is

A composite beam with half the studs full interaction needs reaches 85 per cent of the full plastic moment, if its end studs can slip as far as the beam asks — nearly 9 mm on a 12 m span, past the 6 mm a stud is trusted to give. Keep the same nineteen studs and crowd them toward the supports, and the end studs need 4.4 mm. Nothing about the beam's strength changes; what changes is how soon the slab's force builds up, and the least connection the slip allows falls from 0.69 to 0.40.

internal-forces · Composite action The hogging region cannot give its studs away. For a 457 × 191 × 67 steel beam under a 130 mm slab, continuous over two 12.0 m spans under 30 kN/m, 40 studs a span: the largest slip (solid, left scale) and the force in the slab's bars over the middle support (dashed, its value in the legend), against the density of studs beyond the point of contraflexure as a share of the density elsewhere, the span's total held at 40. At the same density everywhere the largest slip is 0.68 mm and the bars carry 344 kN; at half the density beyond contraflexure, 1.04 mm and 251 kN; at a quarter, 1.69 mm and 118 kN. The support's hogging moment falls from 448 to 398 kN·m as the bars stop working.

The slip that peaks where the moment turns

A simply supported composite beam slips most at its supports, and its studs are crowded there. Make the same beam continuous over a middle support and the slip peaks twice: at the end support, and again, just as hard and the other way, at the point of contraflexure — not over the middle support, where the shear is largest but the slip falls to nothing. Studs graded toward the supports, as a simple span's would be, miss the second peak and buy a tenth; graded to the slip they buy more than a third. And the hogging region cannot give its studs away to the span, because its edge is where the second peak is.

internal-forces · Composite action

Named alongside it

The objects these essays reach for when they reach for this one.

Composite actionPartial interactionSlipDuctilityDeflectionMoment redistributionServiceabilityShear connectionShear flowStiffnessCompatibilityContinuous beam

All concepts