Crane Calculations

How to Calculate Port Crane Loads, Steel Stress, and Hydraulic Test Capacity

The handful of formulas that repeat on every ship-to-shore crane and RTG, worked with real units and numbers, from hoist motor sizing to paint coverage.

Port crane fabrication runs on a small set of calculations that repeat on every ship-to-shore (STS) crane, RTG, and mobile harbor crane. Undersize the hoist motor and the drive stalls at rated load. Get the girder section modulus wrong and the box fails its proof lift. The four that matter most are main hoist power, the structural steel stress check, hydraulic test capacity, and paint spreading rate, with rope tension linking the first to the last. This guide works each one with real units and numbers. The Hoist Motor Load, Structural Steel Yield, Hydraulic System Test Capacity, and Paint Coverage Cost tools automate them, but you should know what sits underneath.

Main hoist power follows P = (m x g x v) / eta, where m is the load under the spreader in kg, g is 9.81 m/s2, v is hoisting speed in m/s, and eta is the mechanical efficiency of gearbox, rope, and drum. Take an STS crane rated at 65 t under spreader hoisting at 90 m/min, which is 1.5 m/s, with eta at 0.90. P = (65,000 x 9.81 x 1.5) / 0.90 = 1,062,750 W, so 1,063 kW. Add spreader and headblock mass of roughly 12 t and the number climbs near 1,260 kW. Size the motor to the next frame, typically 1,400 kW continuous, using the Hoist Motor Load tool.

Structural Steel Yield checks whether a member stays below allowable stress under the design moment. Allowable bending stress is 0.60 x Fy. For S355 plate, Fy is 355 MPa, so the allowable is 213 MPa. Required section modulus is S = M / allowable stress. A trolley girder carrying a design moment of 8,000 kN.m needs S = 8,000,000 / 213,000,000 = 0.0376 m3, or 37,600 cm3. Pick a box section that beats it, then confirm actual stress M / S_actual sits under 213 MPa. Member weight follows from cross-section area times length times 7,850 kg/m3, which feeds every downstream cost and the crane deadweight.

Hydraulic System Test Capacity starts from proof pressure, set at 1.5 x maximum working pressure in most crane specs. A luffing circuit working at 250 bar tests at 375 bar. Cylinder output is F = P x A. A 250 mm bore gives A = pi/4 x 0.25^2 = 0.0491 m2, so at 250 bar, which is 25 MPa, force is 25,000,000 x 0.0491 = 1,227 kN. Reservoir volume follows the 3 to 5 minute rule: for a pump delivering 180 L/min, size the tank at 540 to 900 L. Pump flow itself is displacement x rpm x volumetric efficiency, so 100 cm3/rev at 1,500 rpm and 0.95 gives 142.5 L/min.

Paint Coverage Cost rests on theoretical spreading rate = (volume solids percent x 10) / DFT in microns. A high-build epoxy at 70 percent solids applied at 125 microns gives (70 x 10) / 125 = 5.6 m2/L. Apply a practical loss factor for overspray and surface profile, often 30 percent on structural steel, and you get 3.92 m2/L. An STS crane with roughly 8,000 m2 of coated surface across three coats needs 8,000 / 3.92 x 3, which is about 6,122 L. The blast profile of 50 to 75 microns and film thickness gauge readings feed the same math and the material budget.

Rope tension per fall is T = W / (n x eta_s), where W is total suspended load, n is the number of falls in the reeving, and eta_s is combined sheave efficiency, about 0.98 per sheave. A 77 t suspended load, being 65 t plus a 12 t spreader set, on an 8-fall reeving with combined efficiency near 0.92 gives T = 755,370 / (8 x 0.92) = 102,632 N, so 103 kN per fall. Divide the rope minimum breaking load by this tension and confirm the safety factor clears 5.0, the common crane requirement. This tension also sets drum torque and feeds back into the Hoist Motor Load result.

Every input traces to a source document. Rated load and speeds come from the crane datasheet or the client spec. Fy and plate sizes come from the mill certificate and EN 10025. Working pressures and bore sizes come from the hydraulic schematic. Solids content and recommended DFT come from the paint technical data sheet. Reeving and sheave counts come from the mechanical general arrangement drawing. Run the formulas in order, since hoist load sets rope tension, rope tension sets drum and motor torque, and steel weight sets both paint area and deadweight. Change one input and re-run the whole chain rather than a single number.

Published 2026-07-02.