Vehicular, Crane, and Other Moving Loads

Vehicular, Crane, and Other Moving Loads

Core idea: A moving load is defined by both magnitude and position. The same axle group can produce small, zero, or governing response as it travels, so calculate an envelope of possible effects rather than analyzing one convenient location.

Start With the Requested Response

A load position is only “critical” for a named response: left reaction, shear at a section, moment at a section, member force, or deflection. A position that maximizes midspan moment will not generally maximize support shear. For a linear structure, an influence line gives the response at the selected location caused by a unit load moving across the structure. Its ordinate may be positive, negative, or zero.

For several concentrated loads, the response is

E = Σ(P_i y_i)

where P_i is a wheel or axle load and y_i is the influence ordinate under it. For a distributed load w, the contribution is w times the loaded area under the influence line. Apply only the load arrangements, lanes, presence factors, and simultaneous-loading rules required by the controlling reference.

Influence Line for a Beam-Section Moment

Consider a simply supported span L and a target section a from the left support. The moment influence ordinate for a unit load at coordinate x is

• y_M = x(L - a)/L when 0 ≤ x ≤ a
• y_M = a(L - x)/L when a ≤ x ≤ L

The two straight branches meet at x = a, where y_M = a(L - a)/L. The ordinate has units of length, so P y_M has moment units. This triangular influence line is positive across the span; an influence line for another response may change sign.

Worked axle-placement calculation

A 30-ft simple span has a target section 12 ft from the left. Two axles, 20 kips and 32 kips, are spaced 10 ft apart. Compare the event positions created when each axle reaches the target section.

At x = 12 ft, the peak ordinate is

y_M = 12(30 - 12)/30 = 7.2 ft.

Candidate A: Put the 32-kip axle at x = 12 ft; the 20-kip axle is at x = 2 ft. Its ordinate is 2(18)/30 = 1.2 ft.

M_A = 32(7.2) + 20(1.2) = 254.4 kip-ft.

Candidate B: Put the 20-kip axle at x = 12 ft; the 32-kip axle is at x = 22 ft. The latter ordinate is 12(30 - 22)/30 = 3.2 ft.

M_B = 20(7.2) + 32(3.2) = 246.4 kip-ft.

Candidate A governs these event positions. For a fixed group on a piecewise-linear influence line, also check entry/exit events and any other arrangement required by the load model. If a permitted 0.40 kip/ft lane load simultaneously covers the full positive span, its contribution is

0.40[½(30)(7.2)] = 43.2 kip-ft.

The combined effect would be 297.6 kip-ft only if the governing specification permits that axle-plus-lane combination. The mechanics calculation does not grant permission to combine loads.

Vehicular and Bridge Loads

For a 2026 exam, use the AASHTO LRFD Bridge Design Specifications, 8th edition, including the identified May 2018 errata and PE Exam Collection. Read the prescribed vehicle, lane occupancy, transverse placement, and combination provisions directly. Do not substitute an axle configuration from memory or a newer office edition. Create separate envelopes for positive moment, negative moment, shear, reaction, and fatigue response when the problem requires them. Dynamic allowance is a separate Chapter 4.2 decision and must be applied only where the governing provision directs.

Crane and Traveling-Equipment Loads

A crane produces a system of moving actions. The bridge travels along runway beams; the trolley moves across the bridge; lifted load location changes wheel reactions. A sound workflow is:

1. Position the trolley to maximize the near-side or far-side crane reaction.
2. Convert crane reactions into the specified runway wheel loads while preserving spacing.
3. Move the wheel group along the runway influence line.
4. Evaluate vertical response and the prescribed lateral and longitudinal actions separately.
5. Trace each action through rails, attachments, runway beams, columns, bracing, and foundations.
6. Apply the current ASCE 7-16/AISC 15th provisions and form the required load combinations.

Forklifts, erection equipment, gantries, and other traveling loads follow the same logic: preserve the real footprint, find favorable positions, and envelope the response. A uniform floor live load may be an additional case, but it is not automatically an equivalent substitute for concentrated moving wheels.

Exam Workflow

Write six labels before calculating: response, influence sign, load model, spacing, permitted concurrency, factors. Sketch the influence line, place concentrated loads at favorable ordinates, distribute lane load over allowed favorable regions, sum unamplified effects, then apply each prescribed factor once. Finally check units and whether the selected answer is a maximum positive effect, a maximum negative effect, or an absolute envelope.