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中北大学学位论文
空爆作用下含阻尼线性强化抗力模型梁构件动力系数研究
摘要
目前,建筑结构抗爆设计规范推荐采用等效静载动力系数经验公式,为无阻尼、
理想弹塑性抗力模型的简化结果,其包含参数少,未能实现防护工程防爆减灾的精细
化要求。阻尼作为构件耗能的一种内在机制,影响着振动频率、构件弹性及塑性各阶
段振动位移,进而影响动力系数;理想弹塑性抗力模型实质为线性强化抗力体系的退
化类型,其忽略强化段的假设前提将影响塑性阶段的位移计算。
为完成空爆作用梁构件动力系数的精细化研究,本文采用含阻尼的线性强化抗力
模型来解决梁构件动力系数计算问题,根据塑性阶段强化系数与阻尼比的数值大小关
系区分构件类型,分三种情况理论推导了柔性、临界以及刚性梁构件基于延性比的等
效静载理论动力系数解析式;对延性比 1~4、塑性强化系数 0.001~0.3 和弹塑性阶段不
同阻尼比 0.001~0.1 状态下共 54 种典型工况的动力系数进行计算分析,通过 MATLAB
软件拟合了不同延性比对应的简化计算公式,并与规范推荐使用的经验公式进行对比
验证。通过分析可知:
(1)无阻尼工况塑性强化系数小于 0.01 时,与理想弹塑性抗力模型动力系数计算
结果相差约 0.3%,此时可忽略强化抗力的影响,近似采用理想弹塑性抗力模型 SDOF
方法进行计算,但忽略阻尼参数将带来较大误差。
(2)若梁构件为弹性状态设计时,无塑性残余变形的产生,塑性强化系数的取值
对计算结果无影响,弹性阶段阻尼比是影响动力系数计算结果的主要因素,强阻尼工
况较规范推荐公式降低幅度约 10.2%~13.6%;若梁构件为弹塑性状态设计时,允许延
性比越大、塑性抗力以及阻尼参数强化程度越高,动力系数降低的幅值越明显,较规
范推荐公式降低幅度最高约 16.3%~28.9%,建筑结构抗爆设计应采用多因素的梁构件
动力系数理论。
(3)阻尼比为 0 时,塑性强化系数 0.3 较理想弹塑性工况降低最大幅度 15.2%以
内;弹性阻尼比 0.05、塑性阻尼比取 0.1 时,塑性强化系数 0.3 较理想弹塑性工况降低
最大幅度 14.1%以内;弹塑性阶段阻尼比均取 0.1 时,塑性强化系数取 0.3 较理想弹塑
性工况降低最大幅度 13.7%以内;应充分考虑阻尼和塑性强化抗力对空爆作用梁构件动
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中北大学学位论文
力系数的影响,含阻尼线性强化抗力模型具有较好的经济效益。
(4)进一步通过不同工况多参数的梁构件动力系数计算理论与典型现场试验以及
有限元软件 LS-DYNA 数值模拟结果对比,理论弹塑性位移峰值计算结果与典型工字型
钢梁构件空爆试验结果误差在 8.9%以内,理论动力系数计算值与工字型钢梁构件数值
模拟结果误差在 23.9%以内,与钢筋混凝土梁构件数值模拟结果误差在 20.9%以内;根
据建筑结构防爆等级的要求,可选用不同工况 SDOF 空爆作用梁构件动力系数计算理
论,实现防护工程防爆减灾的精细化设计。
关键词:弹塑性阻尼比,线性强化抗力模型,空爆荷载,动力系数,延性比,有限元
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中北大学学位论文
Study on dynamic coefficients of linear reinforced resistance
model beam members with damping under air blast loading
Abstract
At present, the code for antiknock design of building structures recommends the empirical
formula of equivalent static load dynamic coefficient, which is the simplified result of the ideal
elastic-plastic resistance model without damping. It contains few parameters and fails to
achieve the refined requirements of explosion prevention and disaster reduction in protection
engineering. Damping as an intrinsic mechanism of energy dissipation of the member,
influencing the frequency of vibration, the vibrational displacement of the member in its elastic
and plastic phases, and thus the dynamic coefficient. The ideal elasto-plastic resistance model
is essentially a degradation type of linear reinforced resistance system, whose assumption of
neglecting the reinforced section presupposes that the displacement calculation in the plastic
phase will be affected.
In order to complete the detailed research on the dynamic coefficient of beam members
under air blast loading, adopting the linear reinforced resistance model with damping to solve
the calculation problem of dynamic coefficient of beam members. According to the numerical
relationship between the strength coefficient and the damping ratio at the plastic stage, the
analytical solutions of dynamic coefficient based on the ductility ratio of flexible、critical and
rigid members are deduced in three cases. The dynamic coefficients of 54 typical working
conditions under ductility ratio 1-4、plastic strengthening coefficient 0.001~0.3 and different
damping ratio 0.001~0.1 in elastoplastic stage were calculated and analyzed. The simplified
formulas corresponding to different ductility ratios were fitted by MATLAB software, and
compared with the empirical formulas recommended by the specification. Through the analysis,
it can be known that:
(1) When the plastic strengthening coefficient is less than 0.01 in the undamped condition,
the difference is about 0.3% from the calculated dynamic coefficient of the ideal elastic-plastic
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中北大学学位论文
resistance model. The effect of strengthening resistance can be ignored, and the SDOF method
of ideal elastoplastic resistance model is used to approximate the calculation, but ignoring
damping parameters will bring large errors.
(2) When the beam members are designed in elastic state, there is no plastic residual
deformation, and the value of plastic strengthening coefficient have not influence on the
calculation results. The damping ratio in the elastic stage is the main factor affecting the
calculation result of the dynamic coefficient. The damping ratio in the strong damping condition
decreases by 10.2%~13.6% compared with the recommended formula. When the beam
members are designed in elastoplastic state, the larger the allowable ductility ratio, the higher
the degree of plasticity resistance and damping parameter strengthening, the more obvious the
amplitude of dynamic coefficient reduction. The maximum reduction is about 16.3%~28.9%
compared with the recommended formula. The multi-factor dynamic coefficient theory of beam
members should be adopted in the anti-knock design of building structures.
(3) When the damping ratio is 0, the plastic strengthening coefficient of 0.3 decreases
within 15.2% compared with the ideal elastoplastic condition. When the elastic damping ratio
is 0.05 and the plastic damping ratio is 0.1, the plastic strengthening coefficient of 0.3 decreases
within 14.1% compared with the ideal elastoplastic condition. When the damping ratio is equal
to 0.1 in the elastoplastic stage, the plastic strengthening coefficient is equal to 0.3, which is
less than 13.7%. The effects of damping and plastic strengthening resistance on the dynamic
coefficients of beam members affected by air blast loading should be fully considered. The
linear strengthening resistance model with damping has better economic benefits.
(4) Further, the dynamic coefficient calculation theory of beam members with different
working conditions and multiple parameters were compared with the typical field test and the
numerical simulation results of finite element software LS-DYNA. The error between the
calculation result of theoretical elastic-plastic peak displacement and the result of typical I-
beam member air explosion test is within 8.9%. The error between the calculated theoretical
dynamic coefficient and the numerical simulation results of I-beam members is within 23.9%.
The error is within 20.9% compared with the numerical simulation results of reinforced
![](https://csdnimg.cn/release/download_crawler_static/88484247/bg5.jpg)
中北大学学位论文
concrete beam members. According to the requirements of explosion-proof grade of building
structure, the calculation theory of dynamic coefficient of SDOF beam members under different
working conditions can be used to realize the fine design of explosion-proof and disaster
reduction of protection engineering.
Key words: Elastoplastic damping ratio, Linear hardening resistance model, Air blast load,
Dynamic coefficient, Ductility ratio, Finite element
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