Moving load
Moves a train of wheel loads over a beam of 1 to 6 spans and gives the envelopes of moment, shear, reaction and deflection, the absolute maximum moment, the moment influence line at a station, and the forces at any one position of the train. Use it for crane runways, forklifts, equipment on rails and vehicles on a slab strip. The results are numbers to copy into a member calculation: nothing links them.
Inputs of the moving load #
- Spans, up to 6, with a support at each end of each span. The left and right ends are a pin or fixed.
- Stiffness: an AISC shape (Ix, E = 29,000 ksi, with its self-weight if you choose) or E and I entered, constant along the beam. It sets the moments on continuous spans and all deflections.
- Uniform dead load: on all spans, no pattern.
- Wheels, up to 16: distance from the first wheel and load, without impact. For a crane use the maximum wheel load of ASCE 7-22 4.9.2.
- Impact: the percentages of ASCE 7-22 4.6.3 (machinery) and 4.9.3 (cranes), or entered. A manufacturer's larger value governs. ASCE 7-22 gives none for vehicles and forklifts in this list, so enter yours.
- Run the train both ways: matters for a train that is not symmetrical on a beam that is not symmetrical. On by default.
- Deflection limit (span / n): under the train with impact. 0 = none. Your limit: AISC Design Guide 7 lists limits for runways.
- Influence line at: station for the moment influence line; 0 = where the absolute maximum moment occurs.
- Forces at one position: with the first wheel at a position you give, the moment and shear at that station and the reactions.
Checks performed #
| Result | Basis |
|---|---|
| Absolute maximum moment, one simple span | AISC Manual 16th Ed. Table 3-22, General Rules: under a wheel, with the span's centerline midway between that wheel and the resultant of the wheels on the span. Every wheel and every group of wheels is tried |
| Absolute maximum moment, other beams | Train moved over a grid and with each wheel at each of 24 stations per span, in both directions, the peak refined under each wheel |
| Moment, shear, reactions at each station | Slope-deflection with joint rotations as unknowns, exact for point loads, and statics |
| Deflection at each station | Joint rotations plus the fixed-end deflection under each wheel in that span. Peak at the stations |
| Envelopes with the dead load | The wheels as L and the uniform load as D, ASCE 7-22 2.3.1 or 2.4.1, each station's largest and smallest |
| Deflection limit | Span / n, each span |
The type reads Calculated, or not adequate only against a deflection limit you set.
Limitations #
- Vertical loads only. The lateral and longitudinal crane forces of 4.9.4 and 4.9.5, fatigue and web crippling are not here; the Crane runway type, where available, covers a runway beam on one span.
- A beam of at most 300 ft. A wheel's effect fades within a span or two, so model the spans either side of the part you are designing.
- No overhangs. Supports are rigid and at the span ends. Constant EI. First-order.
- Uniform live load and patterns are not combined with the train: add them in a beam analysis and add the effects.
- The envelope stations are 24 per span, so an envelope's value between stations is slightly under its true peak. The absolute maximum moment is refined; the combined envelope's value is at the stations.
Verification examples #
Verification status: 29 values compared in 13 examples (9 published, 4 hand calculations from the cited equations): 29 within tolerance, 0 recorded deviations. Code basis: the provisions it uses were read in the target edition.
| Example | Source | Values |
|---|---|---|
| Runway beam, 30 ft span, wheels 12 ft apart | AISC Design Guide 7, 3rd Ed. (2019), Example 14.1.1 | Moment 9.60 per kip of wheel, 478 kip-ft with impact, 386 kip-ft without |
| One, two equal and two unequal moving loads | AISC Manual 16th Ed. Table 3-22, cases 43 to 45, p. 3-231 | Mmax on both branches, R1 max |
| Three loads on a simple beam | Udoeyo (2020), Structural Analysis, Example 9.8, PDF p. 261 | Reactions, moment and shear at midspan, influence ordinates |
No published train over continuous spans is on disk. Hand calculations from the three-moment equation cover the load at the center of one of two spans (R = 13/32, 11/16, −3/32 P), the largest moment over the support (−0.0962 P L at a = L/√3), the fixed-ended span and the dead load on two spans.