Restrain / Stopper Force Calculator

Formulas Used

• Thermal movement: ΔL = α · L · ΔT, then effective Δ = max(0, ΔL − gap).
• Thermal restraint force: F = k · Δ (k in N/mm, Δ in mm).
• Inertial force: F = m · a, with optional amplification (DAF).
• Friction limit: F_f = μ · N.
• Impact average force: F_avg = m · Δv / Δt, with optional amplification (DAF).
• Design force: F_design = F_basis · safety factor.

How to Use This Calculator

1. Enable the load sources that apply to your stop or restraint.
2. Enter inputs with consistent units (m, mm, kg, kN, seconds).
3. Choose a combination method: maximum or sum.
4. Set safety and amplification factors per your project criteria.
5. Submit to view results above the form, then export the report.
6. Use the design force to size the stopper, welds, bolts, and anchors.

Professional Article

1) What restrain and stopper forces represent

Stops and restraints limit movement in pipes, ducts, frames, works, and skids. The design force is the action the stop must resist when motion is arrested or prevented. Common sources are thermal growth, wind sway, seismic drift, equipment start‑up, and impact. A clear basis helps coordinate anchors, welds, bolts, and embeds.

2) Thermal movement converted to force

Thermal expansion creates free movement ΔL = α·L·ΔT. If movement is blocked, the system behaves like a spring. With equivalent stiffness k (from spacing, EI, or vendor data), restrain force is F = k·Δ. Field gaps and sliding bearings can reduce locked‑in force.

3) Inertial loads from acceleration

When a moving mass is stopped, use F = m·a as a first model. In construction, a may come from crane braking, trolley travel, conveyor surge, or seismic acceleration. A practical input is a fraction of gravity (g), but project criteria should govern the value.

4) Friction and normal load checks

Some systems rely on friction before a hard stop engages. Maximum friction is Ff = μ·N, where N is the normal force. Dry steel‑on‑steel μ may be about 0.3, while PTFE interfaces may be 0.05 to 0.10. Because μ varies with condition, use conservative assumptions.

5) Impact and impulse approximation

If a component hits a stopper at velocity v, average impact force can be estimated by impulse: Favg = m·Δv/Δt. Short contact times produce high forces; adding a bumper increases Δt and lowers demand. Where required, apply a peak multiplier specified by your standard.

6) Applying design and load factors

For a quick check, multiply the governing force by a chosen safety factor, then compare to stopper capacity and fastener strength. If your project uses load combinations, keep thermal, wind, and inertial effects separate and combine per the governing code. Document assumptions for review.

7) Detailing considerations on site

Good detailing prevents unintended load paths. Provide shims or grout for full bearing, avoid eccentric contact, and align stops with the travel direction. Check concrete breakout, edge distances, weld sizes, and plate bending. Confirm adjacent items can tolerate remaining movement after engagement.

8) Using calculated results effectively

Use the calculator to test scenarios: free movement, partial gap closure, and worst‑case acceleration. Record inputs, units, and factors in the CSV/PDF output. Recheck after changes in span, mass, support type, or temperature. Clear calculations reduce rework and improve commissioning safety.

FAQs

1) What stiffness value should I use for thermal restraint?

Use an equivalent stiffness from vendor data, analysis, or a tested detail. For pipes, stiffness depends on span, guides, and support flexibility. If uncertain, run sensitivity checks and adopt a conservative value with documented assumptions.

2) Should I use “max” or “sum” for combining forces?

Use the approach required by your project method. “Max” is common when loads are alternative cases. “Sum” can be used for conservative screening when multiple effects may act together. Always follow your governing design standard.

3) Why does adding a gap reduce thermal force?

A gap allows free movement before the stop engages. Only movement beyond the gap is restrained, so the effective displacement is smaller. If the gap closes during operation, the force rises sharply with increasing displacement.

4) Is the impact force shown a peak or an average?

The calculation uses an average force from impulse over the stop time. Peak force can be higher depending on stiffness and contact conditions. If your criteria require peak estimates, apply a suitable multiplier or perform a detailed dynamic model.

5) How do I choose friction coefficient μ?

Use values appropriate to materials and surface condition. Clean steel interfaces are often higher than lubricated or PTFE sliding interfaces. Because μ varies with wear, moisture, and debris, use conservative inputs and inspect critical contact surfaces.

6) What safety factor is typical for stopper design?

It depends on the standard, consequence of failure, and uncertainty in inputs. A screening range of 1.3 to 2.0 is common for preliminary checks, but final design should follow your code, specifications, and approved engineering judgement.

7) Can I use this for anchors in concrete?

Yes, as a demand estimate. After you obtain design force, check anchor tension and shear, concrete breakout, edge distance, and embedment. Also confirm load direction, eccentricity, and any prying effects from the stopper plate.

Accurate stopper forces help prevent damage, delays, and injuries.