Composite beam

A simply supported rolled W-shape acting compositely with a concrete slab (solid, or on formed steel deck) through steel headed stud anchors, to AISC 360-22 Chapter I, with ASCE 7-22 load combinations. The calculation covers full and partial composite action, the anchors, the unshored construction stage, shear on the steel section and the deflections before and after composite action.

Inputs of the composite beam #

• Beam: the W-shape, the steel, the span (simply supported) and whether the self-weight is added to the dead load applied before composite action.
• Effective width: the distance to the adjacent beam on each side, or the distance to the slab edge on side 2. Each side contributes the least of span/8, half the distance to the adjacent beam and the edge distance (I3.1a).
• Slab: solid slab, or formed deck with the ribs perpendicular or parallel to the beam; the concrete thickness above the deck tc (the total thickness for a solid slab), the rib height hr, the average rib width wr (not more than the clear width near the top of the deck), f′c, normal weight or lightweight concrete and the unit weight wc (for Ec = wc^1.5 √f′c). For perpendicular ribs the concrete below the top of the deck is neglected (I3.2c.2). For parallel ribs it is included (I3.2c.3) as the fraction wr / rib spacing of the rib zone; enter the rib spacing.
• Anchors: diameter, Fu (65 ksi for AWS D1.1 Type B anchors), installed length, position in the rib (weak: emid-ht < 2 in., Rp = 0.6; strong: Rp = 0.75; the weak position is the conservative choice when it is not controlled), the anchors between the point of maximum moment and the support as groups (number of anchors, anchors per rib or per transverse row, which sets Rg), the spacing along the beam, whether the anchors are welded over the web, and, when there are concentrated loads, whether the anchors are uniformly spaced (I8.2d(a)) or all lie between the support and the load.
• Construction: unshored or shored; the bracing of the compression flange during construction (continuous when the deck is attached, or an unbraced length) and the camber.
• Loads: line and point loads, each with a load type and a stage: before composite (slab, deck, beam; on the steel section and permanent), construction only (the construction live load of ASCE/SEI 37, for example 25 psf over the tributary width; on the steel section only) and after composite (superimposed dead and live loads). See Loads and combinations.
• Deflection limits: span / n before composite (net of camber; AISC Design Guide 3 suggests 360 and 1 in.), for live load and for total load (IBC 2021 Table 1604.3 floor values 360 and 240 prefilled); 0 turns a check off.

Auto-design (editor toolbar) varies the W-shape (lightest first, optional depth limit) and the number of steel headed stud anchors. Objectives: lightest steel, then fewest anchors; lowest cost index (steel + anchors). Every other input is kept; see Auto-design.

Checks performed #

The key results list the effective width, ΣQn, the degree of composite action, the PNA location and ILB. The diagrams show the loading, the section and the shear and moment of the combination that governs composite flexure.

Drawings #

The drawing sheet (PDF / DXF, Drawing sheet button) shows the beam elevation with the slab on the beam, the simple supports, the loads by type and stage (PRE before composite action, CONST. during construction only, POST after) and the span, the member mark in the usual form W21×50 (46) C=2" (total number of anchors, camber); the typical section with the slab or deck as designed, the effective width, the W-shape and the headed stud anchors per rib; and the shear and moment diagrams of the governing combination. The anchor start location, the transverse spacing of anchors in a rib (drawn at four stud diameters), deck anchorage, slab reinforcement and the end connections are not part of the calculation; the sheet notes say so.

Limitations #

• Simply supported spans only: no negative moment (I3.2b), cantilevers or continuous composite beams.
• W-shapes with h/tw ≤ 3.76√(E/Fy) (I3.2a(a)); otherwise not feasible (I3.2a(b) elastic superposition is not covered). f′c must be within I1.3(a) and wc within 90 to 155 pcf, else not feasible.
• For parallel deck with wr/hr < 1.5, Rg is defined for a single anchor only; two or more anchors in a row are reported as not feasible.
• The ILB uses the slab force V′ (ΣQn, or the full-composite force when that is smaller) at the point of maximum moment. Long-term creep and shrinkage deflections, ponding of the wet concrete and floor vibration (Design Guide
  11. are not computed.
• The analytical shear-connection ductility procedure of Design Example I.1 is not computed; the prescriptive conditions are reported.
• Lateral cover, edge distance in the direction of shear (I8.2d(b), (c)), transverse spacing of anchors in a rib and the deck anchorage spacing (I3.2c.1(d)) are noted for the engineer to detail; channel anchors are not covered.
• The construction stage uses the loads entered for that stage; ASCE/SEI 37 construction loads are the engineer's input. The pre-composite deflection limit follows AISC Design Guide 3 as quoted in Design Example I.1 (the Guide is not on file).

Verification examples #

AISC Design Examples v16.0, in LRFD and ASD:

AISC Steel Construction Manual, 16th Ed., Table 3-18 (φbMn / Mn/Ωb, pp. 3-178 and 3-179) and Table 3-19 (ILB, p. 3-203). Each entry is reproduced with a solid slab whose thickness gives the tabulated Y2 for the tabulated ΣQn (b = 120 in., f'c = 4 ksi); for the partial-composite rows the anchor count and Fu are chosen so that n Qn equals the tabulated ΣQn:

Example I.1 reads φMn and ILB from Manual Tables 3-18 and 3-19 at ΣQn = 386 kips and Y2 = 7.00 in.; ILX computes them directly with the provided ΣQn = 391 kips, so its values are 0.4 % and 0.5 % higher. In Example I.2 the Example takes d/2 = 12.0 in. and rounds Mn = 16,955 kip-in. to 17,000 kip-in.; ILX uses d/2 = 11.95 in., 0.8 % lower. All values are within 1 %.