Overhead and Gantry Crane Deflection Calculator

The overhead and gantry crane deflection calculator accurately calculates the vertical deflection of loaded girders by inputting wheel load, span length, and section moment of inertia. It evaluates girder stiffness and structural performance, prevents rail gnawing, permanent deformation, and unstable operation, and verifies whether deflection values comply with the limits set by ISO and FEM standards — ensuring safe crane operation, reduced structural fatigue, and extended service life.

Calculation Formula

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

Symbol	Description	Unit
f	Maximum deflection	m
P	Concentrated wheel load (trolley at mid-span)	N
L	Main beam span	m
E	Elastic modulus of steel (2.06 × 10¹¹)	Pa
I	Moment of inertia of the cross-section	m⁴

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How to Use

1. Input P — Enter the concentrated load in Newtons (N). This is the wheel load when the trolley is positioned at the most unfavorable (mid-span) location.
2. Input L — Enter the main beam span in meters (m).
3. Input I — Enter the moment of inertia in cm⁴. The calculator automatically converts this to m⁴ during computation.
4. Calculate — The tool computes the maximum vertical static deflection and checks compliance against ISO and FEM deflection limits.

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Important Notes

• The elastic modulus of steel is automatically set to 2.06 × 10¹¹ Pa in SI units.
• Moment of inertia values entered in cm⁴ are automatically converted to m⁴ during calculation.
• This calculator is primarily applicable to main girders with rectangular hollow sections.
• The load P is modeled as a concentrated load at mid-span — representing the trolley at the most unfavorable position.
• Only vertical static deflection is calculated; dynamic load coefficients are not considered.

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Applicable Crane Types

Crane Type	Span Limit	Cantilever Limit
Bridge crane (overhead crane)	≤ 30 m	—
Gantry crane	≤ 30 m	No cantilever, or cantilever ≤ 0.15L
Semi-gantry crane	≤ 30 m	No cantilever, or cantilever ≤ 0.15L

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Why Deflection Matters

Excessive girder deflection leads to several operational and structural problems:

• Rail gnawing — misalignment between the trolley wheels and rail caused by excessive beam bending
• Permanent deformation — repeated overloading beyond elastic limits causes irreversible structural damage
• Unstable operation — load swing, vibration, and positioning errors increase with excessive deflection
• Fatigue failure — structural members subjected to repeated stress cycles will fatigue prematurely if deflection limits are not respected

By verifying deflection against ISO and FEM standards at the design stage, engineers can optimize the girder cross-section, reduce unnecessary material weight, and ensure long-term structural reliability.

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Standards Reference

This calculator checks deflection compliance against the following international standards:

• ISO standard — deflection limit typically expressed as a fraction of span (e.g., L/700 or L/800 depending on crane class)
• FEM standard — European Federation of Materials Handling deflection requirements for overhead and gantry cranes

Always consult the specific standard edition and crane duty class applicable to your project for precise limit values.