Steel joist

An open-web steel joist (K-series, LH-series, DLH-series or KCS) checked against the values of its designation in the SJI load tables, to the SJI Standard Specification (SJI 100-2020) and the SJI Code of Standard Practice (COSP 2020), with ASCE 7-22 load combinations. The load tables are the joist manufacturer's design: you choose a designation and type its load-table values at your span; the calculation checks that the designation carries your loads, uniform or not, and tells you what to show on the drawings for the joist manufacturer.

Inputs of the steel joist #

• Joist: the series (K, LH, DLH or KCS), the nominal depth (the depth at midspan, SJI 100 5.3) and the section number (the last digits of the designation: 5 for 18K5, 06 for 32LH06, 3 for 22KCS3). A KCS joist also takes the bridging section number its load table lists (the equivalent K section).
• Span and spacing: the span as SJI 100 Figure 5.2-1 defines it (clear span plus the standard clear bearing lengths) and the joist spacing (the tributary width of the area loads). The joist is analysed on its design length, the span less 4 in.: the end reactions sit 2 in. inside each end of the span (SJI 100 5.2 and 5.4).
• Load table values at the span: for a K, LH or DLH designation, the total load W of the table for your design method (the black figure of the LRFD table, factored, or of the ASD table) and the red figure (the unfactored uniform load that deflects the joist span / 360). Interpolate between span columns where your span falls between them, as the table notes allow. For a KCS joist: the moment capacity, the shear capacity and the gross moment of inertia of the KCS table. The approximate joist weight is added to the dead load when Include joist weight is on. A load/load designation (for example 24K300/175) is checked by entering its equivalent standard section.
• Loads: area loads (psf on the joist spacing, full length), line loads (uniform, partial or linearly varying, a snow drift for example) and point loads (lb), each with its load type (D, L, Lr, S, R, W). Positions are measured from the left reaction along the design length. Every ASCE 7-22 2.3.1 (LRFD) or 2.4.1 (ASD) combination of the load types present is analysed (SJI 100 4.1.2); W acts in both directions. See Loads and combinations.
• Bearing and bridging: the support (steel, or a steel bearing plate on masonry or concrete), the bearing length (the joist end past the face of the support), the bearing plate width on masonry or concrete, whether you accept a shorter bearing on masonry or concrete (SJI 100 5.4.1.2 permits it when the plate and support get a special design), and the shading of the load table at your span (erection bridging).
• Deflection: live load and total load limits as span / n, on the design length. The SJI 100 5.10 roof value 240 is prefilled for live load (360 for floors and for roofs with a plaster ceiling); 0 turns a check off. The shear deformation factor divides the gross moment of inertia (1.15, prefilled, reproduces the red figure exactly).

Auto-design is not offered: the joist capacity comes from the load-table values you type, so there is nothing for the calculation to size. Pick a heavier section or a deeper joist from the table and enter its values.

Checks performed #

The equivalent uniform loads of the COSP 2.4 caution, 8 Mmax / L² and 2 Rmax / L, are shown in the steps and with the key results; for a uniform load they equal the load, and the two envelope checks reduce to w / W.

Deflection. The gross moment of inertia of a standard joist comes from the load-table note Ig = 26.767 W L³ × 10⁻⁶ in⁴ (W the red figure, L the span less 0.33 ft); a KCS joist uses the table's value. The deflection is computed with Ig divided by the shear deformation factor: 1.15 makes the red-figure load deflect the design length / 360 exactly, so for a uniform live load the check equals the load-table proration (the red figure times 360 / n). Point and partial loads are analysed with the same stiffness.

What the calculation does not decide. The joist manufacturer designs the chords, webs, panel points, connections, bearing seats and bridging details, and verifies them per SJI 100 4.7. The specifying professional (you) gives the loads by type and their combinations, the deflection limits, net uplift, the ponding investigation (5.11), the supporting members, bearing plates, anchorage and bridging terminations. With point or partial loads the calculation reminds you to show them on the drawings (COSP Option 2, or a load diagram with an SP designation, Option 5), and, where their locations are not given, the extra web from each load to a panel point on the opposite chord; loads of 100 lb or less per chord panel, concentric with the chord, need none (SJI 100 4.1.2).

The drawings show the joist elevation on its design length with the loads by type (the web drawn as a schematic, since the panel layout is the manufacturer's), the end bearing (seat depth, bearing length, support) and the shear, moment and deflection diagrams of the governing combinations.

Limitations #

• Simple-span joists on two bearings. Top chord extensions, extended ends, cantilevers, continuous (moment) frames, axial loads and end moments are not covered (SJI 100 4.4.4, 5.1.2): use a special designation with a load diagram.
• The capacity is the load-table value you type; the module does not hold the SJI tables. A designation that the table does not list at your span is your responsibility (the bridging check flags spans outside Table 5.5-1).
• Local chord bending from loads between panel points (add-loads and bend-checks, COSP Option 3) is the joist manufacturer's design; the calculation states what to specify.
• Joist girders, CJ composite joists, sloped seats (the high-end seat depth of COSP Tables 2.2-2 and 2.2-3), ponding (5.11) and floor vibration (SJI Technical Digest 5) are not covered.
• The bridging spacing limit (Eqs. 5.5-2 and 5.5-3) needs the top chord radius of gyration, which only the joist manufacturer knows: the calculation reports the number of rows only.

Verification examples #

Verification status: 28 values compared in 7 examples (7 published, 0 hand calculations from the cited equations): 27 within tolerance, 1 recorded deviations. Code basis: the provisions it uses were read in the target edition.

SJI Code of Standard Practice (COSP 2020), Section 2.4(a) Option 4, ASD examples (pp. 181 to 183), loads entered as D on the design length:

The LRFD columns of these examples are the ASD loads times 1.5 (factored loads shown); no ASCE 7 combination of the typed loads reproduces that, so they are not compared.

SJI webinar "Properly Specifying Steel Joists" (2019):

The slide computes 200 / 877 × 3.86 in. and prints 3/4 in.; the product is 0.88 in., which ILX reports (a listed deviation). The 3.86 in. limit is the design length (115.67 ft) / 360, the length ILX uses.

SJI 100-2020 tables and the K-series load-table notes, for the default 18K5 at 30 ft: two rows of bridging (Table 5.5-1), 2-1/2 in. minimum bearing on steel (Table 5.4-1) and seat depth (Table 5.4-3), 3/8 in. camber (Table 4.6-1), Ig = 112.6 in⁴ from the table note (W = 161 plf). The rows for 22K9 at 40 ft (3) and DLH21 at 116 ft (3) and the 7-1/2 in. seat of DLH21 are checked the same way. No published worked example of the moment and shear envelopes of a standard designation under non-uniform loads (COSP Option 1) was found: those checks follow the cited definitions and are covered by hand-verifiable tests (a uniform load gives w / W; a midspan point load meets the 25 % shear floor).