Monorail beam
An S- or W-shape hung from two supports, with or without an overhang past the last one, carrying a hoist trolley on its bottom flange. It follows AISC 360-22 F2 and G2, ASCE 7-22 4.9, Tanner (1985) for the overhang's Cb, and AISC Design Guide 7 (2019) 14.1, 17.2.
Bottom flange local bending NOT checked: enter the allowable wheel load from CMAA 74 or the crane manufacturer. Until you do, the status reads NG, a check row and the key results say it is not checked, and the sheet says so too, whatever the other checks show. The bottom flange is the main limit state of a monorail, so a result without it is not a pass.
Bottom flange local bending under the wheels is not computed. The guide requires that check and points to CMAA 74, which we do not have. Enter the allowable wheel load from the trolley or beam manufacturer, or from CMAA 74. Until you do, the calculation carries an advisory saying the check is open.
Inputs of the monorail beam #
- Beam: the shape, its steel, the layout (overhang or simple span), the back span and the overhang, to the farthest place the trolley goes.
- Hoist: rated capacity, trolley and hoist weight, wheels on the flange. LRFD takes 1.2 on the trolley and 1.6 on the lifted load, as Design Guide 7 Example 14.1.2.
- Impact: by ASCE 7-22 4.9.3, 25 % for powered monorails, none when hand-geared, or entered.
- Lateral force: by ASCE 7-22 4.9.4, 20 % of the capacity and trolley; the clause is written for powered trolleys. Or entered. The longitudinal force, 10 %, is reported for the hangers' bracing and not combined.
- Cb of the overhang: Tanner's Table 1, by k = overhang / whole length, with Lb the whole length, for a beam braced against twist only at the interior support. Tanner derives it for a section with small warping stiffness, as S-shapes are. Here it goes into F2, which also counts warping; that is our reading, and the paper's own formula is given beside it as a cross-check. If your interior hanger cannot restrain twist, this Cb does not apply: enter your own.
- Back span: Lb and Cb are yours.
- Deflection limit: span / 450 on the wheel loads, Design Guide 7 17.2. On the overhang the limit is taken on its own length, on the conservative side, because the guide states it for a span.
- Allowable wheel load on the flange: see above, on the same load basis as the method you use.
Auto-design varies the shape, lightest first, within S- or W-shapes as given. The flange check stays your entered wheel load, so it does not follow the size and takes no part in the search: confirm it for the shape chosen. With none entered, the shape it proposes still reads NOT checked when you run it.
Checks performed #
| Check | Basis |
|---|---|
| Flexure at the exterior support, trolley at the end | F2 with Lb the whole length and Tanner's Cb |
| Flexure in the back span, trolley at midspan | F2; the wheels taken at one point, on the conservative side |
| Lateral load | Eq. 14-1 of Design Guide 7, on the bottom flange alone: Mry over Fy bf² tf / 4 |
| Shear | G2 |
| Deflection | At midspan and at the end of the overhang, wheel loads, no impact |
| Bottom flange under a wheel | Your entered value; with none, a row that reads NOT checked and an NG status (Design Guide 7 17.2) |
Limitations of this calculation #
Not covered: bottom flange local bending by a method; continuous runways, curves and switches; a brace at the end of the overhang; hangers, sway bracing, splices, trolley stops; fatigue, which the guide says hangers are prone to if allowed to sway; the flange wear it asks to inspect. Using a lateral load at the traction surface on the flange alone follows the crane runway's Eq. 14-1 idea; no monorail example on disk shows it, so it is our reading.
CMAA 74 and ANSI MH27.1 are not on disk. When purchased, they would confirm the flange check, the wheel-load factors, and whether a higher impact or lateral force applies.
Verification examples #
Verification status: 16 values compared in 2 examples (2 published, 0 hand calculations from the cited equations): 16 within tolerance, 0 recorded deviations. Thin: only 2 published examples. Code basis: partial. Only some provisions were read in the target edition; the rest rests on older editions, examples or summaries.
Tanner (1985), AISC Engineering Journal, Table 1 (all 11 Cb values) and the numerical example: S12X40.8, 7 ft overhang of 20 ft, 5 kips: k = 0.35, Cb = 0.78, M = 36.0 kip-ft, bending stress 9.5 ksi, allowable 11.3 ksi by the 1978 formula. The paper's S12X35 no good and S15X42.9 good also come out. Its formula is older than AISC 360-22, so the module's F2 strength itself has no published comparison.
By hand only: the loads, the lateral load, the back span, the reactions and the deflections.