About Overturning Moment Calculation
Information
This overturning moment calculation checks structural stability against overturning for walls, slabs, columns, retaining elements, and similar structures subjected to lateral loads. The calculation compares the overturning and stabilizing moments and accounts for the base geometry, structural and foundation mass, additional soil mass for the first scheme, and either a selected horizontal load or a directly specified overturning moment.
The results include the resultant horizontal force, its lever arm, overturning and stabilizing moments, required stabilizing moment, moment reserve or deficit, stability factor, and eccentricity of the resultant vertical load relative to the center of the base.
Guidelines and recommendations
Units and weight conversion
Forces and moments. Loads can be entered in kN or kgf, while moments can be entered in kN·m or kgf·m. The calculation uses the standard acceleration due to gravity g = 9.80665 m/s2 and the following conversion relationships:
1 kgf = 9.80665 N
1 kN = 101.971621 kgf
1 kgf·m = 0.00980665 kN·m
Structural mass. Masses are entered in kg. When calculating the stabilizing moment, mass is numerically converted to weight in kgf, so under standard gravity a mass of 1000 kg corresponds to a weight of 1000 kgf.
Resultant horizontal force and lever arm
Concentrated load. In this case, the resultant force Q is equal to the specified horizontal force. For the first scheme, its lever arm relative to the overturning edge is:
L = h1 + h2
For the second scheme:
L = h1
Load distributed along a length. If the load intensity q is specified in kN/m or kgf/m, the calculator first replaces the distributed load with an equivalent resultant force. For the first scheme, the load acts over a height h3:
Q = q · h3
L = h1 + h2 + h3/2
For the second scheme, the load acts over a height h2:
Q = q · h2
L = h1 + h2/2
Heights are entered in mm and converted to meters before multiplication by the load. The resultant force is assumed to act at the midpoint of the uniformly loaded section.
Load distributed over an area. When pressure q is specified in kN/m2 or kgf/m2, the resultant force is equal to the pressure multiplied by the area of the loaded rectangular section:
Q = q · h · b
For the first scheme, h = h3 is used, while for the second scheme h = h2. The height and width b are entered in mm and converted to meters. The lever arm of the resultant force is then determined in the same way as for a load distributed along a length.
Overturning moment
Calculation from a horizontal load. After determining the resultant force and its lever arm, the overturning moment about the edge of the base is calculated as:
Mover = Q · L
Directly specified moment. If the overturning moment has already been calculated, it is used directly as Mover. In this mode, the horizontal force and load application heights do not take part in the overturning moment calculation.
Stabilizing moment for the first scheme
Base width. The total foundation width in the overturning direction is:
B = a1 + a2
Foundation. Its weight is assumed to act at the center of the base, so its lever arm relative to the overturning edge is B/2.
Supported structure. The lever arm of its weight is taken as a1, which is the distance from the selected overturning edge to the line of action of its weight according to the scheme.
Soil above the foundation. If soil mass is included in the calculation, its weight is also assumed to act at the center of the base with a lever arm of B/2.
The total stabilizing moment for the first scheme is:
Mstab = Gf · B/2 + Gs · a1 + Gsoil · B/2
The last term is included only when the mass of soil above the foundation is taken into account.
Stabilizing moment for the second scheme
Position of self-weight. For a rectangular structure, the resultant self-weight is assumed to act at the center of a base of width a. Its lever arm relative to the overturning edge is therefore a/2:
Mstab = G · a/2
Stability factor and required safety margin
Stability factor. After both moments have been calculated, their ratio is determined:
k = Mstab / Mover
A value of k = 1 means that the stabilizing and overturning moments are equal. The higher the value of k, the greater the margin relative to the overturning limit.
Required coefficient. The calculator compares the calculated factor with the user-defined required value kreq. The initial value is 1.5, and the minimum available value is 1.0. A value of 1.5 is often used as a preliminary reference, but the required margin should be selected according to the design situation and the applicable standards.
The required stabilizing moment is calculated directly from the selected coefficient:
Mreq = kreq · Mover
If Mstab is greater than Mreq, the stabilizing moment reserve is:
ΔM = Mstab - Mreq
If Mstab is lower than the required value, the moment deficit is calculated as Mreq - Mstab.
How the final assessment is selected
Moment comparison. The final assessment is made sequentially. If Mstab < Mover, the stabilizing moment is insufficient even for static equilibrium about the selected edge, so the calculation indicates overturning.
If Mstab ≥ Mover but k < kreq, overturning does not occur according to the simple moment comparison, but the specified stability margin is not achieved. If k ≥ kreq, the required overturning stability margin is considered satisfied.
If the overturning moment is zero, the value of k is not calculated because division by Mover would not be meaningful.
Eccentricity of the resultant vertical load
Position of the resultant load. After the overturning and stabilizing moments have been taken into account, the calculator determines the distance x from the overturning edge to the line of action of the resultant vertical load:
x = (Mstab - Mover) / GΣ
Here, GΣ is the total vertical weight of all masses included in the calculation. The eccentricity relative to the geometric center of the base is then:
e = |B/2 - x|
For the second scheme, the base width a is used instead of B.
Middle third of the base. The allowable limit for this check is taken as one sixth of the base width:
elim = B/6
If e ≤ B/6, the line of action of the resultant vertical load lies within the middle third of the base. If e > B/6, the middle-third condition is not satisfied. This check is performed separately from the comparison of the stability factor k, so the required overturning stability may be achieved while the middle-third condition is not satisfied.
European standards and design references
EN 1990, Eurocode: Basis of structural design. This standard establishes general principles for structural reliability, design situations, and combinations of actions. In engineering design, these principles are used to select the load combinations and safety factors from which the actions for the overturning stability check are derived.
EN 1991-1-4, Eurocode 1: Actions on structures. Part 1-4: General actions. Wind actions. This standard is used to determine design wind actions when the lateral load is caused by wind. The resulting design force or pressure can then be used as the input action for an overturning moment calculation.
EN 1997-1, Eurocode 7: Geotechnical design. Part 1: General rules. This standard sets out principles for checking foundations and bases, including consideration of eccentricity and the position of the resultant load. The required stability factor and design actions should be selected for the specific design situation rather than treating 1.5 as a universal code requirement.
FAQs
Why can a structure have a sufficient stability factor but fail the middle-third condition?
The stability factor k compares the stabilizing and overturning moments, while the middle-third condition evaluates the position of the line of action of the resultant vertical load. Therefore, k ≥ kreq does not automatically mean that e ≤ B/6. These are related but separate checks.
What stability factor k should be used?
For preliminary calculations, k = 1.5 is often used as a practical reference, which is why it is the initial value in the calculator. For a design calculation, the required factor depends on the load combinations, safety factors, design situation, and applicable standards.
When should Q be entered, and when should a known overturning moment be used?
If the horizontal force or distributed lateral load and its geometry are known, it is convenient to calculate Mover from the force and lever arm. If the overturning moment has already been obtained from another calculation, it can be entered directly without recalculating the force and its lever arm.
Why is a distributed load replaced by a single resultant force?
For a uniformly distributed load, the total effect is equivalent to a single force equal to the load intensity multiplied by the loaded length or area. This force acts through the geometric center of the uniformly loaded section, which is why its lever arm includes half of the corresponding height.
How does increasing the base width affect overturning stability?
Increasing the base width usually increases the lever arm of self-weight and therefore the stabilizing moment. It also increases the middle-third limit B/6, so the base width affects both the stability factor and the eccentricity check.