حساب حمولة عجلة الرافعة

This free online crane wheel load calculator computes the maximum and minimum wheel pressure (PMAX and PMIN) acting on each runway rail, based on the crane’s lifting capacity, trolley weight, crane self-weight, span, hook approach distances, and number of wheels. It also includes a built-in wheel diameter inspection tool that verifies whether the selected wheel diameter meets the allowable contact pressure limit for the chosen rail type and wheel material.

Accurate wheel load calculation is the foundation for runway rail selection, runway beam design, wheel and axle specification, and end carriage structural verification. Underestimating wheel loads leads to premature rail wear, rail fastening failure, and runway beam fatigue cracking. Overestimating results in unnecessary structural cost.

---

The Two Calculation Results

PMAX — Maximum Wheel Pressure

PMAX is the largest vertical force transmitted from a single crane wheel to the runway rail. It occurs when the trolley is positioned as close as possible to the rail being calculated (minimum hook approach distance from that rail), with the rated load on the hook.

PMAX governs:

• Runway rail section selection and rail stress check
• Runway beam maximum bending moment and shear force
• Wheel-rail contact stress (Hertzian pressure) verification
• Rail fastening and clamp design load
• Foundation and column base reaction under maximum loading

PMIN — Minimum Wheel Pressure

PMIN is the smallest vertical force on a single wheel, occurring when the trolley is positioned as far as possible from the rail being calculated (maximum hook approach distance), carrying only the trolley self-weight with no lifted load.

PMIN governs:

• Rail uplift check — in some configurations PMIN can approach zero or become negative (uplift), requiring anti-lift rail fastenings
• Buffer stop and end stop design
• Stability check of the crane bridge under no-load wind loading

---

صيغ الحساب

Step 1 — Wheel Count per Rail (n)

\[n = \frac{N_L}{2}\]

Where N_L is the total number of wheels on the crane. For a standard four-wheel crane, n = 2 wheels per rail.

Step 2 — Load Component from Lifted Load and Trolley (PQ)

\[P_Q = \frac{(Q + G_t)(L - e_{min})}{L \times n} \times 10\]

Step 3 — Load Component from Crane Self-Weight (PZ)

\[P_Z = \frac{G - G_t}{N_L} \times 10\]

Step 4 — Maximum Wheel Pressure

\[P_{MAX} = P_Q + P_Z\]

Step 5 — Trolley Component at Far Position (PXZ)

\[P_{XZ} = \frac{G_t(L - e_{max})}{L \times n} \times 10\]

Step 6 — Minimum Wheel Pressure

\[P_{MIN} = P_{XZ} + P_Z\]

---

Parameter Definitions

رمز	المعلمة	وحدة	الوصف
Q	قدرة الرفع	t	Rated safe working load (SWL) on the hook
G_t	Trolley weight	t	Self-weight of the complete trolley assembly
G	Total crane weight	t	Total self-weight of the entire crane including trolley
L	Crane span	m	Centre-to-centre distance between runway rails
e_min	Min hook distance	m	Minimum horizontal distance from hook centreline to the nearer runway rail, at closest trolley approach
e_max	Max hook distance	m	Maximum horizontal distance from hook centreline to the nearer runway rail, at furthest trolley approach
N_L	Total wheels	pcs	Total number of crane wheels (both rails combined)
n	Wheels per rail	—	N_L ÷ 2

Unit note: Q, G_t, and G are entered in tonnes (t). The formula multiplies by 10 to convert to kilonewtons (kN), applying g ≈ 10 m/s² as the standard approximation used in Chinese national standard GB/T 3811.

---

How to Use the Calculator

Part 1 — Wheel Load Calculation

Step 1 — Enter Lifting Capacity (Q) Enter the crane's rated safe working load in tonnes, as stated on the crane data plate or design specification. Do not include hook block weight — this is captured in the trolley weight.

Step 2 — Enter Trolley Weight (G_t) Enter the self-weight of the complete trolley in tonnes, including the hoist unit, frame, wheels, and all electrical equipment mounted on the trolley. This value is available from the hoist or trolley manufacturer's data sheet. G_t must not exceed the total crane weight G.

Step 3 — Enter Minimum Hook Distance (e_min) Enter the minimum horizontal distance in metres from the hook centreline to the centreline of the nearer runway rail, when the trolley is at its closest approach position. This is the "end approach" dimension — typically 0.3 m to 1.5 m depending on the hoist and trolley design.

Step 4 — Enter Crane Span (L) Enter the centre-to-centre distance between the two runway rails in metres. e_min must be less than L.

Step 5 — Enter Total Crane Weight (G) Enter the total self-weight of the entire crane in tonnes, including the bridge girder(s), end carriages, trolley, hoist, electrics, and all permanently mounted equipment.

Step 6 — Enter Total Number of Wheels (N_L) Enter the total number of crane wheels across both rails. A standard single-girder or double-girder overhead crane has 4 wheels (2 per rail). Large-capacity cranes may use 8, 12, or more wheels to distribute load. Must be an even integer of 2 or greater.

Step 7 — Enter Maximum Hook Distance (e_max) Enter the maximum horizontal distance from the hook centreline to the nearer runway rail when the trolley is at its furthest position from that rail. e_max must be greater than e_min. For most cranes, e_max ≈ L − e_min.

Step 8 — Calculate Click Calculate Wheel Load. The calculator returns PMAX and PMIN in kN, and auto-fills PMAX into the wheel diameter inspection section.

---

Part 2 — Wheel Diameter Inspection

After calculating wheel loads, the tool checks whether the selected wheel diameter is adequate for the wheel-rail contact stress at PMAX.

Wheel Diameter Inspection Formula:

\[P_{allowable} = \frac{1.9 \times \sigma \times D \times w}{1000}\]

رمز	Definition
P_allowable	Allowable wheel load for the selected wheel diameter and rail (kN)
σ	Material coefficient based on wheel tensile strength (see table below)
D	Wheel diameter (mm)
w	Effective contact width of rail head = b − 2r (mm)
b	Rail head width (mm) — from track type table
r	Rail head fillet radius (mm) — from track type table

Inspection result:

• Passed: PMAX < P_allowable — the selected wheel diameter is adequate for the rail type and material
• Disqualified: PMAX ≥ P_allowable — the wheel diameter is too small or the rail section is too light; increase wheel diameter or select a heavier rail section

---

Rail Type Parameters

P-Type Crane Rail (Light and Medium Duty)

نوع السكة	Head Width b (mm)	Fillet Radius r (mm)	Effective Width w = b−2r (mm)
P 11	32	7	18
P 15	37	7	23
P 18	40	7	26
P 24	51	13	25
P 38	68	13	42
P 43	70	13	44
P 50	70	13	44

QU-Type Crane Rail (Heavy Duty)

نوع السكة	Head Width b (mm)	Fillet Radius r (mm)	Effective Width w = b−2r (mm)
QU 70	70	6	58
QU 80	80	8	64
QU 100	100	8	84
QU 120	120	8	104

---

Wheel Material Tensile Strength Coefficients (σ)

قوة الشد	Coefficient σ
500–600 N/mm²	5.0
600–700 N/mm²	5.6
700–800 N/mm²	6.5
800–900 N/mm²	7.2
900–1,000 N/mm²	7.8
> 1,000 N/mm²	8.5

Higher tensile strength wheels allow proportionally higher contact loads for the same wheel diameter and rail combination. Crane wheels are typically manufactured from cast steel (ZG340-640, ZG42CrMo) or forged steel, with tensile strengths ranging from 600 to over 1,000 N/mm² depending on heat treatment.

---

Worked Example

Given:

• Lifting capacity Q = 10 t
• Trolley weight G_t = 2 t
• Total crane weight G = 8 t
• Crane span L = 15 m
• Min hook distance e_min = 0.5 m
• Max hook distance e_max = 14.5 m
• Total wheels N_L = 4

Step 1: n = 4 / 2 = 2 wheels per rail

Step 2: PQ = (10 + 2) × (15 − 0.5) / (15 × 2) × 10 = 12 × 14.5 / 30 × 10 = 58.00 kN

Step 3: PZ = (8 − 2) / 4 × 10 = 15.00 kN

Step 4: PMAX = 58.00 + 15.00 = 73.00 kN

Step 5: PXZ = 2 × (15 − 14.5) / (15 × 2) × 10 = 2 × 0.5 / 30 × 10 = 0.33 kN

Step 6: PMIN = 0.33 + 15.00 = 15.33 kN

Wheel inspection (QU 70 rail, wheel diameter 300 mm, tensile strength 700–800 N/mm²): P_allowable = 1.9 × 6.5 × 300 × 58 / 1000 = 215.8 kN → Passed (73.00 kN < 215.8 kN)

---

How Trolley Position Affects Wheel Load

The wheel load on a given rail is not fixed — it varies continuously as the trolley travels across the span. Understanding this relationship is essential for both structural design and fatigue assessment.

Maximum Load Position

When the trolley (carrying the rated load) approaches the rail being checked as closely as possible (trolley at e_min from that rail), the reaction on that rail is at its maximum. The rail on the opposite side simultaneously receives its minimum reaction. This is the governing condition for structural design of the runway beam on the loaded side.

Minimum Load Position

When the trolley is at its furthest position from the rail (at e_max), only the trolley self-weight contributes to the reaction on that rail, and the crane bridge self-weight is shared equally across all wheels. PMIN represents this condition. It is used to check whether rail uplift can occur and to size anti-lift fastenings where required.

Symmetric vs. Asymmetric Cranes

For standard cranes with centred girders and symmetric reeving, e_min on one rail equals (L − e_max) on the opposite rail. For cranes with offset girders, double-trolley configurations, or underslung hoists, e_min and e_max must be determined from the actual trolley geometry and hoist centerline position.

---

Rail Selection Guide Based on PMAX

Once PMAX is known, use it as the primary input for rail selection. The following ranges serve as a starting point — final selection requires confirmation of wheel diameter and material per the inspection formula.

PMAX Range	Typical Rail Selection	التطبيق النموذجي
< 50 kN	P 18 – P 24	Light workshop cranes, ≤ 5 t capacity
50–100 kN	P 38 – P 43	General industrial overhead cranes, 5–16 t
100–200 kN	P 50 – QU 70	Heavy industrial cranes, 20–50 t
200–400 kN	QU 80 – QU 100	Port cranes, heavy gantry cranes, 50–100 t
> 400 kN	QU 120 and above	Very heavy port cranes, shipyard cranes, > 100 t

---

Why the Wheel Diameter Inspection Matters

The contact between a crane wheel and the rail head is a Hertzian contact problem: a cylinder (the wheel) pressing against a flat or near-flat surface (the rail head). The contact stress is not uniform — it peaks at the centre of the contact patch and falls to zero at the edges. Excessive contact stress causes:

Surface fatigue (spalling): Repeated loading beyond the elastic shakedown limit initiates subsurface fatigue cracks that propagate to the surface, eventually breaking out flakes of metal from the wheel tread or rail head. Spalling dramatically increases rolling resistance, vibration, and noise.

Plastic deformation (flattening): Very high contact stress causes permanent deformation of the wheel tread or rail head, creating flat spots that generate impact loads on every revolution.

Rail head wear: Accelerated wear shortens rail replacement intervals and increases maintenance cost. Incorrect wheel-rail matching (too small a wheel on a wide-headed rail) concentrates contact in a narrow band, increasing unit pressure far beyond what the nominal calculation suggests.

The inspection formula P_allowable = 1.9 × σ × D × w / 1000 applies the permissible contact stress principle from GB/T 3811, limiting contact stress to a level consistent with long-term fatigue life at the specified material strength.

---

أنواع الرافعات المناسبة

• Single girder overhead travelling cranes
• Double girder overhead travelling cranes
• Single girder gantry cranes
• Double girder gantry cranes
• رافعات شبه جسرية
• Underslung cranes (adapted — wheel load acts upward on lower flange)
• Portal bridge cranes

---

الأسئلة الشائعة

Q1：What is the difference between wheel load and wheel pressure?

The terms are used interchangeably in most crane engineering contexts. Both refer to the vertical force transmitted from a single crane wheel to the runway rail, expressed in kilonewtons (kN). "Wheel pressure" emphasises the contact mechanics aspect; "wheel load" emphasises the structural load aspect. This calculator outputs both PMAX and PMIN as forces in kN.

Q2：Should I include the hook block weight in the lifting capacity Q or trolley weight G_t?

Include the hook block weight in G_t (trolley weight), not in Q. The lifting capacity Q is the net payload — the load being lifted by the customer. The hook block, shackle, and any lifting beam travel with the trolley at all times and are part of the trolley assembly mass. Many hoist manufacturers publish the hook block weight separately in their data sheets.

Q3：My crane has 8 wheels (4 per rail) — does the formula still apply?

Yes. Enter N_L = 8, and the calculator automatically sets n = 4 wheels per rail. The formula distributes the load equally among all wheels on a given rail. For cranes with unequal wheel spacing or asymmetric end carriages, the equal-distribution assumption is a simplification — a more detailed analysis using the actual wheel positions and beam reactions may be required for very large or non-standard cranes.

Q4：What if PMIN is very close to zero or negative?

A PMIN near zero means the wheels on that rail are nearly unloaded when the trolley is at maximum distance. A negative result (which the formula can theoretically produce for very asymmetric configurations) indicates rail uplift — the crane structure is trying to lift off the rail. This requires anti-lift rail clips or hold-down fastenings and must be flagged to the structural engineer. Check that e_max and G_t values are correct if an unexpected negative PMIN appears.

Q5：Can this calculator be used for the runway beam design directly?

The PMAX value from this calculator is the static wheel load input for runway beam design. For the full runway beam structural check, PMAX must be multiplied by the dynamic factor Φ (typically 1.1–1.3 depending on crane class) to obtain the design wheel load, and the moving concentrated load must be positioned to produce the maximum bending moment and shear in the beam. Runway beam design also requires consideration of lateral horizontal forces (crane surge) per the applicable standard.

Q6：Which standard does this calculator follow?

The wheel load formula and the wheel diameter inspection formula follow GB/T 3811 (Chinese national standard for crane design). The rail parameter table covers both P-type rails (GB/T 11264) and QU-type crane rails (GB/T 2585), which are the two most widely used crane rail series in China and export markets. The underlying engineering principles are consistent with ISO, FEM, and EN crane standards, though those standards may use slightly different notation and safety factors.

Q7：What is the effect of using more wheels (e.g. 8 instead of 4)?

Increasing the total wheel count N_L reduces PMAX proportionally for the self-weight component (PZ), since the crane weight is shared across more wheels. It has a smaller effect on the load component (PQ), which depends on trolley position and span. Using 8 wheels instead of 4 on a heavy crane allows use of a lighter rail section, smaller wheel diameter, and lighter runway beam — at the cost of a more complex end carriage design.