Calculation
S = (G·b/2) / (F·h)
The stabilising moment of self-weight about the tipping edge is compared against the tipping moment of the lateral force.
Dubbel Mechanik B 1.4.5 Standsicherheit: S = ΣMS/ΣMK (Standmomente zu Kippmomente um die Kippkante)
Tipping stability of a body under lateral force
The stabilising moment of self-weight about the tipping edge is compared against the tipping moment of the lateral force.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Tipping safety factor S — Ratio of stabilising to tipping moment about the tipping edge; S<1 means tipping occurs.
- Weight force G — Weight force of the body, acting centrally over the base area.
- Base width b — Width of the base area in the tipping direction; the tipping edge lies at its far side.
- Lateral force F — Horizontal force causing the tipping tendency.
- Application height h — Height at which the lateral force acts on the body.
Example
G=1,000 N, b=0.6 m, F=200 N and h=1.2 m give S=(1000·0.3)/(200·1.2)=1.25.
Assumptions and limits
Rigid body with centrally acting weight and an ideally flat, unyielding base; friction, sliding before tipping and dynamic shock loads are excluded.
Understand Tipping stability of a body under lateral force
This calculator determines the safety factor against tipping of a block-shaped body, such as a cabinet, machine or shelving unit, under a laterally applied force.
What does this quantity describe?
Self-weight G acts stabilising with lever arm b/2 to the tipping edge at the base's far side; lateral force F acts to tip with lever arm h. Safety factor is S=(G·b/2)/(F·h).
Formula and variables
S = (G·b/2) / (F·h)
S = (G·b/2) / (F·h)
| Symbol / input | Meaning |
|---|---|
| Tipping safety factor S | Ratio of stabilising to tipping moment about the tipping edge; S<1 means tipping occurs. |
| Weight force G | Weight force of the body, acting centrally over the base area. |
| Base width b | Width of the base area in the tipping direction; the tipping edge lies at its far side. |
| Lateral force F | Horizontal force causing the tipping tendency. |
| Application height h | Height at which the lateral force acts on the body. |
Choose the inputs correctly
G is the body's weight force, b the base width in the tipping direction, F the lateral force and h its point of application.
How to use the calculator
Determine G from mass (G=m·g), b from the actual base footprint in the tipping direction, and F and h from the worst-case assumed loading.
Worked example
G=1,000 N, b=0.6 m, F=200 N and h=1.2 m give S=1.25.
Understand the result and units
S<1 means calculated tipping; a low F or h close to the base is far more stabilising than a wider base alone.
G and F are forces, b and h lengths. S is dimensionless.
Typical applications
Rough tipping-stability checks of cabinets, machine frames, shelving and similar free-standing objects under lateral load, e.g. from leaning or bumping.
Assumptions, limits and common mistakes
Rigid body with centrally acting weight and an ideally flat, unyielding base; friction, possible sliding before tipping, dynamic shocks and any pre-existing tilt are excluded.
Common mistake: Do not use the full base width instead of half of it (the lever arm to the tipping edge); the formula already accounts for b/2 itself.
Frequently asked questions
What is “Tipping stability of a body under lateral force” used for?
Rough tipping-stability checks of cabinets, machine frames, shelving and similar free-standing objects under lateral load, e.g. from leaning or bumping.
Where do the input values come from?
G is the body's weight force, b the base width in the tipping direction, F the lateral force and h its point of application.
What does the result not cover?
Rigid body with centrally acting weight and an ideally flat, unyielding base; friction, possible sliding before tipping, dynamic shocks and any pre-existing tilt are excluded.