CN112270032B - Method for designing dynamic coefficient of anti-exponential explosion load of critical structure with damping flexible rigidity - Google Patents

Abstract

The invention relates to a dynamic coefficient method for designing an anti-exponential explosion load of a damping-containing flexible rigid critical structure, which belongs to the technical field of antiknock design, and specifically relates to a dynamic coefficient method for designing an anti-exponential explosion load of a damping-containing flexible rigid critical structure, which comprises the following steps: exponential blast load action real time t _i The value is just that the structural vibration reaches the maximum value y of the elastic vibration _T At a certain moment, after the explosive load is unloaded, the structure starts to perform plastic vibration by means of inertia force, and at a certain moment t _m The maximum value y of structural elastoplastic displacement is reached _m The method comprises the steps of carrying out a first treatment on the surface of the According to the action process of explosion on the building structure, dividing the process into two stages of forced vibration in the explosion load action elastic stage and free vibration in the explosion load unloading plastic stage; through the calculation of the different stages, the influence of the structural type, the accurate description of the explosion load and the structural damping on the explosion load dynamic coefficient is fully considered, so that the designed building structure is more practical as much as possible, the cost is reduced, and the antiknock requirement is met.

Description

Design dynamic coefficients of damped flexible rigid critical structures against exponential blast loads method

technical field

The invention relates to a method for designing dynamic coefficients of a flexible rigid critical structure with damping against exponential explosion loads, and belongs to the technical field of explosion-resistant design.

Background technique

At present, when the anti-blast design of existing buildings is carried out, the anti-blast capability of the anti-blast structural components needs to be considered. The duration t _i of the explosive load imposed on the structure by conventional explosion is very short. When the anti-explosion design of civil air defense structures in China and abroad is carried out, it is treated as an equal-impulse linear load, and the peak value of the _overpressure of the explosive dynamic load After multiplied by the resistance dynamic coefficient k _h , it is used as the static load to carry out the anti-blast design value of the structure. Among them, the dynamic coefficient k _h formula given in the code does not consider the structural damping and anti-blast design structure type, which lacks strong support for the precise design of the actual structure; the equivalent duration of the equal-impulse linear attenuation load simplified by the code is also shorter than the real explosion duration . Such as: Geng Shaobo, Li Hong, Ge Peijie. Equivalent static load dynamic coefficient of exponential explosive air-burst load considering transition[J]. Explosion and Shock and 2019,39(03):33-41; BAKER WE.Explosion hazards and evaluation[ M].Amsterdam:Elsevier ScientificPub.Co.1983. In the two documents, it is introduced that the real air explosion shock wave attenuation mode is described by an exponential function, which will make the calculation result more accurate. Therefore, when the existing codes carry out the anti-blast design of the structure, the design is conservative. In some application environments, the conservative design will increase the construction cost.

Contents of the invention

In order to solve the technical problems existing in the prior art, the present invention provides a method for designing dynamic coefficients of a flexible rigid critical structure with damping against exponential explosion loads.

In order to achieve the above-mentioned purpose, the technical solution adopted in the present invention is a method for designing dynamic coefficients of a flexible rigid critical structure with resistance to exponential explosion loads, and the flexible rigid critical structure refers to: the actual duration _t of the explosive load is just When the structural vibration reaches the maximum value of elastic vibration y _T , after the explosion load is unloaded, the structure starts to undergo plastic vibration relying on the inertial force, and at a certain time t _m , the maximum elastic-plastic displacement of the structure y _m is reached;

According to the action process of the explosion on the building structure, the process is divided into two stages: the forced vibration in the elastic stage of the explosion load and the free vibration in the plastic stage of the explosion load unloading;

a. Forced vibration in the elastic stage of explosion load

In the elastic stage and within the range of load duration 0<t≤t _i , the dynamic equation of the structural equivalent system is

为结构等效体系振动加速度，/>

为结构等效体系振动速度，y为结构等效体系振动位移，ΔP_e(t)为结构承受的随时间t变化的爆炸动荷载，等效结构系数计算公式分别为：Among them, t is the structural vibration time parameter, t _i is the duration of the explosion load, M _e is the equivalent structural mass in the elastic stage, C _e is the equivalent structural damping in the elastic stage, K _e is the equivalent structural stiffness in the elastic stage,

is the vibration acceleration of the structural equivalent system, />

is the vibration velocity of the structural equivalent system, y is the vibration displacement of the structural equivalent system, ΔP _e (t) is the explosive dynamic load on the structure that changes with time t, and the calculation formulas of the equivalent structural coefficient are:

Among them, m is the mass per linear meter of the real structure, l is the span length of the real structure, ξ is the damping ratio of the real structure, K is the stiffness of the real structure, k _M is the mass conversion coefficient in the elastic stage, and k _L is the load conversion coefficient in the elastic stage. The exponential explosion dynamic load is:

Among them, t _i is the duration of the blast load, Δp _m is the overpressure peak value of the blast load, a is the exponential load attenuation coefficient, which is composed of the undamped natural frequency ω, the damped natural frequency ω _d , the damping adjustment coefficient γ, and the explosive load The peak value is used as the static displacement y _st corresponding to the static load, and the ratio k _ML of the mass conversion coefficient in the elastic stage to the load conversion coefficient k ML . The parameters are calculated as follows:

It can be seen that the initial displacement and velocity of the structure before bearing the explosion load are both 0. After solving the differential equation, the expression of displacement and velocity at this stage can be determined as:

After the explosion load is unloaded and the vibration in the elastic stage is completed, the displacement y _i and velocity v _i corresponding to time t _i are:

b. Free vibration in the plastic stage of explosion load unloading

When the structural vibration moment is greater than t _i , the explosion load disappears, and the structure just enters the plastic vibration state. At this time, the structure is free vibration in the damped plastic stage with y _i and v _i as the initial conditions, that is, when t _i <t< At t _m , the dynamic equation of the structural equivalent system is

Among them, m _e is the equivalent structural mass in the plastic stage, c _e is the equivalent structural damping in the plastic stage, q _m is the maximum resistance force in the plastic stage of the structure, and its calculation formula is:

Among them, k _m is the mass transformation coefficient in the plastic stage, and k _l is the load transformation coefficient in the plastic stage. Solve this differential equation of motion to obtain the solution of displacement and velocity in this stage:

c. Ductility ratio based on dynamic coefficient in elastic-plastic stage

When the structure vibrates to the maximum displacement y _m , the corresponding moment is t _m , and the velocity v _m =0 at this time, substituting into formula (12), then:

Substituting t _m into (11), the maximum displacement of the structural elastic-plastic vibration is:

Let k _ml be the ratio of the mass conversion coefficient to the load conversion coefficient in the plastic stage, that is, k _ml =k _m /k _l , then

From the anti-knock design in the elastoplastic stage, it can be known that for the flexible structure and the rigid structure critically divided structure, the resistance dynamic coefficient k _h and the ductility β are respectively:

After substituting (15) into the ductility ratio formula (17), we get

Among them, the expressions of y _i and _vi are (7), (8).

Compared with the prior art, the present invention has the following technical effects: according to the actual situation, the present invention fully considers the type of structure and the influence of structural damping on the explosive load dynamic coefficient, and tries to make the designed building structure more realistic, while reducing costs. At the same time, it meets the anti-knock requirements. And through this method, the precise design of the actual structure can be realized, and it also lays the foundation for the anti-knock design.

Detailed ways

In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention clearer, the present invention will be further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

The dynamic coefficient method for designing a flexible rigid critical structure with damping against exponential explosion loads, the flexible rigid critical structure refers to: the real duration t _i value of the explosion load is just the moment when the structural vibration reaches the maximum value of elastic vibration y _T , and the explosion load After unloading, the structure begins to vibrate plastically depending on the inertial force, and at a certain time t _m , the maximum elastic-plastic displacement of the structure y _m is reached;

According to the action process of the explosion on the building structure, the process is divided into two stages: the forced vibration in the elastic stage of the explosion load and the free vibration in the plastic stage of the explosion load unloading;

a. Forced vibration in the elastic stage of explosion load

In the elastic stage and within the range of load duration 0<t≤t _i , the dynamic equation of the structural equivalent system is

为结构等效体系振动加速度，/>

为结构等效体系振动速度，y为结构等效体系振动位移，ΔP_e(t)为结构承受的随时间t变化的爆炸动荷载，等效结构系数计算公式分别为：Among them, t is the structural vibration time parameter, t _i is the duration of the explosion load, M _e is the equivalent structural mass in the elastic stage, C _e is the equivalent structural damping in the elastic stage, K _e is the equivalent structural stiffness in the elastic stage,

is the vibration acceleration of the structural equivalent system, />

is the vibration velocity of the structural equivalent system, y is the vibration displacement of the structural equivalent system, ΔP _e (t) is the explosive dynamic load on the structure that changes with time t, and the calculation formulas of the equivalent structural coefficient are:

Among them, m is the mass per linear meter of the real structure, l is the span length of the real structure, ξ is the damping ratio of the real structure, K is the stiffness of the real structure, k _M is the mass conversion coefficient in the elastic stage, and k _L is the load conversion coefficient in the elastic stage. The exponential explosion dynamic load is:

Among them, t _i is the duration of the blast load, Δp _m is the overpressure peak value of the blast load, a is the exponential load attenuation coefficient, which consists of the undamped natural frequency ω, the damped natural frequency ω _d , the damping adjustment coefficient γ, and the explosive load The peak value is used as the static displacement y _st corresponding to the static load, and the ratio k _ML of the mass conversion coefficient in the elastic stage to the load conversion coefficient k ML . The parameters are calculated as follows:

It can be seen that the initial displacement and velocity of the structure before bearing the explosion load are both 0. After solving the differential equation, the expression of displacement and velocity at this stage can be determined as:

After the explosion load is unloaded and the vibration in the elastic stage is completed, the displacement y _i and velocity v _i corresponding to time t _i are:

b. Free vibration in the plastic stage of explosion load unloading

When the structural vibration moment is greater than t _i , the explosion load disappears, and the structure just enters the plastic vibration state. At this time, the structure is free vibration in the damped plastic stage with y _i and v _i as the initial conditions, that is, when t _i <t< At t _m , the dynamic equation of the structural equivalent system is

Among them, m _e is the equivalent structural mass in the plastic stage, c _e is the equivalent structural damping in the plastic stage, q _m is the maximum resistance force in the plastic stage of the structure, and its calculation formula is:

Among them, k _m is the mass transformation coefficient in the plastic stage, and k _l is the load transformation coefficient in the plastic stage. Solve this differential equation of motion to obtain the solution of displacement and velocity in this stage:

c. Ductility ratio based on dynamic coefficient in elastic-plastic stage

When the structure vibrates to the maximum displacement y _m , the corresponding moment is t _m , and the velocity v _m =0 at this time, substituting into formula (12), then:

Substituting t _m into (11), the maximum displacement of the structural elastic-plastic vibration is:

Let k _ml be the ratio of the mass conversion coefficient to the load conversion coefficient in the plastic stage, that is, k _ml =k _m /k _l , then

From the anti-knock design in the elastoplastic stage, it can be known that for the flexible structure and the rigid structure critically divided structure, the resistance dynamic coefficient k _h and the ductility β are respectively:

After substituting (15) into the ductility ratio formula (17), we get

Among them, the expressions of y _i and _vi are (7), (8).

Through the above method, the actual anti-knock design of the structure is given as an example as follows.

1. When a protective structure is designed for explosion resistance, it is required that the structure be designed as a flexible rigid critical transitional structure. The product ωt i of the circular frequency ω of the structure and the duration _{t i of} the explosive dynamic load is 3.2, and the ductility ratio β is 1.61. When the damping ratio ξ is 1%, the exponential load attenuation coefficient a is 1.27, and the values of k _ml and k _ml are 0.66 and 0.78 respectively ("Underground Protective Structure", edited by Fang Qin and Liu Jinchun, ISBN 9787508470009 China Water Resources and Hydropower Press, 2010 Published in 2010), other parameters were calculated from other formulas, and substituted into formulas (7), (8) and (18), and the resistance dynamic coefficient k _h was obtained as 0.574 by the iterative method.

2. When a protective structure is designed for explosion resistance, it is required that the structure be designed as a flexible rigid critical transition structure. The product ωt i of the circular frequency ω of the structure and the duration _{t i of} the explosive dynamic load is 2.93, and the ductility ratio β is 1.26. When the damping ratio ξ is 5%, the exponential load attenuation coefficient a is 1.27, and the values of k _ml and k _ml are 0.66 and 0.78 respectively ("Underground Protective Structure", edited by Fang Qin and Liu Jinchun, ISBN 9787508470009 China Water Resources and Hydropower Press, 2010 Published in 2010), other parameters were calculated by other formulas, and substituted into formulas (7), (8) and (18), and the dynamic coefficient k _h of resistance was obtained by iterative method, which was 0.616.

3. When a protective structure is designed for explosion resistance, it is required that the structure be designed as a flexible rigid critical transitional structure. The product ωt i of the structure's natural vibration circular frequency ω _and the duration of the explosion dynamic load t _i is 1.46, and the ductility ratio β is 1.10. When the damping ratio ξ is 10%, the exponential load attenuation coefficient a is 1.27, and the values of k _ml and k _ml are 0.66 and 0.78 respectively ("Underground Protective Structure", edited by Fang Qin and Liu Jinchun, ISBN 9787508470009 China Water Resources and Hydropower Press, 2010 Published in 2010), other parameters were calculated from other formulas, and substituted into formulas (7), (8) and (18), and the dynamic coefficient k _h of resistance was obtained by iterative method, which was 0.375.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention should be included within the scope of the present invention .

Claims (1)

1. The dynamic coefficient method for designing a flexible rigid critical structure with damping against exponential explosion loads is characterized in that: the flexible rigid critical structure refers to: the real duration _t of the explosive load is just the value of the structural vibration reaching the maximum value of elastic vibration At time y _T , after the explosion load is unloaded, the structure begins to vibrate plastically depending on the inertial force, and at a certain time t _m , the maximum elastic-plastic displacement of the structure y _m is reached; According to the action process of the explosion on the building structure, the process is divided into two stages: the forced vibration in the elastic stage of the explosion load and the free vibration in the plastic stage of the explosion load unloading; a. Forced vibration in the elastic stage of explosion load In the elastic stage and within the range of load duration 0<t≤t _i , the dynamic equation of the structural equivalent system is

Among them, t is the structural vibration time parameter, t _i is the duration of the explosion load, M _e is the equivalent structural mass in the elastic stage, C _e is the equivalent structural damping in the elastic stage, K _e is the equivalent structural stiffness in the elastic stage,

is the vibration acceleration of the structural equivalent system, />

is the vibration velocity of the structural equivalent system, y is the vibration displacement of the structural equivalent system, ΔP _e (t) is the explosive dynamic load on the structure that changes with time t, and the calculation formulas of the equivalent structural coefficient are:

Among them, m is the mass per linear meter of the real structure, l is the span length of the real structure, ξ is the damping ratio of the real structure, K is the stiffness of the real structure, k _M is the mass conversion coefficient in the elastic stage, k _L is the load conversion coefficient in the elastic stage, and the exponent The type explosion dynamic load is:

Among them, t _i is the duration of the blast load, Δp _m is the overpressure peak value of the blast load, a is the exponential load attenuation coefficient, which consists of the undamped natural frequency ω, the damped natural frequency ω _d , the damping adjustment coefficient γ, and the explosive load The peak value is used as the static displacement y _st corresponding to the static load, and the ratio k _ML of the mass conversion coefficient in the elastic stage to the load conversion coefficient k ML . The parameters are calculated as follows:

It can be seen that the initial displacement and velocity of the structure before bearing the explosion load are both 0. After solving the differential equation, the expression of displacement and velocity at this stage can be determined as:

After the explosion load is unloaded and the vibration in the elastic stage is completed, the displacement y _i and velocity v _i corresponding to time t _i are:

b. Free vibration in the plastic stage of explosion load unloading When the structural vibration moment is greater than t _i , the explosion load disappears, and the structure just enters the plastic vibration state. At this time, the structure is free vibration in the damped plastic stage with y _i and v _i as the initial conditions, that is, when t _i <t< At t _m , the dynamic equation of the structural equivalent system is

Among them, m _e is the equivalent structural mass in the plastic stage, c _e is the equivalent structural damping in the plastic stage, q _m is the maximum resistance force in the plastic stage of the structure, and its calculation formula is:

Among them, k _m is the mass transformation coefficient in the plastic stage, and k _l is the load transformation coefficient in the plastic stage. Solve this differential equation of motion to obtain the solution of displacement and velocity in this stage:

c. Ductility ratio based on dynamic coefficient in elastic-plastic stage When the structure vibrates to the maximum displacement y _m , the corresponding moment is t _m , and the velocity v _m =0 at this time, substituting into formula (12), then:

Substituting t _m into (11), the maximum displacement of the structural elastic-plastic vibration is:

Let k _ml be the ratio of the mass conversion coefficient to the load conversion coefficient in the plastic stage, that is, k _ml =k _m /k _l , then

From the anti-knock design in the elastoplastic stage, it can be known that for the flexible structure and the rigid structure critically divided structure, the resistance dynamic coefficient k _h and the ductility β are respectively:

After substituting (15) into the ductility ratio formula (17), we get

Among them, the expressions of y _i and _vi are (7), (8).