Overturning Moment Calculation

About Overturning Moment Calculation

This calculator checks a structure’s stability against overturning under a lateral load. The check is based on comparing the overturning moment with the stabilizing moment for the selected scheme. The result shows whether the structure would overturn and what stability margin you get.

Guidelines and recommendations

European standards context. The logic of a stability check is commonly aligned with the principles of combinations and reliability in EN 1990 (Eurocode 0). Lateral actions are often defined using EN 1991-1-4 (wind actions). For foundation and ground interaction, approaches from EN 1997-1 (geotechnical design) are typically relevant. If member resistance checks are needed, they are normally performed to EN 1992-1-1 (concrete), EN 1993-1-1 (steel), and EN 1995-1-1 (timber).

Units and load conversion. Internally, all forces are brought to a consistent basis and moments are computed as “force × lever arm”. The calculator uses fixed conversion factors:

1 kN = 101.97 kgf

1 kgf·m = 0.00980665 kN·m

For this reason, the moments can be shown both in kN·m and in the equivalent kgf·m.

Overturning moment M_ot. First, the resultant lateral force Q and its lever arm L to the overturning edge are determined. Then:

Mot = Q · L

Here, Q is either entered as a point load or derived from a distributed intensity (per length or per area). The lever arm L is computed from the heights of the chosen scheme. All lever-arm lengths are converted from mm to m.

How Q is obtained for different load types. Three cases are used:

• Point load. Q is taken directly in kg or kN. Lever arm for scheme 1: L = h1 + h2. Lever arm for scheme 2: L = h1.
• Line load. The resultant force is the load per meter times the loaded length: Q = q · h, where q is in kg/m or kN/m, and h is taken from the scheme (mm → m). The lever arm is L = h1 + h2 + h3/2 (scheme 1) or L = h1 + h2/2 (scheme 2).
• Area load. The resultant force is pressure times loaded area: Q = q · h · b, where q is in kg/m² or kN/m², h is the height of the loaded zone (mm → m), and b is the base width (mm → m). The lever arm is taken the same way as for the line load.

Stabilizing moment M_st. The stabilizing moment is created by the weights (masses) of parts that “press” the base down. In general form:

Mst = Σ (Gi · ai)

Where G_i is the weight (entered as mass and internally treated consistently), and a_i is the lever arm to the overturning edge.

Stabilizing lever arms for scheme 1. For the foundation and the soil above it, the lever arm is taken as half of the total base width:

afnd = asoil = (a1 + a2)/2

For the support (the part above the foundation), the lever arm is taken as:

asup = a1

If the option “soil acts on the foundation” is enabled, the soil is included as an additional stabilizing contribution. If the option is disabled, the soil contribution is zero.

Stabilizing lever arm for scheme 2. The stabilizing moment is based only on the support mass and the base width a:

Mst = m · (a/2)

Stability ratio k. After the moments are computed, the ratio is evaluated as:

k = Mst / Mot

How the final conclusion is selected. The calculator uses three assessment ranges:

• Will overturn. If Mst < Mot, then k < 1.00.
• Will not overturn, but needs margin. If Mot ≤ Mst < 1.5 · Mot, then 1.00 ≤ k < 1.50.
• Will not overturn. If Mst ≥ 1.5 · Mot, then k ≥ 1.50.

Typical practical targets. For everyday use, people often aim for k ≥ 1.5 as a “clear margin” against overturning. In engineering design, the required margin depends on load combinations, partial factors, and the ground model. This is why the result is especially useful as a quick sensitivity check: how k changes with base width, mass, or the height at which the wind load is applied.

FAQs

Why are moments calculated as “force × lever arm”?

Overturning is rotation about the base edge. In that case the decisive quantity is the moment about that edge. That is why the overturning moment from the lateral force is compared with the stabilizing moment from the structure’s weight.

How is a distributed wind load along height handled?

For distributed loads, the resultant force is computed as load intensity times the loaded height. The lever arm is taken to the centroid of the distribution. In the calculator this is reflected by adding h/2 within the lever-arm expression.

Why use the stability ratio k?

It shows how many times the stabilizing moment exceeds the overturning moment. Values k < 1 indicate overturning. The range 1…1.5 is commonly treated as an insufficient stability margin.

Why can this differ from a “Eurocode” design check?

Eurocode-style stability checks are usually performed on design combinations with partial safety factors and with an explicit ground model. Here a simplified scheme is used, with a fixed margin threshold and without automatic combination generation. This is convenient for preliminary assessment and comparing options.

What influences overturning stability the most?

In many cases, increasing the base width (it increases the stabilizing lever arm) and adding mass near the base increases the margin fastest. Stability is reduced most by higher lateral loads and by a higher point of load application, because the overturning lever arm grows.