BIZOMAT MAKEOS · Mechanics
Portable Gantry Crane Check (Beam Stress and Deflection, A-Frame Leg Buckling, Wheel Load)
For a portable A-frame gantry with an I-beam and splayed legs, are the beam stress and deflection within limits, will the legs buckle, and what does each castor carry?
Check of a portable gantry crane: the section properties of the I-beam (as the section shapes tool), the bending moment, stress and deflection with the load at mid-span (as the beam cases tool for a central point load), the end reaction with the load at one end, the axial force in each splayed leg and its buckling capacity and safety factor (as the column buckling tool for a tubular leg), and the load on each castor, against your allowables.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load including hoist and trolley | N | Rated load plus hoist, trolley and an allowance for dynamic effects. |
| Beam span between leg centres | mm | Span of the beam between the centres of the two A-frames. |
| Beam (I) | ||
| Overall depth | mm | Beam depth. |
| Flange width | mm | Flange width. |
| Flange thickness | mm | Flange thickness. |
| Web thickness | mm | Web thickness. |
| Modulus of elasticity | GPa | Modulus of elasticity. |
| Allowable bending stress | MPa | Allowable bending stress for the beam. |
| Deflection limit (span ÷) | Largest deflection as a fraction of the span. | |
| Legs (two per end) | ||
| Leg vertical height | mm | Vertical height of each leg. |
| Leg splay from vertical | ° | Angle of each leg from vertical in the A-frame. |
| Leg tube outside diameter | mm | Outside diameter of each leg tube. |
| Leg wall thickness | mm | Wall thickness of each leg. |
| Leg yield strength | MPa | Yield strength of the leg. |
| Leg effective length factor | Effective length factor for the leg ends. | |
| Required buckling safety factor | Safety factor against leg buckling you need. | |
| Castor rating | N | Load rating of each castor (one under each leg). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Load including hoist and trolley
- What it is
- The total load hanging from the beam: rated load plus the hoist and trolley, with any allowance you make for dynamic effects.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 100000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Every stress, deflection and leg load rises in direct proportion.
- Get it right
- Enter newtons, not kilograms; multiply a mass in kg by standard gravity to get newtons.
What this means: Beam span between leg centres
- What it is
- The beam span between the centres of the two A-frames. The tool places the load at mid-span for the beam checks.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Bending stress rises in direct proportion to span and deflection with its cube.
- Get it right
- Measure leg centre to leg centre, not the overall beam length.
Beam (I)
What this means: Overall depth
- What it is
- The overall depth of the I-beam, from the outside of one flange to the outside of the other.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the actual section depth from the steel table, not the nominal size.
What this means: Flange width
- What it is
- The width of the beam’s flanges.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the steel table for the section.
What this means: Flange thickness
- What it is
- The thickness of each beam flange.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10.7 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the steel table; tapered flanges are given as a mean thickness.
What this means: Web thickness
- What it is
- The thickness of the beam web joining the two flanges.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7.1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the steel table for the section.
What this means: Modulus of elasticity
- What it is
- The elastic modulus of the beam and leg material, used for beam deflection and leg buckling.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter it in GPa, not MPa; take it from the material standard.
What this means: Allowable bending stress
- What it is
- The bending stress you allow in the beam.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 10000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 160 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Set it from the beam material and the crane or structural design code that applies.
What this means: Deflection limit (span ÷)
- What it is
- The divisor of the span that sets the largest beam deflection you accept: allowed deflection = span ÷ this number.
- Units and format
- Enter a plain number with no unit. The form accepts 10 to 100000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- A larger number is stricter; take it from the crane standard or hoist maker.
Legs (two per end)
What this means: Leg vertical height
- What it is
- The vertical height of each A-frame leg from the castor to the beam.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure vertically; the tool works out the sloping leg length from the splay angle.
What this means: Leg splay from vertical
- What it is
- The angle each leg leans out from vertical in the A-frame.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 45°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More splay raises the leg force and the leg length.
- Get it right
- Measure from vertical, not from the floor.
What this means: Leg tube outside diameter
- What it is
- The outside diameter of each leg tube.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 88.9 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For pipe, use the actual outside diameter from the pipe table.
What this means: Leg wall thickness
- What it is
- The wall thickness of each leg tube.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the specified wall, not a nominal schedule name.
What this means: Leg yield strength
- What it is
- The yield strength of the leg tube material, used where shorter legs yield as they buckle.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 5000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the minimum yield from the material standard or mill certificate.
What this means: Leg effective length factor
- What it is
- The multiplier on the sloping leg length that gives its effective buckling length, depending on how the ends are held.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 2.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger factor lowers the buckling load.
- Get it right
- Choose it from a structural design reference for the real end conditions.
What this means: Required buckling safety factor
- What it is
- The lowest ratio of leg buckling load to leg force you will accept.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 20. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Set it from the design code or your company rules.
What this means: Castor rating
- What it is
- The load rating of each castor, one under each leg, compared with the load on a castor when the trolley is at one end.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 100000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the maker’s rating for the floor and speed, in newtons.
Method and formulas
- A, I and Z of the I-beam (as the section shapes tool); M = W L ÷ 4 and deflection W L³ ÷ 48EI at mid-span (as the beam cases tool).
- Load at one end: end reaction = W; leg force = W ÷ (2 cos β); leg length = height ÷ cos β; buckling as the column buckling tool.
- Castor load = W ÷ 2 (two legs at the loaded end).
- Example: beam at 37.505 MPa and 1.6669 mm; legs carry 10,353 N each with a factor of 20.817.
Limitations
- Self-weight of beam and frames left out; add it to the load for long or heavy gantries.
- In-plane loads only; side loads from moving or pulling the gantry need bracing checks.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a workshop gantry for a heavier hoist
- Size the beam and legs of a new gantry
- Check castor ratings for a gantry
Who it is for
- Design engineers
- Maintenance engineers
- Fabricators
What you get
- Beam section, stress and deflection
- Leg force and buckling
- Castor load
Interpreting the result
- Widening the leg splay makes the gantry steadier but raises the leg force and length.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 234–246, 257–277, 281–287. Topic reference; no source tables or recommended settings are reproduced.
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