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Influence of P-Δ effect on the structural residual displacement demands
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Bali LIU1, Zhixuan LI1, Jinjun HU2, 3, Lili XIE2, 3
Earthquake Engineering and Engineering Dynamics | 2025, 45(5) : 65 - 76
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Earthquake Engineering and Engineering Dynamics | 2025, 45(5): 65-76
• Research Paper •
Influence of P-Δ effect on the structural residual displacement demands
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Bali LIU1, Zhixuan LI1, Jinjun HU2, 3, Lili XIE2, 3
Affiliations
  • 1.School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
  • 2.Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China
  • 3.Key Laboratory of Earthquake Disaster Mitigation, Ministry of Emergency Management, Harbin 150080, China
Published: 2025-10-22 doi: 10.13197/j.eeed.2025.0507
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To reveal the effect of P-Δ on the residual displacement ductility demand of structures, the damage-based residual displacement ductility demand ratio spectrum μres of single degree of freedom (SDOF) systems was conducted based on the Park-Ang damage model. The data were statistically processed to evaluate the effect of soil type, elastic stability coefficient θ, ultimate ductility coefficient μu and hysteretic model on damage-based μres. A prediction equation was proposed to estimate damage-based μres of SDOF systems through regression analysis. The differences of μres based on damage approach and ductility approach were compared and analyzed. Results show that the error in the estimation of damage-based μres when mean values along the earthquake population are considered without any soil distinction is inside 10%. When the P-Δ effect is not considered, the influence of μu on damage based μres exceeds 20%. When the P-Δ effect is considered, the influence of μu on damage based μres exceeds 50%. The ductility-based μres tend to be conservative compared to the damage-based ones. Finally, the prediction equation for the estimate of damage-based μres is proposed, which can be applied to the evaluation of residual displacement ductility demand ratio and seismic resilience.

P-Δ effect  /  residual displacement  /  ductility demand  /  damage index  /  performance-based design
Bali LIU, Zhixuan LI, Jinjun HU, Lili XIE. Influence of P-Δ effect on the structural residual displacement demands[J]. Earthquake Engineering and Engineering Dynamics, 2025 , 45 (5) : 65 -76 . DOI: 10.13197/j.eeed.2025.0507
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Year 2025 volume 45 Issue 5
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Article Info
doi: 10.13197/j.eeed.2025.0507
  • Receive Date：2024-06-24
  • Online Date：2026-03-20
  • Published：2025-10-22
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  • Received：2024-06-24
  • Revised：2024-11-07
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Affiliations
    1.School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
    2.Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China
    3.Key Laboratory of Earthquake Disaster Mitigation, Ministry of Emergency Management, Harbin 150080, China
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表12种不同金属材料的力学参数
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小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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