CN112270032B - Method for designing dynamic coefficient of anti-exponential explosion load of critical structure with damping flexible rigidity - Google Patents
Method for designing dynamic coefficient of anti-exponential explosion load of critical structure with damping flexible rigidity Download PDFInfo
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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
Technical Field
The invention relates to a dynamic coefficient design method for an anti-exponential explosion load of a damping-containing flexible rigid critical structure, and belongs to the technical field of antiknock design.
Background
At present, when the antiknock design is carried out on the existing building, antiknock capability of antiknock structural components needs to be considered. Duration t of blast load applied to the structure by conventional blast i When the antiknock design is carried out on civil air defense structures in China and abroad, the antiknock design is carried out according to the linear load treatment of equal impulse, and the overpressure peak value delta p of the explosive dynamic load is further processed m And the resistance power coefficient k in the elastoplastic stage of the structure h And after multiplication, the structural antiknock design value is used as a static load. Wherein the power coefficient k given by the specification h The formula does not consider the structural damping and antiknock design structure types, and lacks powerful support for the accurate design of the actual structure; normalized and simplified equiimpulse linear decayThe load shedding equivalent action duration is also smaller than the real explosion action duration. Such as: geng Shaobo, li Hong, ge Peijie. Exponential explosive empty load equivalent static load dynamic coefficient taking into account transitions [ J ]]Explosion and impact and 2019,39 (03) 33-41; BAKER W E.Explosion hazards and evaluation [ M]Amsterdam Elsevier Scientific Pub.Co.1983, two references, respectively, disclose that the use of exponential function descriptions for the real air blast shock wave attenuation modes will result in more accurate calculation results. Therefore, the existing specifications are conservative in design when the structure antiknock design is carried out, and the conservative design causes the increase of construction cost in part of application environments.
Disclosure of Invention
In order to solve the technical problems in the prior art, the invention provides a method for designing a dynamic coefficient of an anti-exponential explosion load of a damping-containing flexible rigid critical structure.
In order to achieve the above purpose, the technical scheme adopted by the invention is a method for designing a dynamic coefficient for resisting exponential explosion load of a flexible and rigid critical structure containing damping, wherein the flexible and rigid critical structure refers to: the real duration t of the blast load 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 ;
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;
a. forced vibration of the explosion load at the elastic stage
In the elastic stage and under the load, the duration range of t is more than 0 and less than or equal to t i In the internal, the dynamic equation of the structural equivalent system is
Wherein t is a structural vibration time parameter, t i For the duration of the blast load,M e is the equivalent structural mass of the elastic stage, C e Damping for equivalent structure in elastic stage, K e For the equivalent structural rigidity in the elastic phase,vibration acceleration for structural equivalent system, +.>The vibration speed of the structural equivalent system is that y is the vibration displacement of the structural equivalent system, delta P e And (t) is the explosive dynamic load of the structure which is born by the structure and changes along with the time t, and the calculation formulas of the equivalent structural coefficients are respectively as follows:
wherein m is mass per linear meter of the real structure, l is span length of the real structure, ζ is damping ratio of the real structure, K is rigidity of the real structure, and K M Is the mass transformation coefficient, k of the elastic stage L Is the load transformation coefficient in the elastic stage. The exponential explosive dynamic load is:
wherein t is i For duration of the blast load, Δp m For the overpressure peak value of the explosion load, a is an exponential load attenuation coefficient, and the damping-free natural vibration frequency omega and the damping-containing natural vibration frequency omega are used for d Damping adjustment coefficient gamma, and peak value of explosion load as static displacement y corresponding to static load st Ratio k of the elastic phase mass transfer coefficient to the load transfer coefficient M-L The parameters were calculated as follows:
it can be known that the initial displacement and the speed of the structure before bearing the explosion load are all 0, and after solving the differential equation, the displacement and the speed expression at this stage can be determined as follows:
after the explosion load is unloaded, when the vibration in the elastic stage is completed, the corresponding t is i Time of day displacement y i And velocity v i The method comprises the following steps:
b. free vibration in explosive load unloading plastic stage
When the vibration moment of the structure is greater than t i At the moment, the explosion load disappears, and the structure just enters a plastic vibration state, and at the moment, the structure is in y i V i Free vibration in the plastic phase with damping, i.e. when t, for initial conditions i <t<t m When the structural equivalent system power equation is
Wherein m is e Is equivalent structural mass in plastic stage, c e Damping for equivalent structure in plastic phase, q m The maximum resistance in the structural plastic stage is calculated as follows:
wherein the method comprises the steps of,k m For the mass transformation coefficient, k, in the plastic phase l For the load transformation coefficient in the plastic stage, solving the motion differential equation, and solving the displacement and the speed in the stage as follows:
c. ductility ratio based on dynamic coefficient in elastoplastic stage
When the structure vibrates to the maximum displacement y m In the time-course of which the first and second contact surfaces, corresponding time t m At this time velocity v m =0, substituting (12) formula, then:
let t m The maximum displacement of the elastoplastic vibration of the structure obtained by the method brought into the step (11) is as follows:
let k m-l Is the ratio of the mass transformation coefficient to the load transformation coefficient in the plastic stage, namely k m-l =k m /k l Then
From the antiknock design of the elastoplastic stage, the critical distinguishing structure of the flexible structure and the rigid structure can be known, and the resistance power coefficient k h And ductility β are respectively:
after (15) is brought into the ductility ratio formula (17), the product is obtained
Wherein y is i And v i The expression of (2) is (7), (8).
Compared with the prior art, the invention has the following technical effects: according to the practical situation, the invention fully considers the influence of the type of the structure and the damping of the structure on the dynamic coefficient of the explosion load, so that the designed building structure is more practical as much as possible, the cost is reduced, and the antiknock requirement is met. The method can realize the accurate design of the actual structure and lay a foundation for antiknock design.
Detailed Description
In order to make the technical problems, technical schemes and beneficial effects to be solved more clear, the invention is further described in detail below with reference to the embodiments. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The method for designing the dynamic coefficient of the anti-exponential explosion load of the damping-contained flexible rigid critical structure comprises the following steps: the real duration t of the blast load 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 ;
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;
a. forced vibration of the explosion load at the elastic stage
In the elastic stage and under the load, the duration range of t is more than 0 and less than or equal to t i In the internal, the dynamic equation of the structural equivalent system is
Wherein t is a structural vibration time parameter, t i For duration of explosive load, M e Is the equivalent structural mass of the elastic stage, C e Damping for equivalent structure in elastic stage, K e For the equivalent structural rigidity in the elastic phase,vibration acceleration for structural equivalent system, +.>The vibration speed of the structural equivalent system is that y is the vibration displacement of the structural equivalent system, delta P e And (t) is the explosive dynamic load of the structure which is born by the structure and changes along with the time t, and the calculation formulas of the equivalent structural coefficients are respectively as follows:
wherein m is mass per linear meter of the real structure, l is span length of the real structure, ζ is damping ratio of the real structure, K is rigidity of the real structure, and K M Is the mass transformation coefficient, k of the elastic stage L Is the load transformation coefficient in the elastic stage. The exponential explosive dynamic load is:
wherein t is i For duration of the blast load, Δp m For the overpressure peak value of the explosion load, a is an exponential load attenuation coefficient, and the damping-free natural vibration frequency omega and the damping-containing natural vibration frequency omega are used for d Damping adjustment coefficient gamma, explosion load peak value as static loadDisplacement y st Ratio k of the elastic phase mass transfer coefficient to the load transfer coefficient M-L The parameters were calculated as follows:
it can be known that the initial displacement and the speed of the structure before bearing the explosion load are all 0, and after solving the differential equation, the displacement and the speed expression at this stage can be determined as follows:
after the explosion load is unloaded, when the vibration in the elastic stage is completed, the corresponding t is i Time of day displacement y i And velocity v i The method comprises the following steps:
b. free vibration in explosive load unloading plastic stage
When the vibration moment of the structure is greater than t i At the moment, the explosion load disappears, and the structure just enters a plastic vibration state, and at the moment, the structure is in y i V i Free vibration in the plastic phase with damping, i.e. when t, for initial conditions i <t<t m When the structural equivalent system power equation is
Wherein m is e Is equivalent structural mass in plastic stage, c e Damping for equivalent structure in plastic phase, q m The maximum resistance in the structural plastic stage is calculated as follows:
wherein k is m For the mass transformation coefficient, k, in the plastic phase l For the load transformation coefficient in the plastic stage, solving the motion differential equation, and solving the displacement and the speed in the stage as follows:
c. ductility ratio based on dynamic coefficient in elastoplastic stage
When the structure vibrates to the maximum displacement y m At the corresponding time t m At this time velocity v m =0, substituting (12) formula, then:
let t m The maximum displacement of the elastoplastic vibration of the structure obtained by the method brought into the step (11) is as follows:
let k m-l Is the ratio of the mass transformation coefficient to the load transformation coefficient in the plastic stage, namely k m-l =k m /k l Then
From the antiknock design of the elastoplastic stage, the critical distinguishing structure of the flexible structure and the rigid structure can be known, and the resistance power coefficient k h And ductility β are respectively:
after (15) is brought into the ductility ratio formula (17), the product is obtained
Wherein y is i And v i The expression of (2) is (7), (8).
By the above method, the actual antiknock design of the structure is exemplified as follows.
1. When the protection structure is designed for antiknock, the structure is designed into a flexible rigid critical transitional structure, and the self-vibration circular frequency omega and the action duration t of explosion dynamic load of the structure i Product ωt i When the ductility ratio beta is 3.2 and the damping ratio zeta is 1%, the exponential load attenuation coefficient a is 1.27 and k is 1.61 m-l And k is equal to m-l The values are respectively 0.66 and 0.78 (written by the formula Qin, liu Jinchun of the underground protection structure, published by the Chinese water conservancy and hydropower press of ISBN 9787508470009, 2010), other parameters are respectively calculated by other formulas and substituted into the formulas (7), (8) and (18), and the resistance dynamic coefficient k is obtained by an iterative method h 0.574.
2. When the protection structure is designed for antiknock, the structure is designed into a flexible rigid critical transitional structure, and the self-vibration circular frequency omega and the action duration t of explosion dynamic load of the structure i Product ωt i At a ductility ratio β of 2.93 and a damping ratio ζ of 5%, an exponential load decay was obtainedThe subtraction factor a is 1.27, k m-l And k is equal to m-l The values are respectively 0.66 and 0.78 (written by the formula Qin, liu Jinchun of the underground protection structure, published by the Chinese water conservancy and hydropower press of ISBN 9787508470009, 2010), other parameters are respectively calculated by other formulas and substituted into the formulas (7), (8) and (18), and the resistance dynamic coefficient k is obtained by an iterative method h 0.616.
3. When the protection structure is designed for antiknock, the structure is designed into a flexible rigid critical transitional structure, and the self-vibration circular frequency omega and the action duration t of explosion dynamic load of the structure i Product ωt i When the ductility ratio beta is 1.46 and the damping ratio zeta is 10%, the exponential load attenuation coefficient a is 1.27 and k is 1.10 m-l And k is equal to m-l The values are respectively 0.66 and 0.78 (written by the formula Qin, liu Jinchun of the underground protection structure, published by the Chinese water conservancy and hydropower press of ISBN 9787508470009, 2010), other parameters are respectively calculated by other formulas and substituted into the formulas (7), (8) and (18), and the resistance dynamic coefficient k is obtained by an iterative method h 0.375.
The foregoing description of the preferred embodiment of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (1)
1. The method for designing the dynamic coefficient of the anti-exponential explosion load of the damping-contained flexible rigid critical structure is characterized by comprising the following steps of: the flexible rigid critical structure refers to: the real duration t of the blast load 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 ;
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;
a. forced vibration of the explosion load at the elastic stage
In the elastic stage and under the load, the duration range of t is more than 0 and less than or equal to t i In the internal, the dynamic equation of the structural equivalent system is
Wherein t is a structural vibration time parameter, t i For duration of explosive load, M e Is the equivalent structural mass of the elastic stage, C e Damping for equivalent structure in elastic stage, K e For the equivalent structural rigidity in the elastic phase,vibration acceleration for structural equivalent system, +.>The vibration speed of the structural equivalent system is that y is the vibration displacement of the structural equivalent system, delta P e And (t) is the explosive dynamic load of the structure which is born by the structure and changes along with the time t, and the calculation formulas of the equivalent structural coefficients are respectively as follows:
wherein m is mass per linear meter of the real structure, l is span length of the real structure, ζ is damping ratio of the real structure, K is rigidity of the real structure, and K M Is the mass transformation coefficient, k of the elastic stage L As the load transformation coefficient in the elastic stage, the exponential explosion dynamic load is as follows:
wherein t is i For duration of the blast load, Δp m For the overpressure peak value of the explosion load, a is an exponential load attenuation coefficient, and the damping-free natural vibration frequency omega and the damping-containing natural vibration frequency omega are used for d Damping adjustment coefficient gamma, and peak value of explosion load as static displacement y corresponding to static load st Elasticity ofRatio k of stage mass transform coefficient to load transform coefficient M-L The parameters were calculated as follows:
it can be known that the initial displacement and the speed of the structure before bearing the explosion load are all 0, and after solving the differential equation, the displacement and the speed expression at this stage can be determined as follows:
after the explosion load is unloaded, when the vibration in the elastic stage is completed, the corresponding t is i Time of day displacement y i And velocity v i The method comprises the following steps:
b. free vibration in explosive load unloading plastic stage
When the vibration moment of the structure is greater than t i At the moment, the explosion load disappears, and the structure just enters a plastic vibration state, and at the moment, the structure is in y i V i Free vibration in the plastic phase with damping, i.e. when t, for initial conditions i <t<t m When the structural equivalent system power equation is
Wherein m is e Is equivalent structural mass in plastic stage, c e Damping for equivalent structure in plastic phase, q m The maximum resistance in the structural plastic stage is calculated as follows:
wherein k is m For the mass transformation coefficient, k, in the plastic phase l For the load transformation coefficient in the plastic stage, solving the motion differential equation, and solving the displacement and the speed in the stage as follows:
c. ductility ratio based on dynamic coefficient in elastoplastic stage
When the structure vibrates to the maximum displacement y m At the corresponding time t m At this time velocity v m =0, substituting (12) formula, then:
let t m The maximum displacement of the elastoplastic vibration of the structure obtained by the method brought into the step (11) is as follows:
let k m-l Is the ratio of the mass transformation coefficient to the load transformation coefficient in the plastic stage, namely k m-l =k m /k l Then
From the antiknock design of the elastoplastic stage, the critical distinguishing structure of the flexible structure and the rigid structure can be known, and the resistance power coefficient k h And ductility β are respectively:
after (15) is brought into the ductility ratio formula (17), the product is obtained
Wherein y is i And v i The expression of (2) is (7), (8).
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KR20180009888A (en) * | 2016-07-20 | 2018-01-30 | 연세대학교 산학협력단 | Apparatus and system for measuring deformation of concrete structure under internal blast loading |
CN109765025A (en) * | 2018-12-25 | 2019-05-17 | 哈尔滨理工大学 | RPC dash-board injury appraisal procedure under Blast Loads based on P-I curve |
CN111753472A (en) * | 2020-06-16 | 2020-10-09 | 中国人民解放军海军工程大学 | Ship motion response prediction method under underwater explosion effect considering damping effect |
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KR20180009888A (en) * | 2016-07-20 | 2018-01-30 | 연세대학교 산학협력단 | Apparatus and system for measuring deformation of concrete structure under internal blast loading |
CN109765025A (en) * | 2018-12-25 | 2019-05-17 | 哈尔滨理工大学 | RPC dash-board injury appraisal procedure under Blast Loads based on P-I curve |
CN111753472A (en) * | 2020-06-16 | 2020-10-09 | 中国人民解放军海军工程大学 | Ship motion response prediction method under underwater explosion effect considering damping effect |
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