Incorrect Mass Representation Leading to Non-Conservative Seismic Response

Case classification

Illustrative case study. This scenario is constructed from common mass modelling errors observed in seismic analysis reviews.

Scenario description

An equipment frame supporting a 1500 kg vessel was analysed for seismic loading. The vessel mass was lumped at the mounting nodes on the frame without accounting for the CG offset of 0.5 m above the mounting plane. Non-structural mass (insulation, 200 kg) was omitted from the model. The analysis predicted a base shear of 4500 N and an overturning moment of 9000 N*m. During a seismic event, the frame experienced significantly higher loads than predicted, and the anchorage showed signs of distress.

Analysis of the failure

The mass modelling errors produced two effects. First, omitting the 200 kg insulation mass reduced the total mass by 12%, reducing the base shear proportionally. Second, lumping the vessel mass at the mounting nodes without the CG offset eliminated the rotational inertia of the vessel about the mounting plane. The overturning moment from the vessel was: M_ot = m * Sa * h_cg = 1500 * 3.43 * 0.5 = 2573 N*m. This was not captured in the analysis because the mass was at the mounting plane (h_cg = 0). The total overturning moment was underestimated by approximately 2900 N*m — a 32% underestimation.

Root causes

• The vessel mass was lumped at the mounting nodes without a rigid link to the CG, losing the overturning moment from the CG offset
• The non-structural mass (insulation) was omitted, reducing the total mass and the base shear
• The mass model was not verified against the expected total mass and CG location
• The analysis report did not document the mass modelling assumptions, so the error was not caught in review
• The fundamental frequency was overestimated because the mass was underestimated, potentially moving the frequency out of the amplified region in the analysis

Lessons learned

• Equipment mass must be lumped at the CG with a rigid link to the mounting nodes, preserving the rotational inertia and overturning moment
• All mass sources, including non-structural mass, must be included in the model
• The total model mass and CG must be verified against the expected values before the analysis is accepted
• Mass modelling assumptions must be documented in the analysis report for review
• The effect of mass on the fundamental frequency must be assessed — underestimating mass overestimates the frequency, potentially moving it out of the amplified region and producing non-conservative results

Remediation

The model was corrected by adding the insulation mass and connecting the vessel mass to the mounting nodes with a rigid link to the CG at 0.5 m above the mounting plane. The re-analysis predicted a base shear of 5800 N (29% higher) and an overturning moment of 11900 N*m (32% higher). The anchorage was re-checked and found to be marginally adequate; additional anchors were added to provide margin. The mass model was verified against the expected total mass and CG.