How are crane wheel loads positioned for maximum bending moment?

The critical position for maximum bending moment in a simply-supported crane runway beam under moving wheel loads uses the influence line method. For two wheel loads P1 and P2 separated by wheel base a: (1) Calculate the resultant R = P1 + P2. (2) Locate the resultant relative to each wheel. If P1 = P2 = P, the resultant is at mid-wheelbase (a/2 from each wheel). (3) Position the loads so the midpoint between the resultant and the nearest wheel is at the beam midspan. For equal loads: distance from left support to left wheel, x = L/2 − a/4. The maximum moment under the left wheel is then P × (L − a/2)² / (2L) for two equal loads. For four equal wheels on two end trucks (bridge crane with two end trucks, each with two wheels spaced at wheelbase a, and hook approach dictating the minimum distance between the two end truck groups): (1) The two end truck groups approach until hook position limits the minimum distance between them — typically the leftmost and rightmost pairs are separated by crane span minus twice the minimum hook approach. (2) The maximum moment under the inboard wheel of the critical end truck is then computed using the resultant of all four loads. (3) For equal wheel loads P, a common rule: position the spanwise center of the four wheels such that the midspan bisects the distance between the resultant of all loads and the nearest wheel. The exact position depends on whether the controlling moment occurs under the inboard or outboard wheel. For preliminary design, increase the static bending moment by 10-25% for impact (vertical) per ASCE 7 Table 4.11-1 and CMAA 70 Specification. The impact factor depends on crane classification: CMAA Class A (standby/infrequent) = 10%, Class C (moderate) = 20%, Class E (severe) = 25%.

What lateral loads act on crane runway beams?

Crane runway beams resist both vertical and lateral loads. The lateral forces are: (1) Lateral force from crane trolley acceleration — a horizontal force perpendicular to the runway beam, applied at the top of the rail, equal to 20% of the sum of the lifted load and trolley weight per ASCE 7 Section 4.10. For a 20-ton crane with 5-ton trolley: lifted load = 40 kip, trolley weight ≈ 10 kip, lateral force = 0.20 × (40 + 10) = 10 kip distributed among the wheels (per side: 5 kip per runway beam). (2) Crane skewing force — a horizontal force parallel to the runway beam, caused by the crane bridge traveling at an angle, equal to 10% of the maximum wheel load per CMAA. This produces axial load in the runway beam in the longitudinal direction. (3) Longitudinal traction force — from bridge acceleration and braking, also 10-20% of the maximum wheel load per ASCE 7. The lateral force is applied to the top flange of the runway beam, producing weak-axis bending. For a typical W-shape runway beam, the weak-axis section modulus Sy is much smaller than the strong-axis Sx, so even a 10% lateral force can produce significant additional stress. The biaxial bending interaction per AISC H1-1 is: Pr/(φPc) + 8/9 × (Mrx/(φMcx) + Mry/(φMcy)) ≤ 1.0 for Pr/(φPc) < 0.2. For a runway beam with no axial load (Pr = 0), the check simplifies to Mrx/(φMnx) + Mry/(φMny) ≤ 1.0. The lateral-torsional buckling (LTB) check of the top flange under vertical wheel loads is particularly important because the compression flange is loaded between brace points (the full-length rail provides continuous lateral restraint, but the rail-to-flange connection stiffness must be verified).

How is crane runway beam fatigue checked?

Crane runway beam fatigue is checked per AISC 360 Appendix 3, which categorizes connection details by fatigue category (A through F, where A has the highest allowable stress range and F the lowest). The key fatigue details on a crane runway beam: (1) The web-to-flange weld of the runway beam — typically a continuous fillet weld, Category B (allowable stress range = 16 ksi at 500,000 cycles, 10 ksi at 2,000,000 cycles). (2) Stiffener-to-web welds — transverse stiffeners welded to the web and flange, Category C (allowable range = 12 ksi at 500,000 cycles). (3) Rail clip attachment welds — Category E (lowest, 4.5 ksi at 500,000 cycles). The stress range is the difference between the maximum and minimum stress during a single crane pass: Δσ = σmax − σmin, where both are computed from the same load position but represent different times (loaded vs unloaded). The fatigue demand is compared to the allowable stress range: Δσ ≤ F_TH, where F_TH = the constant-amplitude fatigue threshold (CAFT) below which infinite life is predicted for the given detail category. Crane service classification determines the required number of design cycles. Per AISE Technical Report No. 13: Class A (standby) — 20,000-100,000 cycles, Class B (light) — 100,000-500,000, Class C (moderate) — 500,000-2,000,000, Class D (heavy) — 2,000,000+, Class E (severe) — over 5,000,000 cycles, Class F (continuous severe) — over 5,000,000 cycles with impact. For Classes D, E, and F, fatigue typically governs the beam design (especially at stiffener terminations and rail attachment details) rather than static strength. AISC 360 Appendix 3 Table A-3.1 lists the complete fatigue categories and thresholds.

How is LTB (lateral-torsional buckling) checked for a crane runway beam with top flange loading?

Lateral-torsional buckling (LTB) of the top flange is a critical check for crane runway beams because the compression flange is loaded by moving wheel loads. The top flange of a simply-supported runway beam is in compression under vertical bending, while the bottom flange is in tension. Without adequate lateral restraint, the compression flange can buckle laterally, twisting the section. The LTB check per AISC 360 Chapter F: φMn = φ × Cb × [Mp − (Mp − 0.7FySx) × (Lb − Lp)/(Lr − Lp)] for Lp < Lb ≤ Lr. The unbraced length Lb for a crane runway beam is typically the full span length between columns (no intermediate bracing points between the bearing supports). The rail provides a degree of torsional restraint to the top flange because it is continuously clipped to the top flange, but AISC does not permit the rail to be considered a lateral brace unless the rail-to-flange connection and the rail itself can demonstrably resist the required brace force: P_brace = 0.01 × M_f / h_o, where M_f is the flange moment and h_o is the distance between flange centroids. For a W24×68 runway beam under 200 kip-ft moment, the required brace force = 0.01 × 2400 kip-in / 23.3 in = 1.03 kip per brace point. If the rail clips cannot resist this force, the rail does not qualify as a brace. AISC Design Guide 7 (Industrial Buildings) provides specific guidance for crane runway beam LTB: (a) If the rail is continuously welded to the top flange (crane rail welded to a steel top plate on the beam), the rail may be considered a continuous torsional restraint, and Lb may be taken as zero (LTB does not govern). (b) If the rail is clipped, Lb = span length. (c) For runway beams with a cap channel on the top flange (common in heavy industrial cranes), the cap channel's contribution to LTB resistance can be included by computing the combined section properties of beam + channel.

What deflection limits apply to crane runway beams?

Crane runway beam deflection limits are stricter than typical building deflection limits because excessive deflection causes operational problems for the crane. Per CMAA 70 and AISC Design Guide 7: (1) Vertical deflection under maximum wheel loads (static, excluding impact) — L/600 for light to moderate service cranes (Classes A-C), and L/800 to L/1000 for heavy service cranes (Classes D-E). For a 30 ft span: L/600 = 0.60 in, L/1000 = 0.36 in. (2) Horizontal (lateral) deflection under lateral crane forces — L/400 for most cranes. This is the deflection of the top flange perpendicular to the runway, caused by the 20% lateral trolley force. (3) Differential deflection between adjacent runway beams — must be less than 1/4 inch to prevent crane binding on the rails. This requires the two runway beams of a runway pair to deflect similarly, which means their sections and spans should match, and column support conditions should be balanced. (4) Runway girder slope at supports — limited to 0.004 radians (approximately 1/250) to prevent rail kinking at column locations. This often controls for continuous (multi-span) runway beams because the slope at interior supports under adjacent-span loading is higher than the midspan deflection of a simple span. Deflection is calculated using the service-level wheel loads (NOT factored loads) and the static stiffness EI (NOT reduced for plasticity). Impact factor is excluded from the deflection calculation because deflection is a static serviceability concern, not a strength concern. The flange-to-web weld of the runway beam must accommodate the fatigue stress range from the repeated bending, so full-penetration or continuous fillet welds are standard.

Crane Runway Beam — Industrial Beam Design

Q: What is Crane Runway Beam — Industrial Beam Design?

Crane runway beam design for wheel loads. Biaxial bending, lateral-torsional buckling, and fatigue category checks per AISC 360 and CMAA 70.

Crane runway beam design for wheel loads. Biaxial bending, lateral-torsional buckling, and fatigue category checks per AISC 360 and CMAA 70. Educational use only.

This page documents the scope, inputs, outputs, and computational approach of the Crane Runway Beam tool on steelcalculator.app. The interactive calculator runs in your browser; this documentation ensures the page is useful even without JavaScript.

What this tool is for

Checking biaxial bending of crane runway beams under vertical wheel loads and lateral crane forces.
Evaluating lateral-torsional buckling for the top flange loaded by moving crane wheels.
Preliminary fatigue screening for crane duty cycle categories per AISC 360 Appendix 3 and CMAA 70.

What this tool is not for

It does not design the crane rail, rail clips, or crane girder connections.
It does not handle crane runway columns, bracing, or the building frame response to crane loads.
It does not perform a full fatigue assessment with stress range counting and cumulative damage analysis.

Key concepts this page covers

moving wheel load placement for maximum moment and shear
biaxial bending interaction (H1-1 interaction equation)
lateral force from crane trolley and skewing
fatigue categories and stress range limits

Inputs and outputs

Typical inputs: runway beam span, section size, crane capacity, wheel base, number of wheels, maximum wheel load, lateral load (percent of lifted load), and crane duty class.

Typical outputs: maximum bending moment (strong and weak axis), combined stress check (H1-1 interaction), deflection (vertical and lateral), and fatigue category check with allowable stress range.

Computation approach

The calculator positions the crane wheel loads on the span to maximize the bending moment using the influence line approach (for two or four wheels, the critical position is when the midpoint between the resultant and the nearest wheel is at the beam midspan). Lateral forces are applied as a percentage of the vertical load per ASCE 7 or CMAA. Biaxial bending is checked using the AISC H1-1 interaction equation. Fatigue is screened by comparing the live-load stress range to the allowable range for the applicable fatigue category.

Maximum Wheel Load Positioning — Influence Line Method

For a simply-supported beam with two wheel loads P1 and P2 separated by wheel base a:

Maximum moment occurs when the beam midline bisects the distance between
the resultant of the wheel loads and the nearest wheel.

For equal wheels (P1 = P2 = P), wheel base = a:
  Critical position: place wheels so midspan is at a/4 from one wheel
  Maximum moment: Mmax = P × (L - a/2)² / (2L) + P × (L - a/2)² / (2L)

  For P = 40 kips, L = 30 ft, a = 8 ft:
  Mmax = 40 × (30 - 4)² / (2 × 30) = 40 × 676 / 60 = 451 kip-ft

For four-wheel cranes, the critical position must be found by checking all possible arrangements (the calculator automates this).

Maximum shear positioning

Maximum shear occurs when the heaviest wheel is placed as close to the
support as possible. For a two-wheel crane:

Vmax = P1 × (L - x)/L + P2 × (L - x - a)/L

Where x = distance from support to nearest wheel (minimize x)

CMAA Crane Classification

CMAA Class	Service Description	Typical Lifts/Hour	Fatigue Life (cycles)	Typical Application
A	Standby or infrequent	< 2	< 20,000	Power house, maintenance
B	Light service	2-5	20,000-100,000	Warehouse, light assembly
C	Moderate service	5-10	100,000-500,000	Machine shop, paper mill
D	Heavy service	10-20	500,000-2,000,000	Foundry, heavy assembly
E	Severe service	> 20	> 2,000,000	Steel mill, scrap handling
F	Continuous severe	Continuous	> 4,000,000	Steel mill, continuous cast

Fatigue checks are required for CMAA Classes C through F (over 100,000 cycles per AISC Appendix 3).

Fatigue Design Per AISC 360 Appendix 3

Allowable stress ranges by fatigue category

Category	Stress Range (ksi) at 2×10⁶ cycles	Detail Description
A	24.0	Base metal, rolled or cleaned surfaces
B	16.0	Base metal at welded transverse stiffeners
B'	12.0	Base metal at partial-length cover plates
C	10.0	Base metal at fillet-welded attachments
C'	7.8	Base metal at transverse groove welds
D	7.0	Base metal at short attachments (< 2 in)
E	4.5	Base metal at longitudinal fillet welds
E'	2.6	Base metal at long attachments (> 24 in)
F	8.0	Fillet weld metal in shear

For crane runway beams, the most critical details are typically Category C (web-to-flange weld at wheel load point) and Category B (stiffener weld toes). The stress range must not exceed the threshold for the applicable number of cycles.

Threshold cycle count per AISC Appendix 3

Number of Cycles	Stress Range Multiplier
20,000 - 100,000	1.5 × tabular value
100,000 - 500,000	1.0 × tabular value
500,000 - 2,000,000	0.75 × tabular value
> 2,000,000	0.60 × tabular value

Worked Example — Crane Runway Beam Design

Problem: A 10-ton overhead crane (CMAA Class D) has a wheel base of 10 ft, two wheels per runway, maximum wheel load of 25 kips (including impact). The runway beam spans 30 ft between columns. Lateral force = 20% of lifted load + trolley = 4 kips per wheel. Select a runway beam section (A992 steel).

Step 1 — Vertical loads and moment

P_max = 25 kips per wheel (with 25% impact per ASCE 7)
Wheel base a = 10 ft
Span L = 30 ft

Critical position: midline bisects resultant and nearest wheel
For equal wheels, critical position: a/4 = 10/4 = 2.5 ft from midspan

M_max = P × (L - a/2)² / (2L) = 25 × (30 - 5)² / (2 × 30)
M_max = 25 × 625 / 60 = 260 kip-ft (vertical moment)

Factored: Mu = 1.6 × 260 = 416 kip-ft (crane load factor per ASCE 7)

Step 2 — Lateral loads and moment

Lateral force per wheel = 4 kips
Applied at top of rail (rail height ≈ 4 in above top flange)

Weak-axis moment (applied at top flange):
M_lat = 4 × (30 - 5)² / (2 × 30) = 4 × 625 / 60 = 41.7 kip-ft

Factored: Mu_lat = 1.6 × 41.7 = 66.7 kip-ft

Step 3 — Section selection

Try W21x68 (A992): Sx = 140 in³, Sy = 15.1 in³
phiMsx = 0.90 × 140 × 50 = 6,300 kip-in = 525 kip-ft
phiMsy = 0.90 × 15.1 × 50 = 680 kip-in = 56.6 kip-ft

Biaxial interaction (AISC H1-1):
Mu_x / phiMsx + Mu_y / phiMsy = 416/525 + 66.7/56.6 = 0.79 + 1.18 = 1.97

FAILS — weak axis moment far exceeds capacity.

Step 4 — Compound section with channel cap

Add C10x15.3 cap channel welded to top flange of W21x68:
Combined Sy ≈ 15.1 + 21.0 = 36.1 in³ (channel contributes weak-axis capacity)
phiMsy = 0.90 × 36.1 × 50 = 1,625 kip-in = 135 kip-ft

Revised interaction:
416/525 + 66.7/135 = 0.79 + 0.49 = 1.28

Still exceeds 1.0. Try W24x76 with C12x20.7:
Sx = 176 in³, Sy_combined ≈ 18.0 + 27.0 = 45.0 in³
phiMsx = 660 kip-ft, phiMsy = 169 kip-ft

416/660 + 66.7/169 = 0.63 + 0.39 = 1.02 → MARGINAL

W24x84 provides more margin. Final selection: W24x84 with C12x20.7 cap.

Step 5 — Fatigue check

CMAA Class D: 500,000 to 2,000,000 cycles → threshold at 2×10⁶
Category C (web-to-flange weld): Fsr = 10.0 ksi

Live load stress range:
Δf = M_max / Sx = 260 × 12 / 176 = 17.7 ksi
17.7 > 10.0 → FATIGUE GOVERNS (web-to-flange weld at wheel load)

Options:
1. Use complete joint penetration (CJP) web-to-flange weld → Category B (16 ksi)
2. Add transverse stiffeners at wheel load points
3. Reduce wheel load or increase section

Using CJP weld: 17.7 > 16.0 → still fails marginally
Increase to W27x94: Sx = 243 in³ → Δf = 260×12/243 = 12.8 ksi < 16.0 ✓

Deflection Limits for Crane Runway Beams

Crane Service	Vertical Deflection Limit	Lateral Deflection Limit	Source
Light (CMAA A-B)	L/600	L/400	CMAA 70
Moderate (C-C)	L/800	L/400	CMAA 70
Heavy (D-E)	L/1000	L/400	CMAA 70
Severe (F)	L/1200	L/400	CMAA 70
General practice	L/800	—	AISC DG 7

These limits prevent excessive runway misalignment that causes crane wheel binding and premature rail wear.

Frequently Asked Questions

How are crane wheel loads positioned for maximum moment? For a single crane with two wheels per rail, the maximum moment occurs when the beam centerline is midway between the nearest wheel and the resultant of both wheel loads. This is a specific case of the general moving-load theorem. For four-wheel cranes, all possible wheel positions must be checked. The tool automates this positioning to find the critical arrangement.

What lateral forces act on a crane runway beam? Crane lateral forces arise from trolley acceleration/deceleration (typically 20% of the lifted load plus trolley weight, applied at the top of the rail), crane skewing forces (from the crane bridge not tracking straight on the rails), and impact. These lateral forces cause weak-axis bending in the runway beam. A separate channel or plate is often welded to the top flange to resist lateral bending, creating a compound section.

Why is fatigue important for crane runway beams? Crane runway beams experience repeated load cycles every time the crane traverses the span. Over a 25-year service life, a moderate-duty crane may impose 500,000 to 2,000,000 load cycles. AISC 360 Appendix 3 requires fatigue checks when the number of cycles exceeds 20,000, and the allowable stress range decreases with increasing cycle count and worse fatigue category (determined by the connection detail). Fatigue often controls the design of runway beams for medium and heavy-duty cranes.

Typical Crane Capacities and Corresponding Runway Beam Sizes

The following table provides preliminary runway beam sizes for common overhead crane capacities. These assume a simply supported span of 25 ft between columns, A992 steel, and moderate duty (CMAA Class C-D). The actual section must be verified for the specific wheel loads, span, lateral forces, and fatigue requirements of each project.

Crane Capacity (tons)	Wheel Load (kips)	Wheel Base (ft)	Runway Beam Section	Cap Channel	Approx. Weight (lb/ft)
5	12	6	W18x40	C8x11.5	51.5
10	20	8	W21x55	C10x15.3	70.3
15	28	8	W24x62	C10x15.3	77.3
20	35	10	W24x76	C12x20.7	96.7
25	42	10	W24x84	C12x20.7	104.7
30	50	12	W27x94	C12x20.7	114.7
40	65	12	W30x108	C15x33.9	141.9
50	80	14	W33x118	C15x33.9	151.9
60	95	14	W33x130	C15x33.9	163.9
75	115	16	W36x135	C15x33.9	168.9
100	150	16	W36x160	Built-up channel	200+

Notes: Wheel loads include 25% impact per ASCE 7. For spans longer than 25 ft, the beam size increases. For CMAA Class E-F cranes, fatigue requirements may require a heavier section than shown. The cap channel provides additional weak-axis moment capacity for lateral crane forces. For cranes over 50 tons, a built-up asymmetric section (plate girder with integral cap) is often more economical than a rolled section with a separate channel.

Crane Rail Selection

The crane rail transfers wheel loads from the crane to the runway beam and must be selected based on wheel load magnitude, wheel diameter, and traffic frequency. Common crane rail sections include:

Rail Section	Weight (lb/yd)	Wheel Load Range (kips)	Application
ASCE 25	25	Up to 15	Light cranes, monorails
ASCE 40	40	15-30	Moderate duty
ASCE 60	60	30-50	Standard industrial
ASCE 80	80	50-80	Heavy industrial
ASCE 104	104	80-120	Very heavy, steel mill
CR-100 (custom)	100-135	100-150	Steel mill, continuous
Square bar 2-3 in	18-40	Up to 20	Light service, monorails

Key rail selection criteria:

Wheel contact stress: The Hertzian contact stress between the wheel and rail must not exceed the allowable bearing stress. For steel wheels on steel rails, the allowable contact stress depends on wheel diameter and rail head width. A rough limit is F_allowable = 600 x sqrt(D_wheel) psi, where D_wheel is in inches.
Rail wear allowance: The rail must have sufficient head thickness to accommodate wear over its service life. Heavier rails have more wear allowance.
Rail attachment: Rails are typically attached with rail clips (bolted to the top flange) or hook bolts. Rail clips allow some lateral adjustment to align the rail. The clip spacing is typically 2-3 ft along the beam length.
Rail pads: For heavy-duty cranes (CMAA Class D and above), an elastomeric pad between the rail and beam top flange helps distribute the wheel load and reduces impact fatigue on the beam. Pad thickness is typically 1/4 to 3/8 inch.

Channel Cap Connection Detailing

The cap channel is welded to the top flange of the runway beam to provide additional weak-axis section properties for resisting lateral crane forces. Proper detailing of this connection is critical:

Weld type: Fillet welds along both toes of the channel are standard. The weld size is typically 5/16 to 3/8 inch for moderate-capacity cranes, sized to develop the channel's weak-axis plastic moment capacity. Intermittent fillet welds are acceptable for light-duty cranes, but continuous welds are required for CMAA Class D and above to prevent fatigue cracking at weld terminations.

Weld length and position: The channel should extend the full span length. For continuous runway beams over multiple supports, the channel should be spliced with a full-penetration groove weld or bolted splice plate designed for the full lateral moment. Splices should be located away from points of maximum lateral moment (typically near midspan and at supports).

Fit and tolerances: The channel must fit tightly against the beam top flange. Gaps greater than 1/16 inch require fill plates. The channel web must be aligned with the beam web to ensure the combined section's shear center is close to the loading plane.

Rail attachment through the channel: For cranes where the rail is mounted directly on top of the cap channel, bolt holes in the channel web must be located to avoid the beam flange-to-channel weld. Rail clips are typically bolted through the channel flanges with adequate edge distance.

Lateral Bracing Requirements for Crane Runway Beams

Crane runway beams must be laterally braced to prevent lateral-torsional buckling and to resist the lateral forces from crane operation. The bracing requirements depend on the beam span, section properties, and crane duty:

Types of lateral bracing:

Tie-back struts: Diagonal braces from the top flange of the runway beam to the building column or roof framing. These are the most common system. Tie-backs are typically provided at 15-25 ft spacing along the runway, and are designed to resist the full lateral crane force in the tributary length.
Lateral bracing truss: A horizontal truss between two parallel runway beams that provides continuous lateral support. Used for heavy cranes where tie-back spacing would be too close.
Diaphragm bracing: A horizontal diaphragm (metal deck or plate) connecting the runway beam top flange to adjacent framing. Used in heavy industrial buildings.

AISC lateral-torsional buckling check: The runway beam must satisfy AISC Chapter F LTB requirements for the top (compression) flange. The unbraced length Lb is the distance between lateral bracing points. For a W24x84 with Fy = 50 ksi: Lp = 1.76 x ry x sqrt(E/Fy) = 1.76 x 2.31 x sqrt(29000/50) = 97.6 in = 8.1 ft, and Lr depends on the full AISC equation. If Lb > Lp, the moment capacity is reduced. For most crane runway beams, tie-back bracing at 15-20 ft spacing keeps Lb near or below Lp.

Special considerations: At the support brackets, the beam must be laterally restrained at both top and bottom flanges. The connection to the column bracket must prevent rotation of the beam cross-section. For continuous runway beams, the negative moment region at interior supports requires special attention because the bottom flange is in compression and must also be laterally braced.

How do I select a crane rail section? The crane rail must be matched to the wheel load and wheel diameter. For wheel loads up to 15 kips, ASCE 25 or ASCE 40 rail is adequate. For 15-50 kips, use ASCE 40 through ASCE 80. For heavier loads, ASCE 104 or custom crane rail sections are required. The critical check is the Hertzian contact stress between the wheel and rail head. A practical limit is F_allowable approximately equals 600 x sqrt(D_wheel) psi, where D_wheel is the wheel diameter in inches. The rail must also have adequate head thickness for wear over the service life, especially for CMAA Class D-F cranes.

How should the cap channel be connected to the runway beam? The cap channel is typically connected with continuous fillet welds along both toes of the channel to the beam top flange. Weld size is usually 5/16 to 3/8 inch for moderate cranes. For CMAA Class D and above, continuous welds are required (no intermittent welds) to prevent fatigue cracking at weld terminations. The channel must fit tightly against the beam flange with gaps less than 1/16 inch; larger gaps require fill plates. At splices in the channel, use full-penetration groove welds located away from maximum moment regions.

What lateral bracing spacing is required for crane runway beams? Tie-back struts are typically spaced at 15-25 ft along the runway beam length, designed to resist the tributary lateral crane force. The bracing spacing must keep the unbraced length Lb close to or below Lp (the limiting laterally unbraced length for the limit state of yielding) from AISC Chapter F. For a W24x84, Lp is approximately 8 ft, so even at 15 ft spacing the moment capacity is reduced below the plastic moment. Many designers use closer bracing (8-12 ft) for heavy cranes to maintain full moment capacity. At support brackets, both top and bottom flanges must be laterally restrained.

Disclaimer (educational use only)

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All real-world structural design depends on project-specific factors (loads, combinations, stability, detailing, fabrication, erection, tolerances, site conditions, and the governing standard and project specification). You are responsible for verifying inputs, validating results with an independent method, checking constructability and code compliance, and obtaining professional sign-off where required.

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