Calculator Inputs
Formula Used
Loads and basic stresses
- Vd = V·γV and Hd = H·γH
- A = π(D/2)²
- σavg = (Vd·1000)/A in MPa
- τavg = (Hd·1000)/A in MPa
Eccentricity and rotation
- σmax = σavg·(1 + 8e/D)
- σmin = σavg·(1 − 8e/D)
- Lift-off warning when σmin < 0
- θrad = θmrad/1000, δ = θrad·(D/2)
- γ = δ / t and check γ ≤ γallow
How to Use This Calculator
- Enter service vertical and horizontal loads for the bearing.
- Set load factors to match your design combination.
- Provide bearing diameter and any expected eccentricity.
- Enter allowable stresses and rotation limits from standards or supplier.
- Submit to view checks and utilization above the form.
- Export CSV or PDF for traceable project documentation.
Example Data Table
| Case | V (kN) | H (kN) | D (mm) | e (mm) | θ (mrad) | σallow (MPa) | μ | Expected outcome |
|---|---|---|---|---|---|---|---|---|
| Example A | 2500 | 250 | 650 | 15 | 12 | 45 | 0.05 | PASS for typical bridge case |
| Example B | 3200 | 420 | 600 | 40 | 18 | 40 | 0.03 | May FAIL due to σmax or sliding |
| Example C | 1800 | 120 | 550 | 10 | 22 | 45 | 0.06 | May FAIL rotation limit or strain |
Technical Notes and Guidance
1) Purpose of this check
Pot bearings transfer large vertical reactions while allowing rotation with low sliding resistance. This calculator provides a practical screening workflow: factored actions, average and peak stresses, sliding resistance from friction, and a rotation-based shear strain estimate. Use it for early sizing, comparison of options, and consistent reporting.
2) Typical input ranges seen on bridges
For many highway spans, individual bearing service reactions commonly fall between 1,000–6,000 kN, with horizontal actions often 2–15% of the vertical load depending on braking, wind, and restraint layout. Pot diameters in the 350–900 mm range are frequently encountered, while eccentricities of 5–30 mm may occur from geometry, misalignment, or construction tolerances.
3) Load factoring and combinations
The design actions are computed as Vd = V·γV and Hd = H·γH. Many projects adopt γ values around 1.2–1.5 for ultimate checks, but you should enter the factors that match your governing combination and specification. Keeping the unfactored inputs visible helps reviewers trace assumptions.
4) Bearing stress evaluation
Average compressive stress is σavg = (Vd·1000)/A, where A = π(D/2)² in mm² and stress is reported in MPa (N/mm²). The tool also estimates peak stress using a linear pressure model for a circular footprint: σmax = σavg·(1 + 8e/D). This highlights sensitivity to eccentricity as D reduces.
5) Eccentricity, uplift, and seating
The minimum stress is estimated as σmin = σavg·(1 − 8e/D). When σmin becomes negative, partial separation (lift-off) may occur, increasing local demand and risking uneven wear. If the warning appears, consider larger diameter, reduced eccentricity, improved leveling, or refined distribution analysis.
6) Sliding check using friction resistance
A quick sliding screen is performed with Hd ≤ μ·Vd. Low-friction interfaces (for example, PTFE-based) can have μ near 0.03–0.08 depending on pressure, temperature, and surface condition. If sliding fails, review restraint layout, consider guided bearings, or verify μ and design philosophy with the supplier.
7) Rotation demand and shear strain
Rotation demand is entered in mrad and converted to radians. The edge displacement is approximated by δ = θ·(D/2), then shear strain by γ = δ/t. This relates rotation to deformation in the elastomeric layer. Keep thickness and allowable strain consistent with the bearing’s internal detailing and test data.
8) Documentation, review, and quality control
Use the utilization ratios to focus review: stress, shear, rotation strain, and sliding are each reported. As good practice, record the load case name in “Notes”, export the CSV/PDF, and attach it to the design package. For final approval, confirm limits, materials, and long-term effects with the manufacturer and governing code.
FAQs
1) Does this replace manufacturer design?
No. It is a screening and reporting tool. Final bearing selection must follow supplier calculations, test data, and project specifications, especially for stability, seals, and long-term effects.
2) Why does eccentricity increase σmax so much?
The pressure model assumes a linear distribution over a circular footprint. As e grows relative to D, the compression block shifts, raising σmax and reducing σmin, which can trigger partial uplift.
3) What friction coefficient should I use?
Use project-accepted values for the sliding interface. For low-friction sliding surfaces, μ is often in the 0.03–0.08 range, but confirm with supplier data and the governing specification.
4) Why is τavg checked using area A?
It provides a consistent average shear stress indicator for comparing options. Actual shear transfer mechanisms depend on components and detailing, so treat τavg as a simplified check unless your code specifies otherwise.
5) How do I choose σallow and γallow?
Take limits from your code, project notes, and manufacturer documentation. Use values that match the controlling limit state and temperature range, and ensure they correspond to the actual bearing materials.
6) What if rotation fails but stresses pass?
Increase effective deformation capacity by adjusting bearing type, increasing elastomer thickness, reducing rotation demand via geometry, or selecting a different bearing configuration. Always verify rotation with supplier data.
7) Can I use this for multiple bearings at once?
The form evaluates one bearing per submission. For groups, run each case and export CSV files, or adapt the code to loop through a project schedule and generate a consolidated report.