CN112329094A - Method for loading secondary self-reaction structure and calculating support reaction - Google Patents
Method for loading secondary self-reaction structure and calculating support reaction Download PDFInfo
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Abstract
The invention discloses a method for loading a secondary self-reaction structure and calculating a support reaction, which comprises the steps of calculating the total load borne by the secondary self-reaction structure; removing all or part of redundant constraints at the support of the secondary self-reaction structure, enabling the support of the secondary self-reaction structure to be in a first state, and applying a first load on the secondary self-reaction structure; adding all or part of redundant constraints to enable the support of the secondary self-reaction structure to be in a second state, and applying a second load on the secondary self-reaction structure; calculating a first counter force of the secondary self-reaction force structure in the first state based on the first load, calculating a second counter force of the secondary self-reaction force structure in the second state based on the second load, and superposing the first counter force and the second counter force to obtain a target counter force. The calculation method can effectively reduce the secondary reaction of the secondary self-reaction structure support, reduce other reactions and structural internal forces of the homogenization support, improve the economy and avoid misjudgment of feasibility.
Description
Technical Field
The invention relates to the technical field of structural engineering, in particular to a method for loading a secondary self-reaction structure and calculating a support reaction.
Background
The support connected mode of traditional secondary self-reaction structure (secondary self-reaction structure means that the structure such as arch, bow member exists in its symmetrical support junction with the load direction that receives is perpendicular, represents for the counter-force of the mated support that has nothing to do with the load, mated support counter-force size is the same, opposite direction, from balancing mutually, so called secondary self-reaction structure) usually has two kinds of forms: hinged (hinged) and fixed (rigid).
In practical engineering application, in order to analyze and determine the stress performance, the economy and the feasibility of a supporting structure in a secondary self-reaction structure, the judgment is usually carried out by calculating the reaction force and the internal force of the secondary self-reaction structure under the action of bearing load. At present, the following method is generally adopted for calculating the counter force and the internal force under the load bearing effect of the secondary self-counter force structure: and (3) assuming that the support of the secondary self-reaction structure is hinged or fixed, and during calculation, the support state of the support of the secondary self-reaction structure is generated once to apply all loads.
Specifically, the secondary self-reaction force structure is taken as an unarticulated arch (the unarticulated arch refers to a state in which both ends of the arch are fixed branches) (as shown in fig. 1) as an example, and the calculated secondary self-reaction force is a horizontal thrust force and the other calculated internal forces are bending moments as an example: the bending moment diagram of the hingeless arch under the action of the full-span uniformly distributed vertical load q (q is more than 0) is distributed in a parabolic shape. The span length of the non-hinged arch is L, and the axial force influence coefficient of the non-hinged arch under the action of a vertical load q is K2Under the action of the vertical load q uniformly distributed over the full span, the horizontal thrust of the support without the hinged arch
The bending moment at two ends of the hinge-free arch is
I.e. A, B, a bending moment of two
Generating small positive bending moment in the midspan
Bending moment at two ends and spanAmplitude difference of positive bending moment
Therefore, by adopting the mode, the distribution of the internal force of the hinge-free arch is uneven, and the most outstanding problems are that the horizontal thrust of the secondary self-reaction force generated under the action of the vertical load is large and the amplitude difference of the bending moment is also large.
Therefore, in the counter force of the support of the secondary self-reaction structure, the existing secondary self-reaction force is large, and the support of the member and the bending moment in the member are also distributed unevenly and large, so that the conclusion that the structure is not feasible or the section of the member and the section of the support are required to be increased is possibly made, the engineering cost is high, and the technical measure difficulty is large.
Disclosure of Invention
The embodiment of the invention discloses a method for loading a secondary self-reaction structure and calculating the support reaction, which can effectively reduce the support secondary self-reaction of the secondary self-reaction structure, improve the economy, reduce the misjudgment on the structural feasibility and provide a direction for implementing an engineering structural scheme.
It can be known that the secondary self-reaction structure of the invention refers to: under the action of symmetrical load, two symmetrical supports of an arch structure, an arch frame structure and the like generate secondary self-reaction force which is often very large, such as horizontal shear force (horizontal thrust), and the secondary self-reaction force is generated in pairs, has equal magnitude and opposite direction, and has zero resultant force. The horizontal thrust generates corresponding arch shaft pressure, shearing force and bending moment on the arch body. The influence of the arch shaft shearing force on the arch shaft is small, the threat of the arch shaft pressure on the arch shaft is small, and the threat of the arch shaft pressure and the bending moment on the arch is certain. Horizontal shear force (horizontal thrust) serving as secondary self-reaction force of an arch structure acts on a 'support body' as load, and the horizontal thrust is large and difficult to bear by the support body. However, this thrust force is perpendicular to the load direction and appears "independent" of the load, and is therefore referred to as "secondary self-reaction force". This type of structure may be referred to as a "secondary self-reaction structure".
The invention provides a method for loading a secondary self-reaction structure and calculating a support reaction, which comprises the following steps:
calculating the total load borne by the secondary self-reaction structure;
removing all or part of redundant constraints at two symmetrical supports of the secondary self-reaction structure, so that any support of the secondary self-reaction structure is in a first state after the all or part of redundant constraints are removed, and applying a first load on the secondary self-reaction structure;
adding all or part of the unnecessary constraints which are not less than the released constraint so that any support of the secondary self-reaction structure is adjusted to a second state from the first state, and applying a second load on the secondary self-reaction structure;
calculating a first counter force of the secondary self-reaction force structure in the first state based on the first load, calculating a second counter force of the secondary self-reaction force structure in the second state based on the second load, and superposing the first counter force and the second counter force to obtain a target counter force;
wherein the sum of the first load and the second load is equal to the total load.
As an alternative implementation manner, in an embodiment of the present invention, the applying the first load to the secondary self-reaction structure is a uniform load, a concentrated load, a linear load, and/or a displacement load, and the releasing all or part of the redundant constraints at the two symmetrical seats of the secondary self-reaction structure makes any seat of the secondary self-reaction structure in the first state after the releasing all or part of the redundant constraints, and includes:
adjusting the state of the symmetrical support of the secondary self-reaction structure to form the state which is the same as or different from the second state;
calculating the number of the redundant constraints of the two symmetrical supports of the secondary self-reaction structure in the connection state which is the same as or different from the second state;
removing all or part of the redundant constraints on any support of the secondary self-reaction structure according to the number of the redundant constraints so as to enable the redundant constraints to be in a first state;
taking the value of the first load;
applying the first load on the secondary self-reaction structure in the first state.
As an alternative implementation manner, in the embodiment of the present invention, under the action of the first load, the secondary self-reaction force borne by any seat of the secondary self-reaction force structure in the first state is infinitesimal or zero.
As an optional implementation manner, in an embodiment of the present invention, the second load includes one or any several of a uniform load, a concentrated load, a linear load, or a displacement load, and the adding of the no less than released all or part of the redundant constraint makes any one of the seats of the secondary self-counterforce structure adjust from the first state to a second state, and the applying of the second load on the secondary self-counterforce structure includes:
re-adding the removed all or part of the redundant constraints at the positions where the all or part of the redundant constraints are removed;
calculating the second load according to the first load;
applying the second load on the secondary counterforce structure.
As an alternative embodiment, in an embodiment of the present invention, the first reaction force includes a first vertical reaction force, a first bending moment, and a first primary self-reaction force, the second reaction force includes a second primary self-reaction force, a second vertical reaction force, and a second bending moment, the target reaction force includes a target secondary self-reaction force, a target vertical reaction force, and a target bending moment, and the target reaction force is obtained by superimposing the first reaction force and the second reaction force, and the method includes:
and superposing the first self-reaction force and the second self-reaction force to obtain the target secondary self-reaction force, superposing the first vertical reaction force and the second vertical reaction force to obtain the target vertical reaction force, and superposing the first bending moment and the second bending moment to obtain the target bending moment.
As an alternative implementation, in the embodiment of the present invention, the type of the seat of the secondary self-reaction structure includes a fixed hinge seat, a fixed seat or a sliding seat.
As an alternative implementation, in the embodiment of the present invention, the secondary self-reaction structure is an arch or an arch.
As an optional implementation manner, in an embodiment of the present invention, the first state is any one of an unconnected state, a hinged state, or a semi-rigid connection state, the second state is any one of a hinged state, a semi-rigid connection state, or a rigid connection state that is matched with the first state, and in the second state, the seat connection stiffness of the secondary self-reaction force structure is greater than the seat connection stiffness of the secondary self-reaction force structure in the first state.
Compared with the prior art, the embodiment of the invention has the following beneficial effects:
the embodiment provides a method for loading a secondary self-reaction structure and calculating a support reaction, which is characterized in that a plurality of redundant constraints of two symmetrical supports of the secondary self-reaction structure are removed and added, so that the state of any support of the secondary self-reaction structure is generated in stages, borne loads are applied in different stages correspondingly, then the support reaction of the secondary self-reaction structure is calculated respectively based on different states and loads, and then a target reaction is obtained after superposition. The method can effectively reduce the secondary self-reaction force, such as horizontal thrust, generated by the structural support, and can reduce the bending moment on the homogenized structural member, thereby obtaining more economic stress data of the member, reducing misjudgment on structural feasibility, providing a direction for implementing an engineering structural scheme, and reducing the construction cost of the structure.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a diagram of the reaction force of a conventional hingeless arch under load;
FIG. 2 is a flow chart of a method for loading a secondary self-reaction structure and calculating a support reaction according to the present invention;
FIG. 3 is a flowchart detailing step 102 disclosed herein;
FIG. 4 is a moment diagram of the disclosed hingeless arch under a first load;
FIG. 5 is a reverse horizontal thrust diagram of the disclosed hingeless arch under a first load;
FIG. 6 is a reaction force diagram of the disclosed hingeless arch under a second load;
fig. 7 is a target inverse diagram of fig. 4, 5, and 6 superimposed.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the present invention, the terms "upper", "lower", "left", "right", "front", "rear", "top", "bottom", "inner", "outer", "center", "vertical", "horizontal", "lateral", "longitudinal", and the like indicate an orientation or positional relationship based on the orientation or positional relationship shown in the drawings. These terms are used primarily to better describe the invention and its embodiments and are not intended to limit the indicated devices, elements or components to a particular orientation or to be constructed and operated in a particular orientation.
Moreover, some of the above terms may be used to indicate other meanings besides the orientation or positional relationship, for example, the term "on" may also be used to indicate some kind of attachment or connection relationship in some cases. The specific meanings of these terms in the present invention can be understood by those skilled in the art as appropriate.
Furthermore, the terms "mounted," "disposed," "provided," "connected," and "connected" are to be construed broadly. For example, it may be a fixed connection, a removable connection, or a unitary construction; can be a mechanical connection, or an electrical connection; may be directly connected, or indirectly connected through intervening media, or may be in internal communication between two devices, elements or components. The specific meanings of the above terms in the present invention can be understood by those of ordinary skill in the art according to specific situations.
Furthermore, the terms "first," "second," and the like, are used primarily to distinguish one device, element, or component from another (the specific nature and configuration may be the same or different), and are not used to indicate or imply the relative importance or number of the indicated devices, elements, or components. "plurality" means two or more unless otherwise specified.
The embodiment of the invention discloses a method for loading a secondary self-reaction structure and calculating the support reaction, which can effectively reduce the support reaction of the secondary self-reaction structure, improve the economy, reduce the misjudgment on the structural feasibility and provide a direction for implementing a structural scheme.
The following detailed description is made with reference to the accompanying drawings.
Referring to fig. 2 to 3, the present invention provides a method for calculating the loading and support reaction of a secondary self-reaction structure, including
101. And calculating the total load borne by the secondary self-reaction structure.
In this embodiment, the secondary self-reaction force is a pair of self-reaction forces that are different from the load direction, often perpendicular, and independent of the load. In particular, a secondary reaction structure refers to a structure such as an arch, or the like, in which a secondary reaction exists at its seating connection. Taking an arch as an example, the arch structure can be a non-hinged arch or a double-hinged arch. The arch structure can be considered as a structure under which the columns are installed. The total load of the secondary self-reaction structure mainly comprises a constant load and a live load. Specifically, the constant load includes a self weight of the structure, a floor slab laminated layer, a floor slab surface layer, and the like, and is determined by a construction method and a structural method required by a main body function of the engineering. Live loads include loads of personnel, equipment, etc., as determined by engineering functions. That is, the constant load is generated by the engineering entity itself, and the live load is generated by the user and the equipment used. Of course, under the influence of environmental factors, the secondary self-reaction structure can also be acted by dynamic loads such as wind load, earthquake load and the like. In the structural engineering theory, the specific values of the loads of the types of the secondary self-reaction structure can be obtained by calculation according to a formula specified in an engineering specification.
102. And removing all or part of redundant constraints at the two symmetrical supports of the secondary self-reaction structure, so that any support of the secondary self-reaction structure is in a first state after the all or part of redundant constraints are removed, and applying a first load on the secondary self-reaction structure.
In this embodiment, the first state may be any one of unconnected, hinged, or semi-rigid. And in the first state, the secondary self-reaction structure can be a static structure state or a transient structure with non-negligible component geometric deformation.
Further, the step 102 specifically includes the following steps:
1021. and adjusting the state of the two symmetrical supports of the secondary self-reaction structure to form the state which is the same as or different from the second state.
Specifically, the second state may be a hinge, a semi-rigid connection, a rigid connection, or the like that is matched with the first state, and in the second state, the connection rigidity at the support of the secondary self-reaction force structure is greater than the connection rigidity at the support of the secondary self-reaction force structure in the first state. That is, when the first state is unconnected, the second state may be hinged, semi-rigid, or rigid. And when the first state is hinged, the second state may be semi-rigid or rigid. And when the first state is semi-rigid, the second state may be rigid.
That is, the support of the secondary self-reaction structure can be a fixed hinge support, a fixed end support or a sliding support.
The state which is the same as or different from the second state is a conventional connection state, that is, in the conventional connection state, the connection rigidity at the seat of the secondary self-reaction structure is once generated to bear the entire load. It can be known that, in the traditional connection state of the support of the secondary self-reaction structure, the number of connection constraints at the support is larger than that in the first state, but is smaller than or equal to that in the second state. The present invention only takes the conventional connection state and the second state as the same state as an example.
Adjusting the support of the secondary self-reaction structure to be in a second state, and calculating the number of redundant constraints at the support of the secondary self-reaction structure in the second state. That is, in the second state (and the conventional connection state), the secondary self-reaction structure is a statically indeterminate structure state.
1022. And calculating the number of the redundant constraints of the two symmetrical supports of the secondary self-reaction structure in the second state.
In this step, since the original secondary self-reaction structure is a statically indeterminate structure, all or part of redundant constraints can be removed, i.e., the secondary self-reaction structure is adjusted from the second state to the first state. The redundant constraint refers to unnecessary constraint, and the system can still be guaranteed to be constrained with unchanged geometry after the constraint is removed, and the number of the redundant constraint can be calculated according to a degree of freedom calculation formula in the structural mechanics theory, which is not described in detail herein.
1023. And releasing all or part of the redundant constraints at any support of the secondary self-reaction structure according to the number of the redundant constraints.
Specifically, taking the primary secondary self-reaction structure in the hyperstatic structural state (i.e. the second state) as an example of no-hinge arch (i.e. both ends of the member are fixed end supports, and there are three redundant constraints) to make a specific description of removing the redundant constraints: the specific steps for removing the redundant constraints are to remove one constraint, namely an angular constraint, at the mount at one end and two constraints, namely an angular constraint and a horizontal constraint, at the mount at the other end. Thus, the original non-hinged arch structure is changed into a structure that one support is a fixed hinge and the other support is a sliding hinge, the arch structure is a static structure or a transient structure considering the deformation of structural members, namely, the connection state at the support is the first state.
Similarly, taking the primary secondary self-reaction structure in the hyperstatic structural state as an hingeless arch (which can be regarded as a fixed connection upright column at each end of the hingeless arch) as an example, a specific description for removing the redundant constraint is given: the original hingeless arch truss structure has three redundant constraints, and the specific steps of removing the redundant constraints are removing one constraint, namely an angle constraint, at the support at one side of the arch truss and removing two constraints, namely the angle constraint and a horizontal line constraint, at the support at the other side of the arch truss. Thus, the original hingeless arch structure is changed into an arch structure with zero degree of freedom, and is in a statically determinate structural state (statically determinate structure neglecting the deformation effect of structural stress or transient structure considering the deformation effect of structural members).
1024. And taking the value of the first load.
In this step, the first load is an evenly distributed load, a concentrated load, a linear load and/or a displacement load, the value of the first load is smaller than the total load, and the first load needs to be determined according to the actual conditions and experience of the project.
1025. A first load is applied on the secondary self-reaction structure.
As an alternative embodiment, the first load may include a vertical load (the vertical load may include a leveling layer, a floor slab lamination layer, etc.), so that when the first load to be borne by the secondary self-reaction structure in the first state is applied, the vertical load may be applied to the secondary self-reaction structure by calculating the vertical load and then applying the vertical load to the secondary self-reaction structure according to the calculated value of the vertical load.
As another alternative, the first load may include a vertical load and a horizontal load, and before the first load to be borne by the secondary self-reaction structure in the first state is applied, the values of the vertical load and the horizontal load to be borne by the secondary self-reaction structure may be calculated, and then the vertical load and the horizontal load may be applied to the secondary self-reaction structure according to the calculated values.
In this embodiment, under the first load, the seat of the secondary self-reaction structure bears infinitesimal or zero secondary self-reaction in the first state. That is, in the first state, a secondary reaction force is hardly generated at the seat of the secondary reaction force structure (i.e., no horizontal thrust force is generated).
103. And adding the constraint which is not less than the released all or part of the redundant constraint, so that any support of the secondary self-reaction structure is adjusted to a second state from the first state, and a second load is applied to the secondary self-reaction structure.
Wherein, the second load includes equipartition load, concentrated load, line load or displacement load etc..
Further, the step 103 specifically includes the following steps:
1031. all or part of redundant constraints are added again at the positions where all or part of redundant constraints are released, and the other positions where the redundant constraints are conditionally added are added with the conditionally added redundant constraints.
In this step, after the full or partial redundant constraint is added, the secondary self-reaction structure returns to the initial statically indeterminate structure state (i.e. the second state) or the statically indeterminate structure which has more constraint and higher rigidity than the initial statically indeterminate structure state.
The specific description of adding the redundant constraint is also given by taking the initial secondary self-reaction structure in the hyperstatic structural state as an example of a hingeless arch (namely, two ends of the member are fixed end supports, and three redundant constraints are provided): after the step 1023, the hingeless arch is changed into a structure that one support is a fixed hinge support and the other support is a sliding hinge support, in the step, a constraint, namely an angle constraint, is added at the fixed hinge support, and two constraints, namely an angle constraint and a horizontal line constraint, are added at the sliding hinge support, so that the structure returns to the original hingeless arch, namely a secondary self-reaction structure in a hyperstatic structural state.
Similarly, taking the primary secondary self-reaction structure in the hyperstatic structural state as an hingeless arch (which can be regarded as a fixed connection upright column at each end of the hingeless arch) as an example, a specific description for removing the redundant constraint is given: the original hingeless arch frame structure is changed into an arch frame structure with zero degree of freedom and zero redundant constraint after going through the step 1023, and the arch frame structure is in a static structure state. In this step, a constraint and two constraints are respectively added at two nodes, so that the structure returns to the original hingeless arch form again, and the secondary self-reaction structure in the statically indeterminate structure state is formed.
1032. A second load is calculated.
Wherein the sum of the second load and the first load is equal to the total load, i.e. the second load is equal to the total load minus the first load.
That is to say, according to the scheme of the embodiment of the invention, the total load borne by the secondary self-reaction structure is applied in two stages, the first stage is the first load applied when the redundant constraint of the secondary self-reaction structure is removed in the static structure state, and the second stage is the second load applied when the two ends of the secondary self-reaction structure are adjusted to the hyperstatic structure state through adding the constraint on the basis of the static structure state. By adopting the mode, the purposes of reducing the counter force of the secondary self-reaction structure and reducing the bending moment of the homogenized secondary self-reaction structure can be achieved, so that the safety and the stress performance of the secondary self-reaction structure in the structure can be improved.
1033. And applying a second load on the secondary self-reaction structure.
104. Calculating a first counter force of a support of the secondary self-reaction structure in a first state based on the first load, calculating a second counter force of the secondary self-reaction structure in a second state based on the second load, and superposing the first counter force and the second counter force to obtain a target counter force.
This first counter-force includes first moment of flexure and first time self-reaction and first vertical counter-force of giving birth to, and this second counter-force includes second moment of flexure and second time self-reaction and the vertical counter-force of second, and the target counter-force includes target moment of flexure and target horizontal thrust and target vertical counter-force, is obtaining the target counter-force promptly, includes:
and superposing the first bending moment and the second bending moment to obtain a target bending moment, superposing the first self-reaction force and the second self-reaction force to obtain a target secondary self-reaction force, and superposing the first vertical reaction force and the second vertical reaction force to obtain a target vertical reaction force.
The following describes in detail the calculation process of the target reaction force using the present embodiment, taking the secondary self-reaction structure as an example without a hinge arch.
When the secondary self-reaction structure is a hingeless arch, the total load borne by the hingeless arch can be vertically uniformly distributed, the first load can be partially vertically uniformly distributed, and the second load is the residual vertically uniformly distributed load. That is, when the secondary self-reaction structure is a non-hinge arch, only the action of the vertical uniform load applied to the secondary self-reaction structure is considered. At the moment, the secondary self-reaction structure is in a statically indeterminate structure state, and is in a statically indeterminate structure for three times, and three redundant constraints are provided. According to step 102, three redundant constraints of no hinge arch in the statically indeterminate structural state are removed, so that the structure becomes an arch structure with one support being a fixed hinge support and the other support being a sliding hinge support, and the arch structure is in the statically indeterminate structural state.
The first reaction force calculation is performed on the arch structure in the statically determinate structure state (wherein the secondary self-reaction force takes the horizontal thrust as an example), and when the reaction force is calculated, the first vertical reaction force is not specifically calculated:
in the first stage, the connection state of the support of the secondary self-reaction structure is in a first state, and the application of a first load is uniform vertical load q1On the arch structure under the statically determinate structure. Under the first load q1Under the action, the support of the arch structure can generate rotation angle displacement and simultaneously generate sliding line displacement. When the structural mechanics theory is calculated, the stress deformation of the arch structure in the static structure state at this stage can be equivalent to the superposition of two independent stress deformations of the two hinged-arch hyperstatic structures. Specifically, the first part is a two-hinged arch loaded load q1The second part is a forced slip delta of a support with two hinged arches1Acting to produce a forced deformation in which the equivalent two-hinged arch forced slip Δ1Is assumed for ease of calculation to be equal to the glide displacement of the first state arch.
As shown in fig. 4 and 5, the first part: under the first load q1Under the action of the thrust of the two hinged arches, the support is
Two hinged archesThe bending moment of the support is zero, and the mid-span bending moment is
As shown in fig. 5, the second part: when relative displacement delta occurs between two hinged arch supports11I.e. the relative displacement of the first state transient arch support slip, which produces a reverse horizontal thrust H in the two-hinged arch hyperstatic configurationΔ11：
Because of forced slip Δ11At the first load q1Under the action of the force, the arch springing prevented by the self rigidity of the two hinged arch structures slides, so the force action is known from the mechanical law of the mutual action, and the support can prevent the thrust H to the arch springingA11The magnitude is equal to the horizontal thrust of the arch springing to the support, and the directions are opposite. Namely:
then:
midspan bending moment generated by displacement:
i.e. the first load q on both arches1First part of action and11the second part of the calculation of the effect shows that the first part produces a pedestal levelThe thrust is offset in the second part, namely the horizontal thrust of the support borne by the two hinged arches after the two parts are overlapped is zero, namely the first horizontal thrust is zero, and the positive bending moment in the span after the two parts are overlapped is increased, namely the first bending moment is
And
the two hinge arch support thrusts under the two processes are eliminated. The vertical counter force of the support is not generated by the second part (the vertical counter force is not calculated in the embodiment), and the vertical counter force generated by the first part is the same as the vertical counter force generated by the traditional hingeless arch, namely the first vertical counter force generated by the first load in the statically determinate structure in the first state is equal to the vertical counter force generated in the traditional structure, so that the correctness of the equivalent transformation which does not violate the natural law is verified.
According to step 103, the arch structure in the present statically determinate structure (transient structure considering elastic deformation) state is added with three constraints and returns to the original hingeless arch in the statically indeterminate structure state. The following second counter force of the hingeless arch under the hyperstatic structure state is calculated, and when the second counter force is calculated, the second vertical counter force is not specifically calculated:
as shown in FIG. 6, in the second stage of the clamped state, a second load, i.e., the remaining portion of the uniformly distributed vertical load q, is applied2And the second stage is actually the traditional non-hinged arch stress analysis, namely the second bending moment: midspan bending moment of MC2＝(1-K2)q2l2/24, bending moment of support A is MA2＝(1-K2)q2l2/12 bending moment M of the support BB2And MA2Are equal. The second horizontal thrust:
as shown in fig. 7, by using the superposition principle of the structural theory, the first bending moment and the second bending moment are superposed to obtain a target bending moment, and the first horizontal thrust and the second horizontal thrust are superposed to obtain a target horizontal thrust:
target bending moment: mid-span target bending moment MCIs equal to
And MC2＝(1-K2)q2l2The sum of/24. Neglect K1And K2On the assumption that the two are equal, the target mid-span bending moment
The target midspan bending moment of the two-state hingeless arch is larger than the midspan bending moment under the action of one-time applied total load q in the traditional calculation method.
Target bending moment of two symmetrical supports: because the two symmetrical supports have no bending moment in a static structure state, only the second load q is generated2The support bending moment of the non-hinged arch under the action is smaller than that of the non-hinged arch under the action of one-time application of total load q in the traditional method (comparing the load q)2And q is sufficient).
Target horizontal thrust: since the first target horizontal thrust is zero in the statically determinate structural condition, only the second load q is applied2The target horizontal thrust exists in the non-hinged arch under the action, so that the horizontal thrust is smaller than the horizontal thrust borne by the non-hinged arch under the action of the total load q applied by the support generated at one time in the traditional method (the comparison load q is smaller than the horizontal thrust borne by the non-hinged arch under the action of the total load q2And q is sufficient).
In summary, the internal force diagram with the horizontal thrust and the bending moment of the support disappearing and the midspan bending moment increasing in the static structure state in the first state is superposed with the unchanged internal force diagram in the hyperstatic structure state in the second state to obtain the full-load internal force diagram loaded in stages, and when the loads q in the two stages are q1And q is2When the proportion is appropriate, better bending moment homogenization effect can be obtained, and the horizontal thrust at the support can be reduced as far as possible.
Similarly, when the secondary self-reaction structure is an arch without hinges, the calculation process and the calculation result are similar to those of the arch without hinges, and are not described herein again.
By adopting the loading and support counterforce calculation method of the secondary self-counterforce structure, the horizontal thrust of the component can be reduced by applying the load in a staged state, and meanwhile, the purpose of reducing the homogenized full-span bending moment distribution can be achieved due to applying the load in a staged state. Therefore, the controlled secondary self-reaction force, namely the horizontal thrust is reduced or even eliminated, is beneficial to simplification during construction (manufacturing), and the section of the support is reduced compared with the traditional support, thereby saving materials, reducing the cost of protective measures such as corrosion prevention, fire prevention and the like, and reducing the manufacturing cost; the dead weight can be reduced, the shock resistance is improved, the stress deformation performance is comprehensively improved, and the safety is improved; the method provided by the invention can give full play to stress data with more sufficient material performance, economy and reasonability, reduces misjudgment on structural feasibility, provides a direction for implementing an engineering structural scheme, and can realize the engineering scheme which seems to be unsatisfiable.
The loading of the secondary self-reaction structure and the counter-force calculation method of the support disclosed by the embodiment of the invention are described in detail, a specific example is applied in the description to explain the principle and the implementation mode of the invention, and the description of the embodiment is only used for helping to understand the method and the core idea of the invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present specification should not be construed as a limitation to the present invention.
Claims (8)
1. A loading and support counterforce calculation method for a secondary self-counterforce structure is characterized by comprising the following steps:
calculating the total load borne by the secondary self-reaction structure;
removing all or part of redundant constraints at two symmetrical supports of the secondary self-reaction structure, so that any support of the secondary self-reaction structure is in a first state after the all or part of redundant constraints are removed, and applying a first load on the secondary self-reaction structure;
adding all or part of the unnecessary constraints which are not less than the released constraint so that any support of the secondary self-reaction structure is adjusted to a second state from the first state, and applying a second load on the secondary self-reaction structure;
calculating a first counter force of the secondary self-reaction force structure in the first state based on the first load, calculating a second counter force of the secondary self-reaction force structure in the second state based on the second load, and superposing the first counter force and the second counter force to obtain a target counter force;
wherein the sum of the first load and the second load is equal to the total load.
2. The method of claim 1, wherein the first load is a uniform load, a concentrated load, a linear load, and/or a displacement load, and the relieving all or part of the redundant constraints at the two symmetrical seats of the secondary self-reaction structure so that any seat of the secondary self-reaction structure is in a first state after relieving the all or part of the redundant constraints, and applying the first load on the secondary self-reaction structure comprises:
adjusting the state of two symmetrical supports of the secondary self-reaction structure to form the state which is the same as or different from the second state;
calculating the number of the redundant constraints of the two symmetrical supports of the secondary self-reaction structure in the connection state which is the same as or different from the second state;
removing all or part of the redundant constraints on any support of the secondary self-reaction structure according to the number of the redundant constraints so as to enable the redundant constraints to be in a first state;
taking the value of the first load;
applying the first load on the secondary self-reaction structure in the first state.
3. The method of claim 2, wherein under the first loading, any seat of the secondary counterforce structure bears a secondary counterforce of infinitesimal or zero in the first state.
4. The method of claim 1, wherein said second loading comprises one or any of uniform loading, concentrated loading, linear loading or displacement loading, said adding all or part of said no less than released redundant constraints such that said any seat of said secondary self-counterforce structure adjusts from said first state to a second state, applying a second loading on said secondary self-counterforce structure, comprising:
re-adding the removed all or part of the redundant constraints at the positions where the all or part of the redundant constraints are removed;
calculating the second load according to the first load;
applying the second load on the secondary counterforce structure.
5. The method of any one of claims 1 to 4, wherein the first counter force comprises a first vertical counter force, a first bending moment, and a first induced self-reaction force, wherein the second counter force comprises a second induced self-reaction force, a second vertical counter force, and a second bending moment, wherein the target counter force comprises a target secondary self-reaction force, a target vertical counter force, and a target bending moment, and wherein the step of superposing the first counter force and the second counter force to obtain the target counter force comprises:
and superposing the first self-reaction force and the second self-reaction force to obtain the target secondary self-reaction force, superposing the first vertical reaction force and the second vertical reaction force to obtain the target vertical reaction force, and superposing the first bending moment and the second bending moment to obtain the target bending moment.
6. The method of any of claims 1 to 4, wherein the type of seat of the secondary self-reaction structure comprises a fixed hinge seat, a fixed seat, or a sliding seat.
7. The method of any of claims 1 to 4, wherein the secondary counterforce structure is an arch or arch.
8. The method of claim 1, wherein the first state is any one of unconnected, hinged, or semi-rigid, the second state is any one of hinged, semi-rigid, or rigid mated to the first state, and the second state has a greater standoff connection stiffness of the secondary self-reaction structure than in the first state.
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