Crane Main Girder Section Moment of Inertia Calculator

The crane main girder section moment of inertia calculator computes the bending stiffness of crane main girders. A higher moment of inertia indicates greater rigidity and less deformation under load. For overhead and gantry cranes, this value directly defines load capacity and evaluates risks of plastic deformation and fracture. The calculated result can also be substituted directly into the deflection formula to prevent girder distortion and sway during travel and braking.

Calculation Formula

The section moment of inertia Iₓ is calculated by summing the individual contributions of each plate component using the parallel axis theorem:

\[
\begin{aligned}
I_x &= \frac{B_1 t_1^3}{12} + A_1 d_1^2 + \frac{B_2 t_2^3}{12} + A_2 d_2^2 \\
&\quad + \frac{\delta_1 h_w^3}{12} + A_3 d_3^2 + \frac{\delta_2 h_w^3}{12} + A_4 d_4^2
\end{aligned}
\]

Section Centroid

\[\bar{y} = \frac{A_1 y_1 + A_2 y_2 + A_3 y_3 + A_4 y_4}{A_1 + A_2 + A_3 + A_4}\]

Plate-to-Centroid Distances

\[d_1 = \bar{y} – y_1 \quad d_2 = \bar{y} – y_2 \quad d_3 = \bar{y} – y_3 \quad d_4 = \bar{y} – y_4\]

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Parameter Definitions

Symbol	Description	Unit
B₁	Top flange width	cm
B₂	Bottom flange width	cm
t₁	Top flange thickness	cm
t₂	Bottom flange thickness	cm
δ₁	Main web thickness	cm
δ₂	Secondary web thickness	cm
h_w	Web height	cm
A₁	Top flange area	cm²
A₂	Bottom flange area	cm²
A₃	Main web area	cm²
A₄	Secondary web area	cm²
d₁ ~ d₄	Distance from each plate centroid to section centroid	cm
ȳ	Section centroid position	cm
Iₓ	Section moment of inertia (output)	cm⁴

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How to Use

1. Input section dimensions — Enter beam height h, top and bottom flange widths (B₁, B₂), top and bottom flange thicknesses (t₁, t₂), main web thickness δ₁, and secondary web thickness δ₂. All inputs are in cm.
2. Review intermediate parameters — The calculator automatically outputs each plate area (A₁ to A₄), plate centroid coordinates (y₁ to y₄), and the section centroid ȳ.
3. Get the result — Click Calculate to obtain the section moment of inertia Iₓ in cm⁴.
4. Feed into deflection calculation — Enter the Iₓ result directly into the Crane Deflection Calculator to complete the girder deflection check.

Note: Iₓ corresponds to vertical loading and vertical bending of the crane main girder. It is the I value used in the deflection formula:

\[f = \frac{PL^3}{48EI}\]

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Important Notes

• This calculator is primarily applicable to rectangular hollow box-section girders (welded sections composed of top and bottom flanges and webs).
• Iₓ represents vertical bending stiffness only; horizontal-axis inertia is not included.
• Intermediate parameters (A₁ to A₄, d₁ to d₄, ȳ) are derived automatically and can be used for manual cross-checking.
• The output unit is cm⁴. When entered into the deflection calculator, values are automatically converted to m⁴.

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Why the Moment of Inertia Matters

Iₓ is the key parameter governing main girder bending resistance and directly affects the following structural properties:

• Deflection control — A higher Iₓ produces less deflection under the same load, making it easier to satisfy ISO and FEM limits.
• Load capacity — Determines whether the girder will undergo plastic deformation under the rated lifting load.
• Fatigue life — Insufficient stiffness increases stress cycle amplitude, accelerating structural fatigue failure.
• Travel stability — Low girder stiffness causes vibration and sway during trolley travel and braking.

Optimizing the cross-section at the design stage using this calculator allows engineers to maintain adequate safety margins while minimizing steel weight and reducing fabrication costs.

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Applicable Crane Types

Crane Type	Notes
Single girder overhead crane	Applicable to single box-section main girder
Double girder overhead crane	Applicable to each individual main girder
Single / double girder gantry crane	Including semi-gantry configurations
Shipyard gantry crane	Large span, heavy-duty applications
Rail-mounted gantry crane (RMG)	Heavy port lifting scenarios
Rubber-tyred gantry crane (RTG)	Mobile port applications
Metallurgical crane	High-temperature, heavy-duty special conditions

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Combined Use with the Deflection Calculator

This calculator works together with the Overhead and Gantry Crane Deflection Calculator to provide a complete main girder structural verification workflow:

1. Use this calculator — input section dimensions → obtain Iₓ (cm⁴)
2. Enter Iₓ into the deflection calculator → obtain maximum deflection f (m)
3. Compare against ISO / FEM deflection limits → confirm structural compliance

The two tools used in sequence cover the full process from cross-section design to deflection compliance verification.