CN111814276B - Optimization method for T-shaped beam web section design - Google Patents
Optimization method for T-shaped beam web section design Download PDFInfo
- Publication number
- CN111814276B CN111814276B CN202010805949.4A CN202010805949A CN111814276B CN 111814276 B CN111814276 B CN 111814276B CN 202010805949 A CN202010805949 A CN 202010805949A CN 111814276 B CN111814276 B CN 111814276B
- Authority
- CN
- China
- Prior art keywords
- shaped beam
- shaped
- web
- section
- cross
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 17
- 238000013461 design Methods 0.000 title claims abstract description 14
- 238000005457 optimization Methods 0.000 title abstract description 7
- 238000005452 bending Methods 0.000 claims abstract description 14
- 230000000694 effects Effects 0.000 claims abstract description 13
- 238000010008 shearing Methods 0.000 claims abstract description 13
- 239000000463 material Substances 0.000 claims abstract description 9
- 238000012937 correction Methods 0.000 claims description 3
- 238000005381 potential energy Methods 0.000 abstract description 7
- 230000015556 catabolic process Effects 0.000 abstract description 4
- 238000005336 cracking Methods 0.000 abstract description 4
- 238000006731 degradation reaction Methods 0.000 abstract description 4
- 230000009286 beneficial effect Effects 0.000 abstract description 3
- 238000011160 research Methods 0.000 abstract description 3
- 229910000831 Steel Inorganic materials 0.000 abstract description 2
- 201000010099 disease Diseases 0.000 abstract description 2
- 208000037265 diseases, disorders, signs and symptoms Diseases 0.000 abstract description 2
- 238000004088 simulation Methods 0.000 abstract description 2
- 239000010959 steel Substances 0.000 abstract description 2
- 238000011426 transformation method Methods 0.000 abstract description 2
- 238000006073 displacement reaction Methods 0.000 description 5
- XEEYBQQBJWHFJM-UHFFFAOYSA-N Iron Chemical compound [Fe] XEEYBQQBJWHFJM-UHFFFAOYSA-N 0.000 description 2
- 230000007547 defect Effects 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000009826 distribution Methods 0.000 description 2
- 230000007847 structural defect Effects 0.000 description 2
- 238000010276 construction Methods 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 229910052742 iron Inorganic materials 0.000 description 1
- 238000012423 maintenance Methods 0.000 description 1
- 238000011089 mechanical engineering Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000007935 neutral effect Effects 0.000 description 1
- 230000002035 prolonged effect Effects 0.000 description 1
- 230000002787 reinforcement Effects 0.000 description 1
- 238000012216 screening Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 239000013589 supplement Substances 0.000 description 1
- 238000009827 uniform distribution Methods 0.000 description 1
- 238000012795 verification Methods 0.000 description 1
- 239000002023 wood Substances 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Geometry (AREA)
- Theoretical Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- Computer Hardware Design (AREA)
- General Engineering & Computer Science (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Computational Mathematics (AREA)
- Rod-Shaped Construction Members (AREA)
- Buildings Adapted To Withstand Abnormal External Influences (AREA)
- Bridges Or Land Bridges (AREA)
Abstract
The invention discloses an optimization method for a T-shaped beam web section design. Firstly, considering the influence of shear hysteresis effect, introducing shearing hysteresis warp stress and bending moment self-balancing conditions, and further obtaining the vertical bending deformation potential energy of the T-shaped beam. Then, an energy transformation method is utilized to obtain a T-beam vertical bending control differential equation and natural boundary conditions, the mechanical properties of the T-beam web are accurately analyzed based on the differential equation and the natural boundary conditions, finally, the T-beam web mechanical property research and the material properties are used as criteria, the T-beam web section size or the steel bar configuration is optimized, and the finite element simulation further proves the effectiveness of the invention. Because the method has accurate mechanical analysis, the optimized T-shaped beam has more excellent mechanical property, which is beneficial to avoiding the diseases such as cracking, rigidity degradation and the like of the bridge web of the T-shaped beam. The method has clear mechanical concept and good application value, thereby providing theoretical and technical support for the design of the cross section of the T-shaped beam web of the structural engineering.
Description
Technical Field
The invention relates to the technical field of structural engineering, in particular to an optimization method for a T-shaped beam web section design.
Background
The T-shaped structure has good mechanical properties, so that the T-shaped structure is widely applied to bridges with small and medium spans and mechanical engineering. Moreover, because the structure is always in a vertical bending state, the selection of reasonable cross section size of the web plate of the structure can lead the T-shaped structure to have good mechanical property. This not only reduces the maintenance costs of the T-shaped structure, but will also further increase the durability of this type of structure. Therefore, the invention has certain theoretical significance and engineering practical value.
At present, a plurality of T-shaped structures in operation generate serious structural defects, such as rigidity degradation of T-shaped beam bridges, web cracking and the like in civil engineering, and the serious structural defects threaten the safety of the whole structure. However, due to the limitations of the related design theory, no deep study is currently made on optimizing the cross section of the web of the T-beam, and the design of the cross section size of the web of the T-beam bridge is unreasonable. On the premise of meeting the using function of the structure, how to adapt to the mechanical characteristics of the structure, and screening the T-shaped structure with excellent output mechanical property becomes a target of continuous efforts of researchers. Because of the reasonable web section form, not only the mechanical property of the structure can be improved, but also the service life of the structure can be effectively prolonged.
Disclosure of Invention
The invention aims to solve the technical problem of overcoming the defects of the prior art and providing an optimization method for the design of the web section of the T-shaped beam.
The invention adopts the following technical scheme for solving the technical problems:
according to the optimization method of the T-shaped beam web section design provided by the invention,
first, the energy variance method is used to derive the values of w (z), θ (z) and v j Differential equation set of (z)
EIθ”(z)+kGA(w'(z)-θ(z))＝0
kGA(w”(z)-θ'(z))+q y ＝0
Further, the following equation is obtained
Finally, the positive stress sigma of the T-shaped beam web ZF
σ ZF ＝Eyθ'(z)+E(y-β)v″ j (z) (1)
Wherein:
the structural span is L, the symmetrical bending state w (z), and theta (z) is the vertical deflection and the section vertical corner of the primary equal beam theoretical T-shaped beam; v j (z) is vertical deflection caused by T-beam shear hysteresis; eta is about v j (z) solution coefficients of the characteristic equation; ch () is a hyperbolic cosine function; sh () is a hyperbolic sine function; E. g is Young's modulus and shear modulus of elasticity of the T-shaped beam material respectively; q y Uniformly distributing load for acting on the T-shaped beam; i is the moment of inertia of the T-beam about the x-axis; z, y, x are the axial, vertical and transverse coordinates, respectively, through the centroid of the T-beam cross section; i G Moment of inertia being a shearing effect associated with the T-beam flanges; beta is a correction coefficient of the T-shaped beam meeting the shearing and warping stress self-balancing condition; c 1 、c 2 、c 3 、c 4 、s 1 、s 2 、s 3 、s 4 Solving for a constant coefficient according to the T-beam related boundary condition; a is the cross-sectional area of the T-beam, the superscript' is the first derivative, the superscript "is the second derivative, the superscript (4) Is the fourth derivative, k is the T-shaped cross-sectional shape factor, I 2 Moment of inertia corresponding to T-beam wing plate shearing effect;
according to equation (1), the positive stress of the T-shaped beam web plate under the simple support boundary condition is obtained, and the positive stress of the T-shaped beam web plate is taken as a criterion, so that the section size T of the T-shaped beam is optimized w The method comprises the steps of carrying out a first treatment on the surface of the And finally, the mechanical property of the T-shaped structure is improved through the selection of the cross section size of the T-shaped beam.
Compared with the prior art, the technical scheme provided by the invention has the following technical effects:
(1) Firstly, considering the influence of shear hysteresis effect, introducing shearing hysteresis warp stress and bending moment self-balancing conditions, and further obtaining vertical bending deformation potential energy of the T-shaped beam; then, an energy transformation method is utilized to obtain a T-beam vertical bending control differential equation and natural boundary conditions, the mechanical properties of the T-beam web are accurately analyzed based on the differential equation and the natural boundary conditions, finally, the mechanical property research and the material properties of the T-beam web are used as criteria, the section size or the reinforcement configuration of the T-beam web are optimized, and the effectiveness of the invention is further proved by finite element simulation;
(2) Because the method has accurate mechanical analysis, the optimized T-shaped beam has more excellent mechanical property, which is beneficial to avoiding the diseases such as cracking, rigidity degradation and the like of the bridge web of the T-shaped beam;
(3) The method has clear mechanical concept and good application value, and is a beneficial supplement to the current bending-resistant design of the T-shaped structure.
Drawings
FIG. 1 is a cross-section and coordinate system diagram of a T-shaped structure in accordance with an embodiment of the present invention.
FIG. 2 is a diagram of boundary conditions and a coordinate system according to an embodiment of the present invention.
FIG. 3 is a graph showing the positive stress value (L 1 ＝L 2 =8m, concentrated load).
Detailed Description
The technical scheme of the invention is further described in detail below with reference to the accompanying drawings:
differential equation and natural boundary condition controlled by 1T-shaped beam
1.1 setting of longitudinal buckling Displacement function of T-shaped Beam wing plate
In the T-shaped beam shown in FIG. 1, if the structural span is L, the symmetrical bending state w (z), and theta (z) are the vertical deflection and the vertical rotation angle of the section of the primary equal beam theoretical T-shaped beam, v j And (z) is vertical deflection caused by T-beam shear hysteresis. Longitudinal displacement u of the T-beam flanges z (z, y, x) is the sum of the theoretical value of the primary beam and the longitudinal buckling displacement of the wing plate caused by the shear hysteresis effect; z, y, x are the axial, vertical and transverse coordinates, respectively, through the centroid of the T-beam cross section. Can be expressed as:
longitudinal displacement of the T-beam wing plates:
wherein v' j (z) is v j (z).
Wherein:the function of uneven distribution of the T-shaped beam wing plates is adopted; alpha and beta are wing plates to meet shearing stagnationWarp stress self-balancing condition correction coefficient, b is the width of a T-shaped beam wing plate, T w Is the cross-sectional dimension of the T-shaped beam. Wherein: t is t w /2≤x≤(b+t w /2)。
Then, the shear warp stress of the T-shaped beam wing plate is as follows:
wherein v j (z) is v j (z).
Wherein z, y and x are the axial, vertical and transverse coordinates passing through the centroid of the T-beam section respectively; e is Young's modulus of elasticity of T-shaped beam material, and alpha and beta are satisfied as ≡ A σ YB dA=0 and ≡ A σ YB Constant coefficient, σ, obtained by ydA =0 YB The shear-stagnation buckling stress of the T-shaped beam wing plates is achieved, and A is the cross-sectional area of the T-shaped beam. And:wherein h is 1 The distance from the wing plate of the T-shaped beam to the neutral axis is given, and I is the moment of inertia of the T-shaped beam about the x axis.
The longitudinal displacement of the T-shaped beam web is as follows:
u f (x,y,z)＝yθ(z)+(y-β)v' j (z) (3)
here, the shear stress of the T-shaped beam wing plate is taken as an independent stress system, which can satisfy the self-balancing of the shear warp stress, namely: the T-shaped cross section will satisfy both shear warp stress and bending moment balance.
1.2T-shaped Beam Total potential energy
(1) The positive stress and the shear stress of the T-shaped beam wing plate are respectively
Where θ' (z) is the first derivative of θ (z).
G is the shear modulus of elasticity of the T-beam material,
positive stress sigma of T-beam web ZF
σ ZF ＝Eyθ'(z)+E(y-β)v″ j (z) (6) (2) T-beam bridge deformation potential energy
Wing and web strain energy
Wherein:the existing formula is expressed without explanation.
Iron and wood Xin Ke shear strain energy
Where w' (z) is the first derivative of w (z) and k is the T-shaped cross-sectional shape factor.
Potential energy of load
Then, the total potential energy of the system
U＝U z1 +U G +U p (10)
Wherein: m is M 1 (z) is a bending moment about the x-axis generated by the shearing hysteresis effect of the T-beam wing plates; m is M z (z) bending moment about the x-axis when a vertical angle θ (z) is produced for the beam segment ends; q (z), Q y (z) is the vertical shearing force of the beam section end and the vertical distribution force on the T-shaped beam; e, G is Young's modulus and shear modulus of elasticity of the T-shaped beam material; a is that 1 ,A f Is T-beam wing plate and web cross section area, and A=A 1 +A f The method comprises the steps of carrying out a first treatment on the surface of the I is the moment of inertia of the T-beam about the x-axis, q y To uniformly distribute load on T-beam, I G Is T-shapedMoment of inertia of the beam-wing plate related shear effect.
1.3T-beam control differential equation and natural boundary conditions
From the variational principle δu=0, a T-beam control differential equation can be derived
Wherein delta is a variation symbol, U is the total potential energy of the T-shaped beam
EIθ″(z)+kGA(w'(z)-θ(z))＝0 (11)
kGA(w″(z)-θ'(z))+q y ＝0 (12)
Natural boundary conditions
The differential equations (11) and (12) are subjected to arrangement substitution to obtain w (z) and theta (z) equations
In c 1 ；c 2 ；c 3 ；c 4 Is a constant coefficient obtained according to the corresponding boundary conditions of w (z) and theta (z).
Also, from differential equation (13):
the characteristic equation is solved as follows: r is (r) 1,2 = ±η, η is related to v j (z) solution coefficients of the characteristic equation.
The solution of differential equation (20) is:
also, in s 1 ；s 2 ；s 3 ；s 4 Based on equation v j (z) constant coefficients obtained by corresponding boundary conditions, ch () being a hyperbolic cosine function; sh () is a hyperbolic sine function.
From the differential equations (11) - (13), it is known that: the mechanical property of the T-shaped beam is formed by superposing 2 independent mechanical systems, namely an elementary beam theory system and a shear stagnation theory system.
2T-beam common boundary conditions
According to equations (14) - (15), the theoretical specific boundary conditions of the primary beam can be obtained:
(1) Boundary conditions of correlation w (z) and θ (z)
A) Uniform load
B) Concentrated load
For simply supported T-beams, if the span is subjected to one or more concentrated forces (see FIG. 2), the concentrated force P 0 The distance between the left and right adjacent boundaries is L 1 And L 2 And w (z) and θ (z) subscripts represent z 1 Or z 2 Coordinate system, 0 1 ,0 2 Z respectively 1 Or z 2 Origin of coordinate system, and 0 2 The point is introduced intoColumn continuous boundary conditions:
likewise, according to equations (16) - (17), the shear theoretical boundary conditions can be obtained:
(2) Correlation v j Boundary conditions of (z)
A) Uniform distribution force
B) Force concentration
Also, if the bay is stressed by one or more concentrated forces (see FIG. 2), and v j The subscript number indicates that it is at z 1 Or z 2 Coordinate system of 0 2 The point also needs to introduce boundary conditions:
v j1 (0)＝0；v j1 (L 1 )＝v j2 (0)；v' j1 (L 1 )＝v' j2 (0)；v″ j1 (L 1 )＝v″ j2 (0)；v j2 (L 2 )＝0；v″ j1 (0)＝0；
3. optimization of cross-sectional dimensions of T-shaped structures
Based on the mechanical property refined analysis of the T-shaped beam and the material property thereof. According to the invention, the shearing hysteresis effect is considered, and the difference between the first-class beam theory and the shearing hysteresis theory of the T-shaped beam web is compared and analyzed through the mechanical property research of the T-shaped beam web. Further, considering the characteristics of the T-shaped structure, the cross section size of the web plate of the T-shaped beam is optimized.
Note that: b is half of the length of the upper wing plate of the T-shaped beam; t is t w Is the thickness of a T-shaped beam web; t is the thickness of the T wing plate; h is the T-beam height.
Practical application and effect verification:
for T-shaped sectionThe material parameters and the geometric parameters of the face beam are as follows: e=3.5×10 4 MPa；G＝1.5×10 4 MPa；t w =0.2m; t=0.1m; b=2.4m; beam height h=1.2m. Concentration force P in mechanical analysis k (z) =l×9800N, where L is the T-beam span and the concentrated force is applied in the simply supported T-beam span. Further, the T-beam web normal stress is calculated according to the derivation formula and other algorithms of the present invention.
TABLE 1 simple T-beam web normal stress L 1 ＝L 2 ＝8m](concentrated load)
By analysis of mechanical properties of the simply supported T-beam web (Table 1, FIG. 3), the effect of shear hysteresis at the intersection of the wing and web has a greater impact on the normal stress value. Based on elementary beam theory, the positive stress at the intersection of the wing plate and the web plate of the T-shaped beam is-14.369 multiplied by 10 5 pa, and the actual stress is- (14.369+5.370). Times.10 5 pa, wherein-5.370X 10 5 pa is the calculated theoretical cause missing parts. Then the actual stress is reduced to the theoretical design value of the elementary beam and the web width is increased by Δt. Namely: 14.369 = [ (14.369+5.370) × (1.2×0.2)]/[1.2×(0.2+Δt)]Δt=0.075 m, based on design and construction considerations, here taken: Δt=0.1m, i.e. at this time: t is t w =0.3m. In addition, the arrangement of the longitudinal steel bars can be increased through the intersection of the wing plates and the web plates. Based on the method, the defects of cracking, rigidity degradation and the like of the T-shaped bridge web plate can be effectively avoided, and the durability design of the T-shaped structure is further realized.
The foregoing embodiments are merely illustrative of the technical concept and features of the present invention, and are not intended to limit the scope of the invention. All equivalent changes or modifications made according to the spirit of the main technical proposal of the invention should be covered in the protection scope of the invention.
Claims (1)
1. A method for optimizing the design of the cross section of a T-shaped beam web is characterized in that,
first, the energy variance method is used to derive the values of w (z), θ (z) and v j Differential equation set of (z)
EIθ”(z)+kGA(w'(z)-θ(z))＝0
kGA(w”(z)-θ'(z))+q y ＝0
Further, the following equation is obtained
Finally, the positive stress sigma of the T-shaped beam web ZF
σ ZF ＝Eyθ'(z)+E(y-β)v″ j (z) (1)
Wherein:
the structural span is L, the symmetrical bending state w (z), and theta (z) is the vertical deflection and the section vertical corner of the primary equal beam theoretical T-shaped beam; v j (z) is vertical deflection caused by T-beam shear hysteresis; eta is about v j (z) solution coefficients of the characteristic equation; ch () is a hyperbolic cosine function; sh () is a hyperbolic sine function; E. g is Young's modulus and shear modulus of elasticity of the T-shaped beam material respectively; q y Uniformly distributing load for acting on the T-shaped beam; i is the moment of inertia of the T-beam about the x-axis; z, y, x are the axial, vertical and transverse coordinates, respectively, through the centroid of the T-beam cross section; i G Moment of inertia being a shearing effect associated with the T-beam flanges; beta is a correction coefficient of the T-shaped beam meeting the shearing and warping stress self-balancing condition;c 1 、c 2 、c 3 、c 4 、s 1 、s 2 、s 3 、s 4 solving for a constant coefficient according to the T-beam related boundary condition; a is the cross-sectional area of the T-beam, the superscript' is the first derivative, the superscript "is the second derivative, the superscript (4) Is the fourth derivative, k is the T-shaped cross-sectional shape factor, I 2 Moment of inertia corresponding to T-beam wing plate shearing effect;
according to equation (1), the positive stress of the T-shaped beam web plate under the simple support boundary condition is obtained, and the positive stress of the T-shaped beam web plate is taken as a criterion, so that the section size T of the T-shaped beam is optimized w The method comprises the steps of carrying out a first treatment on the surface of the And finally, the mechanical property of the T-shaped structure is improved through the selection of the cross section size of the T-shaped beam.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010805949.4A CN111814276B (en) | 2020-08-12 | 2020-08-12 | Optimization method for T-shaped beam web section design |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010805949.4A CN111814276B (en) | 2020-08-12 | 2020-08-12 | Optimization method for T-shaped beam web section design |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111814276A CN111814276A (en) | 2020-10-23 |
| CN111814276B true CN111814276B (en) | 2024-04-02 |
Family
ID=72859246
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010805949.4A Active CN111814276B (en) | 2020-08-12 | 2020-08-12 | Optimization method for T-shaped beam web section design |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111814276B (en) |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE4039335A1 (en) * | 1990-12-10 | 1991-06-13 | Gernot Wolperding | Rolled steel section beam - bridge piece and two flanges with concrete layer |
| CN105046027A (en) * | 2015-09-01 | 2015-11-11 | 盐城工学院 | Optimized design method for section of multi-rib type T-shaped beam bridge |
| CN105117574A (en) * | 2015-10-14 | 2015-12-02 | 盐城工学院 | Design optimization method for T-beam bridge section |
| CN106894328A (en) * | 2017-02-20 | 2017-06-27 | 重庆大学 | A kind of processing method of Π shapes bondbeam Shear Lag |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| TWI328177B (en) * | 2007-01-30 | 2010-08-01 | Ind Tech Res Inst | Method of evolutionary optimization algorithm for structure design |
-
2020
- 2020-08-12 CN CN202010805949.4A patent/CN111814276B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE4039335A1 (en) * | 1990-12-10 | 1991-06-13 | Gernot Wolperding | Rolled steel section beam - bridge piece and two flanges with concrete layer |
| CN105046027A (en) * | 2015-09-01 | 2015-11-11 | 盐城工学院 | Optimized design method for section of multi-rib type T-shaped beam bridge |
| CN105117574A (en) * | 2015-10-14 | 2015-12-02 | 盐城工学院 | Design optimization method for T-beam bridge section |
| CN106894328A (en) * | 2017-02-20 | 2017-06-27 | 重庆大学 | A kind of processing method of Π shapes bondbeam Shear Lag |
Non-Patent Citations (1)
| Title |
|---|
| 双肋式T形梁力学性能的理论分析;甘亚南等;《力学与实践》;20170608;全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111814276A (en) | 2020-10-23 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Wright et al. | BEF analogy for analysis of box girders | |
| Barrois | Stresses and displacements due to load transfer by fasteners in structural assemblies | |
| WO2018151298A1 (en) | Analysis method, design method, production method, and program | |
| CN106767667B (en) | Using the appraisal procedure of the steel-concrete composite beam fatigue additional deformation of Welded-Stud Conectors | |
| CN110032829B (en) | Stress calculation method of steel-concrete composite beam | |
| Chang | Shear lag effect in simply supported prestressed concrete box girder | |
| Alinia et al. | A parametric study on the longitudinal stiffeners of web panels | |
| JP2018131883A (en) | Floor structure | |
| CN114218658B (en) | Internal force deformation analytic calculation method suitable for anchor cable frame structure | |
| CN111753357B (en) | Distribution method of shear stress of web plate of variable-cross-section multi-chamber corrugated steel web plate box girder | |
| CN111814276B (en) | Optimization method for T-shaped beam web section design | |
| CN105046027A (en) | Optimized design method for section of multi-rib type T-shaped beam bridge | |
| Luo et al. | Finite segment method for shear lag analysis of cable-stayed bridges | |
| CN108763667B (en) | Simplified design method of large-curvature curve steel-concrete combined box girder bridge | |
| JP4813893B2 (en) | Bond stress calculation method, stud shear force calculation method, design method, steel plate concrete structure | |
| CN113656861A (en) | Method for calculating space mapping deformation of ballastless track caused by railway bridge deformation | |
| CN111723428A (en) | Continuous rigid frame bridge forming pre-camber setting method based on displacement influence line distribution | |
| Kumar et al. | Stress concentration in composite cantilever plates—effect of stiffeners and remedy | |
| Tauchert | Plane piezothermoelastic response of a hybrid laminate—a benchmark problem | |
| CN115630458A (en) | Method for casting continuous beam in situ based on elastic foundation beam theory and application thereof | |
| CN106649921B (en) | Optimization method for torsional section design of T-shaped beam | |
| Seide et al. | Elastic and Plastic Buckling of Simlpy Supporetd Solid-core Sandwich Plates in Compression | |
| Johnson | Loss of interaction in short-span composite beams and plates | |
| CN109024233A (en) | Get higher the construction method of the Long span Wavelike steel webplate composite beam bridge of back boxing concrete | |
| CN112131631B (en) | Optimization method for section of rectangular box Liang Kangniu |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |