CN110990922A - Method for calculating bending resistance bearing capacity of cross-section beam under action of negative bending moment - Google Patents
Method for calculating bending resistance bearing capacity of cross-section beam under action of negative bending moment Download PDFInfo
- Publication number
- CN110990922A CN110990922A CN201911184101.8A CN201911184101A CN110990922A CN 110990922 A CN110990922 A CN 110990922A CN 201911184101 A CN201911184101 A CN 201911184101A CN 110990922 A CN110990922 A CN 110990922A
- Authority
- CN
- China
- Prior art keywords
- bearing capacity
- section
- concrete
- action
- moment
- 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.)
- Granted
Links
- 238000005452 bending Methods 0.000 title claims abstract description 86
- 230000009471 action Effects 0.000 title claims abstract description 44
- 238000000034 method Methods 0.000 title claims abstract description 27
- 239000002131 composite material Substances 0.000 claims abstract description 19
- 230000006835 compression Effects 0.000 claims abstract description 12
- 238000007906 compression Methods 0.000 claims abstract description 12
- 230000007935 neutral effect Effects 0.000 claims abstract description 10
- 238000009826 distribution Methods 0.000 claims abstract description 9
- 229910000831 Steel Inorganic materials 0.000 claims description 106
- 239000010959 steel Substances 0.000 claims description 106
- 238000004364 calculation method Methods 0.000 claims description 21
- 229910001294 Reinforcing steel Inorganic materials 0.000 claims description 16
- 210000002435 tendon Anatomy 0.000 claims description 10
- 230000000694 effects Effects 0.000 claims description 4
- 230000003472 neutralizing effect Effects 0.000 claims description 4
- 239000011241 protective layer Substances 0.000 claims description 3
- 238000012360 testing method Methods 0.000 description 58
- 238000013461 design Methods 0.000 description 14
- 238000006073 displacement reaction Methods 0.000 description 12
- 230000008569 process Effects 0.000 description 7
- 238000004088 simulation Methods 0.000 description 7
- 230000008859 change Effects 0.000 description 4
- 238000011160 research Methods 0.000 description 4
- 238000011161 development Methods 0.000 description 3
- 239000000463 material Substances 0.000 description 3
- 230000033228 biological regulation Effects 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000002474 experimental method Methods 0.000 description 2
- 238000010008 shearing Methods 0.000 description 2
- 238000009864 tensile test Methods 0.000 description 2
- 238000010998 test method Methods 0.000 description 2
- 238000003466 welding Methods 0.000 description 2
- 229910000746 Structural steel Inorganic materials 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000002457 bidirectional effect Effects 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 230000000052 comparative effect Effects 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 238000005336 cracking Methods 0.000 description 1
- 230000007423 decrease Effects 0.000 description 1
- 238000009415 formwork Methods 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 239000010410 layer Substances 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000012544 monitoring process Methods 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 230000002787 reinforcement Effects 0.000 description 1
- 230000003014 reinforcing effect Effects 0.000 description 1
- 238000005464 sample preparation method Methods 0.000 description 1
- 238000004062 sedimentation Methods 0.000 description 1
- 238000004901 spalling Methods 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
- 239000003351 stiffener Substances 0.000 description 1
Images
Landscapes
- Rod-Shaped Construction Members (AREA)
Abstract
本发明公开了一种负弯矩作用下截面梁的抗弯承载力计算方法，判断完全抗剪连接新型截面组合梁在负弯矩作用下达到承载力极限状态时截面中和轴的位置；根据中和轴位置代入对应公式求解极限抗弯承载力，塑性中和轴在波纹侧板内时截面应力分布此时满足公式fybdtd+α1fc(b‑hr)β1(ha‑td‑tu)≥fpyAp+2fybutu+fysAs (1)；根据力的平衡算出混凝土等效受压区高度x，fpyAp+2fybutu+fysAs＝fybdtd+a1fc(b‑hr)x (2a)
The invention discloses a method for calculating the flexural bearing capacity of a cross-section beam under the action of negative bending moment, which judges the position of the neutral axis of the section when a new type of section composite beam with complete shear connection reaches the ultimate state of bearing capacity under the action of negative bending moment; Substitute the position of the neutral axis into the corresponding formula to solve the ultimate flexural bearing capacity. When the plastic neutral axis is in the corrugated side plate, the section stress distribution satisfies the formula f y b d t d +α 1 f c (b‑h r )β 1 (h a ‑t d ‑t u )≥f py A p +2f y b u t u +f ys A s (1); Calculate the concrete equivalent compression zone height x according to the balance of forces, f py A p + 2f y b u t u +f ys A s =f y b d t d +a 1 f c (b‑h r )x (2a)
Description
Technical Field
The invention relates to a method for calculating the bending resistance bearing capacity of a combined beam, in particular to a method for calculating the bending resistance bearing capacity of a section beam under the action of negative bending moment.
Background
In order to actively respond to the application and development of the assembly type structure carried out by the state in the building industry, the report provides a beam body of the assembly type structure: crustal beam, as shown in figure 1. The beam side web plates are made of corrugated steel and are welded with the bottom steel plate and the top steel plate. The top plates on the two sides are connected by utilizing C-shaped steel to restrain the steel plates on the two sides and enhance the restraint effect of the side web plates on concrete. Besides, concrete is filled in the beam, and the prestressed steel strands are tensioned by a post-tensioning method to enhance the bending resistance of the beam. Stiffeners may be placed in the quarter of the main beam to make the connection to the steel secondary beam.
For a structural beam, its load bearing capacity is the foundation for construction and design. Generally, the method for obtaining the structural beam body is generally a simulation method, a test method or a formula calculation method, but the test cost is high, and the simulation and calculation methods are more common. The simulation and calculation formula for the bearing capacity of a common structural beam body is mature, but for the novel section combination beam, the structural change is large, influence factors are more, and at present, the simulation and calculation formula for the bearing capacity of the novel section combination beam has no clear result. Although the finite element simulation can be used to accurately simulate the bearing capacity of the fabricated structural beam body, the finite element simulation process is tedious and time-consuming. In the conventional formula calculation methods, the following three categories are mainly theoretically classified. The first category is the "unified theory" based on experimental regression, which was first proposed by professor calotropis of the university of harbin, and means that "the properties of concrete filled steel tube elements change as physical parameters, geometrical parameters, stress states and section patterns change, and the changes are continuous, related and unified. The theory mixes steel and concrete into a combined material, and the steel and the concrete are not distinguished, so that the concept of internal force distribution or superposition is abandoned. The specifications adopting the theory are electric power industry standard DL/T5085 and Fujian province standard DBJ 13-51-2003. The second is a conversion theory, where concrete is converted into steel and then designed as a pure steel structure. The core of the theory is that the filling concrete is used for improving the yield strength and the elastic modulus of the steel pipe wall on the premise of not changing the cross section area of the steel pipe, so that the property of the equivalent steel pipe is converted, and the bearing capacity of the equivalent steel pipe member is used as the bearing capacity of the original steel pipe concrete member. "typical specifications such as AISC360, national specification CECS 159: 2004. CECS 28: 90 and european norm. The third type is the stacking theory, which essentially adds the bearing capacity of the steel tube and the bearing capacity of the concrete to obtain the bearing capacity of the concrete-filled steel tube member. However, this method considers that if the axial pressure is less than the bearing capacity of the concrete, the whole is borne by the concrete, otherwise, the rest is borne by the steel pipe, and the mode of preferential stress of the concrete may not be in accordance with the reality.
Disclosure of Invention
The invention provides a method for calculating the bending resistance bearing capacity of a section beam under the action of negative bending moment, which is characterized in that on the basis of a calculation theory, the bending resistance performance of a combined beam under the action of negative bending moment is subjected to parameter analysis, and the beam is designed into complete shear connection during design, so that the combination effect of a carapace beam can be fully exerted, and the bearing capacity of the carapace beam is improved.
A method for calculating the bending resistance bearing capacity of a section beam under the action of a hogging moment comprises the following steps:
s1, judging the position of a section neutral axis when the completely shear-resistant connecting novel section composite beam reaches the bearing capacity limit state under the action of a hogging moment;
s2, substituting the position of the neutral axis into a corresponding formula to solve the ultimate bending resistance bearing capacity,
the section stress distribution of the plastic neutralizing shaft in the corrugated side plate satisfies the formula (1)
fybdtd+α1fc(b-hr)β1(ha-td-tu)≥fpyAp+2fybutu+fysAs(1)；
In the formula: f. ofysDesigned value of tensile strength of hogging moment reinforcing steel bar, N/mm2；
AsIs the area of the hogging moment reinforcing steel bar, mm2；
haIs the section height of the steel armor shell.
And calculating the height x of the equivalent compression area of the concrete according to the balance of the forces, as shown in the formula (2):
fpyAp+2fybutu+fysAs＝fybdtd+α1fc(b-hr)x (2a)
taking a moment from the equivalent rectangular resultant force point of the concrete in the compression area to obtain the ultimate bending resistance bearing capacity M of the shell beamuAs in formula (3):
in the formula: c is the thickness of the protective layer, mm;
d is the diameter of the hogging moment reinforcing steel bar, mm;
hpthe distance from the center of the section of the prestressed tendon to the upper surface of the flange steel plate on the beam is mm.
The section still accords with the assumption of a flat section after being loaded, and the section is in linear distribution when yielding.
The concrete compressive stress is distributed in a rectangular shape under the condition of ultimate bearing capacity, the value is α 1fcbx, and the concrete action in a tension area is ignored.
When a positive section bending resistance bearing capacity calculation formula is established, the resultant force action point of the equivalent rectangular stress of the concrete is positioned at the center of the concrete compression area.
The influence of the local buckling of the steel beam of the composite beam on the bearing capacity is ignored under the action of the hogging moment.
The tensile contribution of the corrugated side panels is neglected.
Because the novel section composite beam has novel structure, the existing design specifications and regulations at home and abroad do not provide a specific design formula for the novel section composite beam. On the basis of a calculation theory, the invention refers to relevant regulations of 'composite structure design specifications' (JGJ 138-. A report is combined with experimental research and finite element simulation analysis to provide a design formula of the bending resistance and the bearing capacity of the positive section of the novel section composite beam.
The invention has the following advantages:
this scheme has carried out the static test to two carapace roof beam test pieces, has studied the bending resistance of this kind of combination beam under the hogging moment effect, has considered the influence of bottom flange steel sheet thickness to combination beam bending resistance in the experiment. The crustal beam is subjected to parameter analysis, and the influence of the steel strength, the concrete strength, the section area of the prestressed tendon, the section area of the negative-moment reinforcing steel bar and the thickness of the lower flange steel plate on the flexural bearing capacity is considered. And finally, establishing a cross section bending resistance bearing capacity calculation formula under the action of the hogging moment of the complete shear connection shell beam based on a cross section plasticity design theory. Through the research and analysis in this chapter, the following conclusions are obtained:
(1) the crustal beam has good mechanical properties, which are mainly characterized by high ultimate bending bearing capacity, large rigidity, good deformation performance and good ductility. Under the action of negative bending moment, the steel beam is in a tension state, and the concrete is in a compression state, but the overall working performance of the combined beam is better. Therefore, in a normal use state, the cracks and deflection of the composite beam can be effectively controlled through the reasonable design of the composite beam.
(2) The cross section area of the prestressed tendon is increased, so that the bending resistance bearing capacity and the bending rigidity under the action of the cross section negative bending moment of the shell beam can be obviously improved; the thickness of the lower flange steel plate, the strength grade of steel and the cross section area of the negative bending moment reinforcing steel bar are improved, so that the bending resistance bearing capacity under the negative bending moment action of the component can be improved. The improvement of the strength grade of the concrete has little influence on the bending resistance bearing capacity under the action of the negative bending moment of the member.
(3) Based on the cross-section plasticity design theory, a bending resistance bearing capacity design formula under the action of the hogging moment of the completely shear-connected shell beam is deduced, the mean value of the bending resistance bearing capacity under the action of the hogging moment of the shell beam obtained by the calculation formula and the ultimate bending moment ratio obtained by finite element analysis is 0.99, the variance is 0.0005, and the bending resistance bearing capacity of the shell beam with the prestressed tendons can be accurately calculated.
Drawings
FIG. 1 is a view of a beam structure;
FIG. 2 is a cross-sectional stress profile of the present invention when the plastic neutralizing shaft is inside the corrugated side plate;
FIG. 3 Lb-1 is used to embody test piece design parameters;
FIG. 4 is a schematic diagram of a prestressed reinforcement arrangement structure;
FIG. 5 is LbA size structure schematic diagram of a group of 2mm thick steel tensile test pieces;
FIG. 6 is a view of the loading device layout;
FIG. 7 is a strain gage layout view;
FIG. 8 is a plot of specimen load versus mid-span deflection.
In the figure, 1, a lower flange steel plate; 2. a corrugated plate; 3. channel steel; 4. a top flange steel plate; 5. a secondary beam connecting plate; 6. and (4) prestressed tendons.
Detailed Description
A method for calculating the bending resistance bearing capacity of a section beam under the action of negative bending moment comprises the following steps of firstly designing a test piece; for researching the stress performance of the crust beam under the action of negative bending moment, the pair2 test pieces of this type of simply supported beam 2/5 reduced scale were subjected to a bending resistance load test. The influence of the thickness of the bottom plate on the bending rigidity and the bending bearing capacity under the action of the hogging moment of the crust beam is mainly considered in the test. 2 combined beam test pieces are designed, all are acted by negative bending moment and are respectively numbered as Lb-1、Lb-2, the span is uniformly taken to be 3.6m, and the beam width is 200 mm. L isbThe test pieces are convenient to test, the test pieces are loaded in an inverted mode, and the influence of the tension of the concrete floor on the bending resistance bearing capacity of the combined beam is small when the concrete floor is inverted, so that the widths of the flanges of the test piece floor under the action of the negative bending moment are 280mm, and the thicknesses of the flanges of the test piece floor are 60 mm. The U-shaped steel is made of Q345 steel, the channel steel shear connector is made of Q345 steel, and the channel steel shear connector is formed by bending a steel plate with the thickness of 3 mm. The strength grade of the concrete was C40. The prestressed steel strand adopts a high-strength low-relaxation steel strand of GB/T5224-2014 standard.
In the Lb group test piece, 4 reinforcing steel bars with the diameter of 12mm are arranged in a tension area of a pure bending section, and the HRB400 is adopted as the reinforcing steel bar. Reference specimen LbThe-1 design parameters are shown in FIG. 3. Test piece Lb-2 remaining section parameters and Lb1-1 same, only the thickness of the base plate is changed in order to compare the influence of the thickness of the base plate on the bending resistance of the beam under the action of the hogging moment. Specific comparative parameters are shown in table 3.
TABLE 3 carapace Beam LbComparative parameters of test pieces
Designing the prestress: prestressing is applied to the test beams, 2 steel strands with the diameter of 15.2mm are uniformly arranged, and the sectional area of each steel strand is 138.44mm2. In order to simulate the stress condition at the support and ensure that the prestressed tendon is pulled, inverted loading is adopted.
The test piece structure is as follows:
the U-shaped steel beam is formed by welding six corrugated steel webs, a bottom steel plate and two top steel plates. The thickness of the corrugated steel web of the pure bending section is 1mm, the thickness of the corrugated steel web of the shearing span section is 3mm, two adjacent corrugated side plates are welded on the secondary beam connecting plate to form side plates of the U-shaped steel beam, and the secondary beam connecting plate is welded with a stud with the diameter of 16mm to enhance the bonding between the stud and the concrete. And a channel steel shear connector with the thickness of 3mm is arranged at the top of the welded U-shaped steel, and the channel steel is connected with the U-shaped steel through a fillet weld. After the channel steel is welded, corrugated pipes are arranged in the steel beams and prestressed tendons are placed in the steel beams. After the U-shaped steel beam is welded, double-layer bidirectional structural steel bars are arranged in a concrete slab, the upper steel bar parallel to the beam is 6@250, the lower steel bar parallel to the beam is 6@140, the upper steel bar and the lower steel bar perpendicular to the beam are 6@250, the steel bars are bound into a steel bar mesh in a factory and are directly placed in a formwork before concrete is poured. Before concrete pouring, a test piece is firstly supported, reinforcing mesh sheets are arranged according to design requirements after the test piece is supported, and then concrete is poured. And (4) naturally curing the test piece, and removing the mold after curing for 48 hours. And (5) after the concrete is cured for 20 days, the concrete reaches the designed strength, prestress tensioning is carried out, the concrete is cured for 10 days after grouting in the pipeline, and the test piece is finished.
The experimental protocol was designed as follows:
material property experiment:
the steel plate of the test beam under the action of the hogging moment is a Q345 steel plate with nominal thicknesses of 1mm, 2mm, 3mm and 6mm respectively. The sample preparation and test methods are the same as those of the La group of test pieces and are not repeated. Because the Lb group test pieces 1mm, 3mm and 6mm and the channel steel blanking steel materials are the same as those of the La group test pieces, 3 Lb group test pieces with the thickness of 2mm and the number of F are only needed to be manufactured. The dimensions of a 2mm nominal thickness steel standard tensile test piece are shown in figure 5. Table 3 records the measured values of the mechanical property indexes of the steel.
TABLE 3 measured values of mechanical properties of steels
The loading mode is as follows:
in order to research the stress condition of the support under the action of the negative bending moment, the stress performance of the support in the continuous composite beam is simulated mainly by inverting the test piece beam and adopting a top-down trisection symmetrical loading mode. The method mainly researches the ultimate bending bearing capacity of the beam under the action of the negative bending moment and the occurrence and development conditions of the local buckling of the pressed steel beam. The loading device is shown in fig. 6 a). The test beam adopts a 1000 t-level oil jack to carry out two-point symmetrical loading, and the load is transmitted to the loading point of the test piece through the distribution beam. The distance between the loading points is 1.2 meters.
The test adopts graded loading, the load control loading is adopted in the elastic range, each grade of load is 1/10 of the predicted limit load, the duration time of each grade of load is about 2 minutes, when the component enters the elastoplasticity stage, the displacement control graded loading is adopted, each grade of load is loaded for 2mm, and when the component approaches the limit load, a slow displacement control continuous loading mode is adopted until the test piece is damaged.
The measurement point arrangement is as follows:
stress
Each test piece of the Lb group is provided with a strain gauge for monitoring the strain development process of steel, negative bending moment steel bars and concrete flanges in the stress process, wherein 13 unidirectional strain gauges are arranged on a steel shell, 2 strain gauges are arranged on a strain flower, 4 unidirectional strain gauges are arranged on a floor slab, one strain gauge is arranged on each negative bending moment steel bar in a span, and 1 strain gauge is attached to an anchorage device to measure the stress change of prestressed bars. The specific arrangement positions and part of the strain gage numbers are shown in fig. 7.
Deflection
By measuring the displacement condition of each characteristic section of the combined beam in the test process, the relationship between the force and the displacement of the beam in the elastic stage, the elastoplastic stage and the final plastic failure stage can be obtained. A total of 9 displacement sensors (LVDT) are arranged on each test piece in the test to measure the displacement of the test piece. The displacement meters with the numbers of L1, L2 and L3 are used for measuring the deflection of the midspan and the loading point of the test piece, the displacement meters L4 and L5 are used for measuring the sedimentation of the test piece support, the displacement meters L6 and L7 are used for measuring the rotating angle of the test piece support, and the displacement meters L8 and L9 are used for measuring the slippage between the concrete slab and the upper flange of the steel plate.
The experimental phenomena are as follows:
test piece Lb-1 is a reference specimen. In the elastic stage, load is controlled by adopting load, and the deflection of the beam linearly increases along with the increase of the load. When the load reaches 160kN, the method is carried outThe concrete slab at the position of the channel steel near the loading point is provided with a first transverse crack, when the load reaches 180kN, the concrete slab at the position of the channel steel is provided with three transverse cracks and extends to the side of the slab, when the load is increased to 340kN, the transverse cracks are formed at equal intervals in the pure bending section and the bending and shearing section close to the loading point, and the transverse cracks are mainly formed at the position where the channel steel is arranged in the slab. And an inclined crack extending from the position of the hogging moment reinforcing steel bar to the flange steel plate at the loading point is formed near the loading point. When the load reaches 380kN, a transverse crack also appears at the arrangement position of the channel steel of the bending shear section. And continuously loading to 560kN, wherein the upper flange steel plate is subjected to tensile yielding, the test piece enters an elastoplastic stage, the crack at the bottom of the midspan concrete plate is wider, the concrete plate basically exits from working, no other obvious phenomenon except that the crack which appears before is wider and wider is generated, and then the displacement control loading is adopted.
When the load is continuously loaded to 692kN, the lower flange steel plate in the pure bending section near the loading point is locally pressed and bent, the concrete at the bottom of the concrete plate is peeled off, the load is slowly increased, and the mid-span deflection is rapidly increased. And continuously loading, wherein the deformation of the partially bent lower flange steel plate is more and more serious, when the load reaches 717kN, the mid-span deflection is 64.58mm, the load starts to slowly drop to 705kN, the partially bent lower flange steel plate is separated from the side plate, the other side plate bends outwards, the load drops rapidly, the test piece is damaged and cannot be continuously loaded, the limit bearing capacity is 717kN, and the section limit bending-resistant bearing capacity is 430.2 kN.m. During the whole test process, no obvious slippage is generated between the concrete and the steel member. Test phenomena during and after beam loading and failure.
Comparing the test pieces Lb-2 and Lb-1, the thickness of the lower flange steel plate is changed to 2mm according to the influence of the thickness of the lower flange steel plate on the bending resistance of the crustal beam under the action of the negative bending moment. Lb-2 shows a uniform slight local buckling phenomenon during welding due to the thinness of the lower flange steel plate. At the initial loading stage, load control loading is adopted, and the deflection of the beam linearly increases along with the increase of the load and is in an elastic stage. When the load reaches 140kN, the concrete slabs of the pure bending section and the bending shear section close to the loading point have transverse cracks extending to the plate side at the position of the channel steel. When the load reaches 240kN, an inclined crack which extends from the position of the hogging moment reinforcing steel bar to the flange steel plate at the load point appears near the load point. And (4) continuously loading, continuously extending and widening the crack, gradually deepening the buckling degree of the lower flange steel plate, and avoiding other obvious phenomena. When the load reaches 400kN, the upper flange steel plate is tensioned and yields, the concrete crack of the pure bending section is wider at the moment, the crack at the loading point is widest, and then the displacement control loading is changed.
And continuously loading, when the load reaches 569kN, concrete falls off from the middle of the concrete slab near the right loading point, and when the load reaches 579kN, concrete with an inclined crack near the left loading point falls off. The hogging moment reinforcing steel bar is exposed, at the moment, the load is slowly increased, and the deflection is rapidly increased. And (2) continuing loading, wherein local buckling at each position of the lower flange steel plate is more and more serious, buckling at one position on a pure bending section near a right loading point is most serious, the load slowly rises to 604kN, the midspan deflection is 71.36mm, the deflection is kept unchanged, the deflection is rapidly increased, the limit bearing capacity is reached at the moment, the buckling at one position on the pure bending section near the right loading point is rapidly developed and has a tearing tendency with a side plate, the side plate at the position obviously bulges outwards, the load begins to decline, the test piece is destroyed, and the section limit bending bearing capacity is 362.4kN m. The concrete spalling is significantly more severe than Lb-1 upon failure of Lb-2. During the whole test process, no obvious slippage is generated between the concrete and the steel member. Test phenomena during and after beam loading.
The test results were analyzed as follows: in the test process, the mid-span deflection of the test piece changes with the load as shown in figure 8. As can be seen from the figure, the curves of both trends are consistent: the load-deflection relation curve of the member basically presents a linear relation at the initial loading stage of the member and before the concrete wing plate is not cracked; since the concrete panel is cracked, the rigidity of the composite girder is weakened, and thus the entire bending deformation of the structural member is increased. From the cracking of the concrete wing plate to the yielding of the upper flange steel plate, the curve of the relation between the load and the deflection is turned; after the upper flange steel plate is tensioned and yielded, the load and deflection curve of the composite beam has more obvious turning. FIG. 8 basically reflects the bearing capacity, rigidity and ductility of the composite beam, the bearing capacity of the composite beam can be increased by increasing the thickness of the bottom plate, and the composite beam has better ductility under the action of the negative bending moment. The lower flange steel plate of Lb-2 has uniform local buckling during processing due to thinness, so that the ductility of the lower flange steel plate is stronger than that of Lb-1.
The following assumptions are made when a positive section bending resistance bearing capacity calculation formula under the action of the shell beam hogging moment is established:
the section still accords with the assumption of a flat section after being loaded, and the section is in linear distribution when yielding.
The concrete compressive stress is distributed in a rectangular shape under the condition of ultimate bearing capacity, the value is α 1fcbx, and the concrete action in a tension area is ignored.
When a positive section bending resistance bearing capacity calculation formula is established, the resultant force action point of the equivalent rectangular stress of the concrete is positioned at the center of the concrete compression area.
The influence of the local buckling of the steel beam of the composite beam on the bearing capacity is ignored under the action of the hogging moment.
The tensile contribution of the corrugated side panels is neglected.
The calculation is as follows: according to the structural characteristics of the crust beam, the cross section plasticity neutral axis is generally in the corrugated side plate when the complete shear-resistant connection crust beam reaches the bearing capacity limit state under the action of the hogging moment, so that the prestressed tendons are pulled.
S1, judging the position of a section neutral axis when the completely shear-resistant connecting novel section composite beam reaches the bearing capacity limit state under the action of a hogging moment;
s2, substituting the position of the neutral axis into a corresponding formula to solve the ultimate bending resistance bearing capacity,
the calculation formula is as follows.
The section stress distribution of the plastic neutralizing shaft in the corrugated side plate is shown in FIG. 2, and the formula (1) is satisfied:
fybdtd+a1fc(b-hr)β1(ha-td-tu)≥fpyAp+2fybutu+fysAs(1)
in the formula: f. ofysDesigned value of tensile strength of hogging moment reinforcing steel bar, N/mm2；
AsIs the area of the hogging moment reinforcing steel bar, mm2；
haIs the section height of the steel armor shell.
Firstly, calculating the height x of the equivalent compression area of the concrete according to the balance of forces, as shown in a formula (2):
fpyAp+2fybutu+fysAs＝fybdtd+α1fc(b-hr)x (2a)
taking a moment from the equivalent rectangular resultant force point of the concrete in the compression area to obtain the ultimate bending resistance bearing capacity M of the shell beamuAs in formula (3):
in the formula: c is the thickness of the protective layer, mm;
d is the diameter of the hogging moment reinforcing steel bar, mm;
hpthe distance from the center of the section of the prestressed tendon to the upper surface of the flange steel plate on the beam is mm.
Comparing formula value with test result
The comparison condition of the bending resistance bearing capacity test result under the action of the crustal beam hogging moment and the formula calculation result is shown in the table 1. The difference value between the bearing capacity calculated by the formula and the test result is within 10 percent, so that the design formula is better in coincidence with the test result.
TABLE 1 comparison of the calculated results with the test results
Comparing formula values with finite element results
The results of the formula calculations are shown in Table 2 in comparison to the results of the finite element parameter analysis calculations. The calculation result shows that: the average value of the bending bearing capacity under the action of the shell beam hogging moment obtained by the report calculation formula and the ultimate bending moment ratio obtained by finite element analysis is 0.99, the variance is 0.0005, and the calculation result has good accuracy and reliability.
TABLE 2 comparison of the calculated results with finite element results
Claims (6)
1. A method for calculating the bending resistance bearing capacity of a section beam under the action of a hogging moment is characterized by comprising the following steps of:
s1, judging the position of a section neutral axis when the completely shear-resistant connecting novel section composite beam reaches the bearing capacity limit state under the action of a hogging moment;
s2, substituting the position of the neutral axis into a corresponding formula to solve the ultimate bending resistance bearing capacity,
the section stress distribution of the plastic neutralizing shaft in the corrugated side plate satisfies the formula (1)
fybdtd+α1fc(b-hr)β1(ha-td-tu)≥fpyAp+2fybutu+fysAs(1)；
In the formula: f. ofysDesigned value of tensile strength of hogging moment reinforcing steel bar, N/mm2；
AsIs the area of the hogging moment reinforcing steel bar, mm2；
haIs the section height of the steel armor shell.
And calculating the height x of the equivalent compression area of the concrete according to the balance of the forces, as shown in the formula (2):
fpyAp+2fybutu+fysAs＝fybdtd+α1fc(b-hr)x (2a)
taking a moment from the equivalent rectangular resultant force point of the concrete in the compression area to obtain the ultimate bending resistance bearing capacity M of the shell beamuAs in formula (3):
in the formula: c is the thickness of the protective layer, mm;
d is the diameter of the hogging moment reinforcing steel bar, mm;
hpthe distance from the center of the section of the prestressed tendon to the upper surface of the flange steel plate on the beam is mm.
2. The method for calculating the bending resistance bearing capacity of the section beam under the action of the hogging moment as claimed in claim 1, wherein the section still conforms to the assumption of a flat section after being loaded, and the section is in a linear distribution when yielding.
3. The method for calculating bending resistance bearing capacity of a section beam under negative moment of claim 1, wherein the concrete compressive stress is distributed in a rectangular shape at the ultimate bearing capacity, and the value is α1fcbx and neglecting the concrete action in the tension area.
4. The method for calculating the bending resistance bearing capacity of a section beam under the action of the hogging moment as claimed in claim 1, wherein when a positive section bending resistance bearing capacity calculation formula is established, the resultant force action point of the equivalent rectangular stress of the concrete is positioned at the center of the concrete compression area.
5. The method of claim 1, wherein the effect of the local buckling of the composite beam and the steel beam on the bearing capacity is neglected under the action of the negative bending moment.
6. The method for calculating bending resistance bearing capacity of a section beam under negative bending moment of claim 1, wherein the tensile contribution of the corrugated side plates is ignored.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911184101.8A CN110990922B (en) | 2019-11-27 | 2019-11-27 | Bending-resistant bearing capacity calculation method for section beam under hogging moment effect |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911184101.8A CN110990922B (en) | 2019-11-27 | 2019-11-27 | Bending-resistant bearing capacity calculation method for section beam under hogging moment effect |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110990922A true CN110990922A (en) | 2020-04-10 |
| CN110990922B CN110990922B (en) | 2024-02-27 |
Family
ID=70087567
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201911184101.8A Active CN110990922B (en) | 2019-11-27 | 2019-11-27 | Bending-resistant bearing capacity calculation method for section beam under hogging moment effect |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110990922B (en) |
Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111611642A (en) * | 2020-05-26 | 2020-09-01 | 江南大学 | A method for calculating the flexural stiffness of concrete composite beams with outer corrugated side slabs |
| CN112697608A (en) * | 2020-12-10 | 2021-04-23 | 太原理工大学 | Method for judging plastic bending resistance bearing capacity of full section of steel member under bidirectional bending |
| CN112982506A (en) * | 2021-02-08 | 2021-06-18 | 浙江工业大学 | Anchor pile performance detection method capable of recycling steel strands |
| CN114062151A (en) * | 2021-11-18 | 2022-02-18 | 中冶建筑研究总院有限公司 | Method for measuring secondary bending moment of prestressed concrete frame beam in plastic stage |
| CN114330019A (en) * | 2022-01-10 | 2022-04-12 | 广西北投公路建设投资集团有限公司 | Calculation method of flexural capacity of composite beams with unbonded prestressed corrugated steel webs in vivo |
| CN117951791A (en) * | 2024-02-05 | 2024-04-30 | 深圳大学 | Method for rechecking positive section of FRP-concrete beam and bending-resistant design method |
| CN118313287A (en) * | 2024-06-12 | 2024-07-09 | 中铁十八局集团建筑安装工程有限公司 | Method for calculating anti-cracking bearing capacity of hogging moment area of composite beam |
| CN118520556A (en) * | 2024-05-13 | 2024-08-20 | 中国建筑第五工程局有限公司 | Simple supporting and converting continuous structure system of track beam and design method thereof |
| CN118761145A (en) * | 2024-09-09 | 2024-10-11 | 浙江华东工程建设管理有限公司 | A method for calculating the bearing capacity of a wind turbine foundation on collapsible soil |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102650579A (en) * | 2011-12-22 | 2012-08-29 | 上海同吉建筑工程设计有限公司 | Flexural bearing capacity designing method for frame beam adopting pre-stressed steel reinforced concrete structure |
| CN108229006A (en) * | 2017-12-29 | 2018-06-29 | 华南理工大学 | A kind of honeycomb combines negative moment of girder bearing capacity computation method |
| CN109885925A (en) * | 2019-02-15 | 2019-06-14 | 河海大学 | A calculation method for the bearing capacity of fabricated PEC composite beams |
-
2019
- 2019-11-27 CN CN201911184101.8A patent/CN110990922B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102650579A (en) * | 2011-12-22 | 2012-08-29 | 上海同吉建筑工程设计有限公司 | Flexural bearing capacity designing method for frame beam adopting pre-stressed steel reinforced concrete structure |
| CN108229006A (en) * | 2017-12-29 | 2018-06-29 | 华南理工大学 | A kind of honeycomb combines negative moment of girder bearing capacity computation method |
| CN109885925A (en) * | 2019-02-15 | 2019-06-14 | 河海大学 | A calculation method for the bearing capacity of fabricated PEC composite beams |
Non-Patent Citations (2)
| Title |
|---|
| 王静峰等: "负弯矩作用下钢管混凝土组合框架端板连接节点的抗弯承载力计算方法", 《土木工程学报》, vol. 47, no. 2, pages 52 - 61 * |
| 马宏伟等: "负弯矩作用下蜂窝组合梁的承载力", 《华南理工大学学报（自然科学版）》, vol. 47, no. 1, pages 75 - 85 * |
Cited By (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111611642A (en) * | 2020-05-26 | 2020-09-01 | 江南大学 | A method for calculating the flexural stiffness of concrete composite beams with outer corrugated side slabs |
| CN111611642B (en) * | 2020-05-26 | 2024-01-30 | 江南大学 | Method for calculating bending rigidity of concrete composite beam with externally-wrapped corrugated side plates |
| CN112697608A (en) * | 2020-12-10 | 2021-04-23 | 太原理工大学 | Method for judging plastic bending resistance bearing capacity of full section of steel member under bidirectional bending |
| CN112982506A (en) * | 2021-02-08 | 2021-06-18 | 浙江工业大学 | Anchor pile performance detection method capable of recycling steel strands |
| CN114062151A (en) * | 2021-11-18 | 2022-02-18 | 中冶建筑研究总院有限公司 | Method for measuring secondary bending moment of prestressed concrete frame beam in plastic stage |
| CN114062151B (en) * | 2021-11-18 | 2023-07-04 | 中冶建筑研究总院有限公司 | Method for measuring secondary bending moment of prestressed concrete frame beam in plastic stage |
| CN114330019A (en) * | 2022-01-10 | 2022-04-12 | 广西北投公路建设投资集团有限公司 | Calculation method of flexural capacity of composite beams with unbonded prestressed corrugated steel webs in vivo |
| CN117951791A (en) * | 2024-02-05 | 2024-04-30 | 深圳大学 | Method for rechecking positive section of FRP-concrete beam and bending-resistant design method |
| CN118520556A (en) * | 2024-05-13 | 2024-08-20 | 中国建筑第五工程局有限公司 | Simple supporting and converting continuous structure system of track beam and design method thereof |
| CN118313287A (en) * | 2024-06-12 | 2024-07-09 | 中铁十八局集团建筑安装工程有限公司 | Method for calculating anti-cracking bearing capacity of hogging moment area of composite beam |
| CN118313287B (en) * | 2024-06-12 | 2024-09-13 | 中铁十八局集团建筑安装工程有限公司 | Method for calculating anti-cracking bearing capacity of hogging moment area of composite beam |
| CN118761145A (en) * | 2024-09-09 | 2024-10-11 | 浙江华东工程建设管理有限公司 | A method for calculating the bearing capacity of a wind turbine foundation on collapsible soil |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110990922B (en) | 2024-02-27 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110990922A (en) | Method for calculating bending resistance bearing capacity of cross-section beam under action of negative bending moment | |
| Zou et al. | Experimental study on flexural behavior of hollow steel-UHPC composite bridge deck | |
| Bastien-Masse et al. | Experimental investigation on punching resistance of R-UHPFRC–RC composite slabs | |
| Al-Gasham et al. | Flexural behavior of laced reinforced concrete moderately deep beams | |
| Liu et al. | Flexural behavior of concrete-filled rectangular steel tubular composite truss beams in the negative moment region | |
| Hasan et al. | The strength of hollow concrete block walls, reinforced hollow concrete block beams, and columns | |
| He et al. | Investigation on interfacial anti-sliding behavior of high strength steel-UHPC composite beams | |
| Arrayago et al. | Experimental investigation on ferritic stainless steel composite slabs | |
| Scott et al. | Effect of stay-in-place PVC formwork panel geometry on flexural behavior of reinforced concrete walls | |
| Jiang et al. | Experimental study and numerical analysis on mechanical behavior of T-shape stiffened orthotropic steel-concrete composite bridge decks | |
| Zhou et al. | Seismic behavior of corrugated double-skin composite wall (DSCW) with concrete-filled steel tubes: Experimental investigation | |
| Liu et al. | Experimental study on the flexural behavior of cold-formed U-shaped steel-encased confined prestressed RC beam | |
| CN209261052U (en) | A prefabricated partially prefabricated steel-concrete composite beam | |
| Mahdi et al. | Experimental investigation into the structural behaviour of ultra-high performance fibre-reinforced concrete box-celled composite panels | |
| Pang et al. | Study on behavior of waffle-type UHPC-GFRP composite slab under three-point loading | |
| Zhan et al. | Experimental study on crack performance of steel and early-age BFRC composite beams in negative moment region | |
| Baqi et al. | Experimental study of prestressed masonry flexural elements | |
| Gu et al. | Experimental study on eccentric compressive behavior of precast concrete double-faced superposed shear walls | |
| Frosch et al. | Development and Splice Lengths for High-Strength Reinforcement, Volume I: General Bar Development | |
| Salama | Punching shear behavior Of GFRP-RC edge slab column connections with and without shear stirrups reinforcement | |
| Ojo | Performance of Steel Fiber Reinforced and Conventionally Reinforced Post-Tensioned Flat Plates | |
| Bonett et al. | Behavior of ungrouted and unbonded post-tensioned masonry beams and slabs | |
| Chithra et al. | Studies on prefabricated cage reinforced steel–concrete composite beams | |
| Minelli et al. | Full-scale tests on HPSFRC prestressed roof elements subjected to longitudinal flexure | |
| Yang et al. | Experimental research on seismic performance of dry-wet combined precast concrete beam-to-column connections |
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 |