Seismic Base Shear and Overturning Example
A worked example calculating base shear and overturning moment for a simple equipment support structure under seismic loading.
Problem definition
A skid-mounted equipment assembly with total mass 3000 kg and centre of gravity at 1.5 m above the base is subjected to a horizontal seismic acceleration of 0.25g. Calculate the base shear, overturning moment and check the stability against sliding and overturning.
Inputs
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Total mass | m | 3000 | kg |
| CG height | h_cg | 1.5 | m |
| Seismic acceleration | Sa | 0.25g | - |
| Skid width | B | 2.0 | m |
| Skid depth | D | 1.2 | m |
| Friction coefficient | mu | 0.45 | - |
| Number of anchors | n | 8 | - |
Step 1: Calculate base shear
Sa = 0.25 x 9.81 = 2.45 m/s^2. V = m x Sa = 3000 x 2.45 = 7350 N.
Step 2: Calculate overturning moment
M_ot = V x h_cg = 7350 x 1.5 = 11,025 N*m.
Step 3: Check sliding stability
Friction resistance = mu x m x g = 0.45 x 3000 x 9.81 = 13,244 N. Sliding safety factor = 13,244 / 7350 = 1.80 > 1.0 - adequate against sliding (without anchors). However, seismic design typically requires positive anchorage - friction alone is not sufficient for qualification.
Step 4: Check overturning stability
Resisting moment = m x g x B/2 = 3000 x 9.81 x 1.0 = 29,430 N*m. Overturning safety factor = 29,430 / 11,025 = 2.67 > 1.0 - adequate against overturning (without anchors). However, as with sliding, positive anchorage is typically required.
Step 5: Calculate anchor loads
Assume 8 anchors in a 2 x 4 pattern with 2.0 m x 1.2 m spacing. Tension per anchor: T = M_ot/(n/2 x B) - m*g/n = 11,025/(4 x 2.0) - 3000*9.81/8 = 1378 - 3679 = -2301 N. Negative - no tension, compression only. The CG is low enough that the assembly does not uplift. Shear per anchor: V = 7350/8 = 919 N (before directional combination).
Results
| Quantity | Value | Unit |
|---|---|---|
| Base shear | 7350 | N |
| Overturning moment | 11,025 | N*m |
| Sliding safety factor | 1.80 | - |
| Overturning safety factor | 2.67 | - |
| Anchor tension | 0 (no uplift) | N |
| Anchor shear per bolt | 919 | N |
Checks
- Base shear: 3000 kg at 0.25g gives 7350 N - consistent with m x Sa
- No uplift because h_cg/B = 1.5/2.0 = 0.75 < 1.0 - the CG is within the base footprint
- Friction alone resists sliding (SF = 1.80) but positive anchorage is still required by most seismic qualification standards
Interpretation
The skid-mounted equipment assembly has a base shear of 7350 N and an overturning moment of 11,025 N*m. The assembly is stable against both sliding (safety factor 1.80) and overturning (safety factor 2.67) without anchorage. However, seismic qualification standards typically require positive anchorage regardless of stability calculations. The anchors carry shear only (919 N per bolt) with no tension, because the CG height-to-base-width ratio is less than 1.0.