Spreader Beam Design Calculator — methodology & sources

Most spreader spreadsheets start from an assumed sling angle. This tool starts from the geometry — beam, lugs, slings, hook, load and its centre of gravity — and finds the attitude the assembly actually hangs at. Sling tensions, the beam's axial force with its sense, the bending diagram with its pin couples, and every check demand follow from that one solve.

Two configurations, one engine

A two-point spreader takes two top slings to a single hook, putting the beam mainly into axial compression between its lugs. A single-lug lifting beam hangs from one lug and works in bending. EN 13155's own definitions (§3.8) note that a lifting beam whose loading is purely compressive is the same device the trade calls a spreader beam. The same engine solves both; which structural job the beam is doing falls out of the geometry, not out of a mode switch.

The counts above are read from the engine's own check register at this render. Alongside the engine cases, an independent published benchmark pins the ASME bending implementation — the full evidence lives on the verification record.

The mechanics cluster

Before any code route runs, a cluster of route-independent checks reports the solved arrangement itself. These cite public-domain statics only and carry no code coefficients.

The model is deliberately spare: the beam and the lifted load are rigid bodies; slings are straight, inextensible and weightless; the hook is a frictionless point where the top slings meet; and everything lives in the vertical plane through the beam axis. Within that model, equilibrium of the suspended assembly is exactly the stationarity of potential energy, and a stable attitude is a constrained minimum. In level mode the beam is asserted level and the solver reports the sling lengths that realise it — and flags when the asserted attitude is not actually an equilibrium for the given lug placement. In solved-tilt mode the attitude itself is the unknown.

What the solver refuses

• Statically indeterminate arrangements. Three or more bottom attachment points make the load sharing indeterminate for rigid bodies. The tool never assumes equal sharing — it requires declared per-point shares from your rigging analysis, and gates until they exist.
• Slack slings. A sling that would have to push is not a solution; the solve reports the failure instead of returning a negative tension.
• Unbracketed equilibria. If no stable attitude exists inside ±45° of tilt, the solve stops rather than extrapolating beyond its bracket.
• Closure residuals above tolerance. Every solve checks its own force and moment balance. The residuals are normalised by the total weight and by the weight times the span, so the tolerances are dimensionless by construction — a tolerance with hidden units answering a structural question is a defect class this platform has met before and designs against.

Each solved sling force lands on the beam at its pin — which sits a distance $e$ from the beam's centroidal axis, because a padeye on a flange face cannot have $e=0$. The force's horizontal component $H$ acting at that offset applies a concentrated transfer couple $H\cdot e$ to the beam, visible as a jump in the moment diagram. Self-weight is applied as a uniform line load resolved into axial and perpendicular components under the solved tilt. Between load points the diagrams are exact polynomials — no discretisation, no mesh.

The diagrams close on a checked identity: integrating from end 1 must land on zero force and moment at end 2, and the solve is flagged INDETERMINATE when it does not. Checks then read the diagrams at critical stations — every pin, midspan, and the exact positions of maximum moment and shear — and every check names its governing station in words: “governs at the end-1 top lug”, never a bare coordinate.

Every gate states its reason and its remedy. The full set:

Design categories and service classes

The nominal design factor comes from §3-1.3.1: $N_d=2.00$ for Design Category A, $N_d=3.00$ for Category B (the default), and $N_d=6.00$ for Category C; connection and fracture-governed limits use $1.20\cdot N_d$ (§3-1.3.2). Category A is limited to Service Class 0 by §2-2.1(b), and the engine enforces that combination rather than trusting the form. Service classes follow Table 2-3-1 — Service Class 0 covers up to 20 000 load cycles, Service Class 4 sits beyond 2 000 000 — and Service Class 0 needs no fatigue analysis at all (§3-1.4).

Impact is already inside the factors

§3-5.1 states that the design factors embed peak impact allowances of 50 % for Category A and 100 % for Category B. The tool therefore never silently adds a dynamic factor on this route: the load basis is the rated load plus solved component weights (§3-1.2), an additional impact factor is an explicit input that defaults to zero, and stacking the DNV overlay on this route raises a written double-counting warning.

Hollow sections design on a reduced wall

§3-1.7 requires the design wall thickness of a hollow section: 0.93 × nominal for ERW or unknown manufacture, nominal for SAW. This is an ASME rule only — the EN and CSA routes design on the nominal wall per their own conventions — and the wall basis is printed in the report so the difference is visible, not implicit.

The suspended-beam LTB treatment

A shackle restrains neither twist nor lateral sweep of the compression flange, so the default lateral-torsional condition of a lifted beam is “not braced against twist at the ends of the unbraced length”. BTH-1 is unusual in having a provision for exactly this — the reduction

applied where the bending provisions of §3-2.3.2 call for it. Declaring the ends braced is an input, recorded in the report as your statement. Section 10 explains why the EN and CSA routes gate on the same question instead of computing it.

Marking and proof obligations

The companion safety standard ASME B30.20-2021 makes a load test recommended (“should”), at 125 % of rated load with a +5/−0 % tolerance when performed, and requires marking that includes the BTH-1 Design Category and Service Class (§20-1.2.1). Separately, OSHA 29 CFR 1926.251 mandates proof testing of lifting accessories in US construction use. The report prints these obligations; performing them is the manufacturer's and employer's work, not the calculation's.

On the default 6 m CHS spreader, this route reports axial utilisation 0.037, bending 0.104, combined 0.141, with the largest strength utilisation carried by the padeye attachment weld — bth-1 §3-3.4 at 0.557 (pin bearing 0.508) — every value, including which check leads, computed by the engine as this page rendered. The guide's worked example walks the same case end to end.

The two-condition load basis

For lifting attachments at or below 16 000 load cycles, EN 13155 §5.1.2.1 poses two conditions on the same solved demands: the attachment must withstand 2 × the sustained load without permanent deformation (the elastic condition), and 3 × without releasing the load (the yielded condition). The coefficients cover load uncertainty and the hoisting impact factor, and fatigue proof is not necessary below the threshold. Above 16 000 cycles §5.1.2.2 hands the proof to EN 13001-1/-2/-3-1 with ${\gamma }_n=1.4$ — outside this assessment, so the route gates.

The mandatory design-tilt case

§5.1.2.3 and §5.2.6.3.1 require a lifting beam not intended to tilt to tolerate ±6° from horizontal — intended-to-tilt beams take their maximum working angle plus 6°. The tool implements this as a genuine re-closed statics case: the beam is held at the design tilt, the force closure is solved again at that attitude, and the demands are enveloped with the as-rigged solve, station by station. The tilt case verifies its own end-closure identity and gates instead of guessing.

Resistances: EN 1993 with the recommended factors

Cross-section and buckling resistances come from EN 1993-1-1 §6.2 and §6.3 with the recommended partial factors ${\gamma }_{M0}={\gamma }_{M1}=1.00$ and ${\gamma }_{M2}=1.25$ (National Annexes may differ, and the report says which values were used); member interaction uses Annex B Method 2; pins follow EN 1993-1-8 Table 3.9/3.10 and welds §4.5.3. EN 1993-1-1 defines the elastic critical moment $M_{cr}$ but gives no formula for it — it is computed from the classical doubly-symmetric fork-support solution with $C_1=1.00$ as a conservative default, and that provenance is declared in the assumptions register below. CHS and square RHS members are not susceptible to lateral-torsional buckling per §6.3.2.1(2).

Verification routes and static tests

EN 13155 Table 9 makes calculation a full alternative to testing for lifting beams — Annex A.1 for both type and individual verification. If tests are performed instead, the magnitudes are: generic type test $F_3=3\times$ WLL ± 2 % (Annex A.2), individual test $F_2=2\times$ WLL (Annex A.3), and the lifting-beam type test of Annex E.2 at 1.5 × $F_S$ — where $F_S$ is not defined in the standard's §3 terms. The tool surfaces that ambiguity and deliberately does not resolve it. Marking per §7.2.1 includes manufacturer, designation, serial number, year, the WLL per configuration, and the unloaded weight when it exceeds 5 % of the WLL or 50 kg.

On the default spreader this route's yielded condition governs at utilisation 0.624 (the padeye pin), with the weld at 0.596 — computed at this render.

The declared load factor

S16-09 Cl.7.2 requires $\varphi R\ge \sum {\alpha }_i{S}_i$ with the load factors taken from NBCC Art. 4.1.3.2 — and the NBCC is outside this assessment. The route therefore runs on a user-declared load factor ${\alpha }_f$ applied to every solved force, and gates INDETERMINATE until it is declared — a sub-unity declaration also gates. No NBCC default is invented. Cl.6.3.3.1 likewise places the provision for impact with the designer; the DNV overlay can supply it explicitly if the project basis wants it. The held edition is S16-09, stated everywhere the route appears; later editions exist.

Resistances

Resistance factors per Cl.13.1: $\varphi =0.90$ for steel, ${\varphi }_u=0.75$, ${\varphi }_w=0.67$. Compression uses the unified curve of Cl.13.3.1,

with $F_e$ the least of the flexural and torsional elastic buckling stresses (Cl.13.3.2). For a thin-walled CHS an identity worth writing down: $J=2I$ and $A{\bar{r}}_o^2=2I$ make the torsional stress $F_{ez}\approx G$ — 77 000 MPa — so torsional buckling never governs a CHS, and the engine's tests prove the identity rather than assume it. Bending follows Cl.13.5 and Cl.13.6: $M_r=\varphi Z{F}_y$ for Class 1/2, $\varphi S{F}_y$ for Class 3; closed square and circular sections are exempt from lateral-torsional buckling by 13.6(c); rectangular HSS take $C_w=0$; and above $M_u>0.67M_p$ the inelastic cap $M_r=1.15\varphi M_p(1-0.28M_p/M_u)\le \varphi M_p$ applies. ${\omega }_2=1.00$ is the conservative default, and ${\omega }_1=1.0$ is Cl.13.8.5(b)'s own value for a series of point loads between supports — cited, not assumed. Shear uses the three unstiffened-web branches of Cl.13.4.1.1, tubes $V_r=0.66\varphi (A/2)F_y$ (13.4.1.3), pins $V_r=0.66\varphi A{F}_y$ (13.4.4); unstiffened webs take no moment–shear reduction. The member interaction runs all three Cl.13.8.3 cases — cross-sectional, overall member, and lateral-torsional — and reports the governing one. E = 200 000 MPa and G = 77 000 MPa are the values Cl.2.2 itself says may be assumed.

The padeye chain

Pinhole tension $T_r=0.75\varphi A_n{F}_y$ (Cl.13.2(b)); tear-out toward the plate edge via the Cl.13.11 second term, which the clause's own note endorses for this geometry; bearing $B_r=1.5\varphi F_{y}A$ on the projected pin area (13.10(a)); and the attachment weld per Cl.13.13.2.2 evaluated at θ = 0 with $M_w=1.0$ — the directional strength bonus is deliberately not claimed.

On the default spreader at a declared ${\alpha }_f=1.50$, member utilisations are small — compression 0.021, bending 0.045, interaction 0.066 — and the route is governed by the padeye weld at 0.310, all computed at this render.

• DAF comes from Table 16-1 by environment column, evaluated at the solved hook load — rated load plus rigging plus the beam's own weight — with the table's 3 t floor applied. An override is an input, recorded as yours.
• SKL is 1.00 only when the standard's own conditions for it hold: a statically determinate arrangement with every sling between 45° and 80° to the horizontal (±0.5 % sling length tolerance assumed, per §16.2.6.9). Anything else requires the rigging-analysis value, or the result gates. SKL is never fabricated.
• γ_c = 1.30, fixed. Table 16-5 row 1 names “spreader frames or beams” among lifting equipment not subjected to load testing — and a load-tested spreader stays at 1.30 as a lift-point attachment per §16.8.5.1. Either way the value is 1.30, so it is not a knob.

Stacking warnings are route-aware: on ASME the design factors already embed impact (§3-5.1); on EN the §5.1.2.1 coefficients already cover the hoisting impact factor; on CSA the declared ${\alpha }_f$ is already the project's dynamics decision. Each combination prints a written double-counting warning and shows both stacks in the ledger — the combination remains your engineering decision, made with the arithmetic visible.

The capacity envelope plots the working load limit against span: at each span the arrangement is scaled to shape and the WLL is found by monotone bisection to the load at which the engine's own maximum utilisation equals 1.00. Every point is therefore a genuine solve — the envelope's self-consistency test re-runs each point's own analysis and requires it to reproduce the curve — and every point carries its governing check and the beam's axial sense. Where the sense flips from compression to tension along the span axis, the curve is split at the boundary rather than drawn through it.

The solve-for tools invert the same engine: maximum WLL at the current geometry, maximum span at the current load, and the pick-point positions that level a given centre of gravity. The section finder walks the section catalogue with the full check set and reports the lightest passing candidates; scenario compare holds two configurations side by side, solved identically. None of these tools has private physics — each one is a search over the one engine.

The beam and the lifted load are treated as rigid bodies for the attitude solve — beam deflection does not feed back into the tilt. Valid while deflections are small relative to the geometry; the small-deflection validity screen warns when they are not.

Slings are straight, inextensible, and weightless in the geometry solve (no catenary, no elongation compatibility). Below-the-beam rigging weight is lumped at the load's centre of gravity.

The hook is a frictionless point at which the top slings meet; shackle pins are frictionless and transmit no moment.

The solve is in the vertical plane containing the beam axis. A transverse (out-of-plane) centre-of-gravity offset is outside the current solve and must be assessed separately.

With more than two bottom attachment points the load distribution is statically indeterminate: the declared per-point shares are the engineer's own, and the bottom slings are treated as vertical.

Beam self-weight is applied as a uniform line load over the span (prismatic member), resolved into axial and perpendicular components under the solved tilt.

The axial-buckling length is the full span with K = 1.0 about both axes unless overridden — shackle pins restrain neither end rotationally, and using the full span is exact for end lugs and conservative for inboard ones.

For the §3-2.5 critical-stress check, the peak normal stress and peak shear stress at a section are conservatively combined at the same point, although they occur at different fibres.

Fatigue stress ranges assume full 0 → rated-load cycles. A measured or spectrum loading basis belongs to the §3-4.6 cumulative method, which this pack does not compute.

One padeye specification (plate, hole, pin, edge distance, weld) is applied at every lug; each pin is evaluated with its own solved force and the governing pin is named.

The padeye weld group is modelled as two parallel fillet lines under the plate; the pin force's direct shear and the in-plane moment from its horizontal component at the pin height are combined linearly on the throat — a conservative weld-line treatment.

The deflection diagnostic integrates bending curvature only (no shear deformation), relative to the chord between the beam ends, and is serviceability information — never a code pass/fail (BTH-1 §3-5.3 places deflection limits with the qualified person).

EN HYBRID route: design loads use the EN 13155:2020 §5.1.2.1 coefficients (2 × elastic / 3 × yielded, incl. the 6° design-tilt case) but resistances come from EN 1993-1-1/-1-8 with the recommended partial factors (γ_M0 = γ_M1 = 1.00, γ_M2 = 1.25; National Annexes may differ) — NOT from EN 13001-1/-3-1, which EN 13155 Annex A.1 nominates and which are not part of this assessment. Full EN 13155 compliance is not claimed. Annex A.1's own NOTE routes buckling and stability guidance to the EN 1993-1 series.

EN route classification: elements are classified against the pure-compression Table 5.2 limits whenever the member carries net axial compression anywhere, else the pure-bending limits — conservative with respect to the exact combined bending-plus-compression columns, which need the plastic stress-block position α.

EN route LTB: EN 1993-1-1 defines but does not give M_cr. It is computed from the classical doubly-symmetric fork-support elastic critical moment with C₁ = 1.00 (uniform moment — conservative); closed sections take I_w = 0. Equivalent-uniform-moment factors C_my = C_mLT = 1.00 in the Annex B interaction for the same reason.

The EN design-tilt case re-closes the statics with the beam held at the design tilt (both signs) and envelopes the demands — a strength load case per EN 13155 §5.1.2.3/Annex A.1, not a claim that the free hang equilibrates at that angle.

CSA HYBRID route: factored resistances per CSA S16-09 (the held edition — S16-14 and S16:24 are later editions) against demands multiplied by the USER-DECLARED load factor α_f. S16-09 Cl.7.2 takes load factors from NBCC Art. 4.1.3.2 and Canada has no below-the-hook device standard, so the load side is the project's engineering decision — the route gates until α_f is declared, and no S16 compliance is claimed for the load side. ω₂ = 1.00 conservative; ω₁ = 1.0 per Cl.13.8.5(b).

DNV overlay: SKL = 1.00 for the statically determinate arrangement assumes sling length tolerance within ±0.5 % of nominal (DNV-ST-N001 §16.2.6.9). Verify against the actual sling certificates.

Out of scope, with reasons

• Out-of-plane centre-of-gravity offset. The solve is in the vertical plane of the beam axis; a transverse CoG offset needs the future out-of-plane extension and must currently be assessed separately.
• Catenary and elastic slings. Slings are straight and inextensible in the geometry solve; no elongation compatibility is modelled.
• Fatigue on the hybrid routes. On the EN route, §5.1.2.1 itself waives fatigue proof at or below 16 000 cycles and the route gates above; on the CSA route the fatigue basis belongs to the project. The ASME route computes fatigue per §3-4.
• Class 4 / slender sections and deep-web shear buckling. The implemented provisions stop at their own validity limits and gate rather than extrapolate (section 4).

All internal calculation runs in canonical SI — newtons, millimetres, megapascals — and converts only at the display boundary. The unit toggle re-renders numbers in US customary units; it never re-runs the solve.