Structural Engineering & Statics
where the load goes
Concept

Shear connection — where it appears

Whatever stops two layers of a member sliding past one another, working hardest where the shear is largest and not at all at mid-span. The elastic demand is a triangle peaking at the supports, and uniform spacing is justified by the connectors being ductile enough to share.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

Shear stress across a section. The distribution of shear stress over an I-section, computed as VQ/It by accumulating the first moment of the area above every height. The peak is 0.41 against a mean of 0.19 — a ratio of 2.15 — and it falls at the neutral axis, where the bending stress is zero.

The shear nobody draws

A stack of loose planks slides at its ends when it is loaded. Glue them and the sliding stops — and whatever the glue is now carrying is a stress that no bending calculation contains.

sections · Shear flow Shear stress across a section. The distribution of shear stress over an I-section, computed as VQ/It by accumulating the first moment of the area above every height. The peak is 82.77 against a mean of 38.46 — a ratio of 2.15 — and it falls at the neutral axis, where the bending stress is zero. At the junction between flange and web the flow is 820.0 per unit length, so connectors of 20000 each have to be spaced no further apart than 24 — which is what turns two pieces into one section.

The section made of pieces

Two plates bolted together are twice as strong as one plate. Two plates made to act as one section are eight times as stiff. The difference is entirely in the joint, and the joint has a calculable spacing.

sections · Second moment Two beams, or one beam four times as stiff. Two 200 × 150 planks spanning 4 m under 6 per millimetre. Loose, they have 112.5×10⁶ mm⁴ between them and deflect 16.2 mm, with the two faces at the interface sliding past one another. Bonded, the pair has 450.0×10⁶ — exactly 4 times as much, because doubling a depth cubes — and deflects 4.0 mm at half the extreme-fibre stress. Nothing was added but a restraint on slip. With connectors of stiffness 200 the same beam deflects 5.4 mm, which is 89% of the way from one bound to the other.

Two beams, or one beam four times as stiff

Stack two planks and they bend as two beams whose faces slide past one another. Bond the faces and the pair has one neutral axis, four times the second moment and half the stress. Nothing was added but a restraint on slip.

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

Named alongside it

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

DelaminationFirst moment of areaNeutral axisShear flowBuilt-up sectionComposite actionSecond moment of areaDuctilityI-sectionParallel-axis theoremPartial interactionPlane sections

All concepts