Study On Dynamic Coefficients Of Linear Reinforced Resistance Model Beam Members With Damping Under Air Blast Loading

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 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 Ibeam 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 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.