CN108229006A - A kind of honeycomb combines negative moment of girder bearing capacity computation method - Google Patents
A kind of honeycomb combines negative moment of girder bearing capacity computation method Download PDFInfo
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Abstract
The invention discloses a kind of honeycombs to combine negative moment of girder bearing capacity computation method, including step：One：Draw corresponding stress sketch；Two：Calculate simple bending bearing capacity M when bearing section is only acted on by hogging momentm1；Three：Pure shear bearing capacity V when calculating bearing section only by shearing actionm1；Four：When hogging moment is born with shearing in bearing section simultaneously, nominal anti-bending bearing capacity M is calculatedn1；Five：Calculate the simple bending bearing capacity M of the first hole central cross-sectionm2；Six：Calculate the pure shear bearing capacity V of the first hole central cross-sectionm2；Seven：When the first hole central cross-section bears hogging moment with shearing simultaneously, its nominal anti-bending bearing capacity M is calculatedn2；Eight：When two sections are destroyed simultaneously, distance L of the first hole central cross-section away from bearing is solvedc；Nine：Calculate the nominal anti-bending bearing capacity M in bearing sectionn.The checking computations situation of the invention for considering two sections comprehensively can obtain combining beam-ends bearing capacity when beam destroys when honeycomb.
Description
Technical field
The present invention relates to the structural engineering field in civil engineering, in particular to a kind of honeycomb combination negative moment of girder bearing capacities
Computational methods.
Background technology
The combination beam of steel and concrete can give full play to the advantages of steel and concrete material, have intensity height, saving steel
The characteristics of.It punches on the web of combination beam, girder steel is made into Honeycomb Beam, walk equipment pipe using these holes, can effectively drop
Low building floor height, so as to reduce engineering cost.When honeycomb combination beam is applied in frame, had at bearing larger negative curved
Square acts on.External specification gives the calculation formula of the anti-bending bearing capacity of honeycomb combination beam component level, but these specifications are simultaneously
Disunity, and focus mostly in the bearing capacity calculation in sagging moment area.China has focused largely on honeycomb group for the research of such component
Close mechanical property research when joist support is acted on by sagging moment.The blank of the bearing capacity research of honeycomb combination beam negative moment area is very
Limit to big degree the application of honeycomb combination beam.
Invention content
It is an object of the invention to solve current requirement of engineering, for stress of the honeycomb combination beam when frame structure is applied
Feature has larger hogging moment at bearing, this project proposes the anti-bending bearing capacity calculation formula of component, has stronger engineering should
With value.
The present invention adopts the following technical scheme that realization：
A kind of honeycomb combines negative moment of girder bearing capacity computation method, including step：
Step 1：Given divergence ratio K, determines hogging moment area beam computational length L0, it is assumed that the first hole central cross-section is away from branch
Seat spacing draws corresponding stress sketch, M is obtained according to stress sketch from for L1With M2Relationship, M1And M2Respectively bearing section
With the first hole central cross-section institute bending moment；
Step 2：Calculate simple bending bearing capacity M when bearing section is only acted on by hogging momentm1；
Step 3：Pure shear bearing capacity V when calculating bearing section only by shearing actionm1；
Step 4：When hogging moment is born with shearing in bearing section simultaneously, consider that shearing has weakening to its anti-bending bearing capacity,
It is defined as nominal anti-bending bearing capacity Mn1, and calculate Mn1；
Step 5：Calculate the simple bending bearing capacity M of the first hole central cross-sectionm2；
Step 6：Calculate the pure shear bearing capacity V of the first hole central cross-sectionm2；
Step 7：When the first hole central cross-section bears hogging moment with shearing simultaneously, its nominal anti-bending bearing capacity is calculated
Mn2；
Step 8：When bearing section and the first hole central cross-section destroy simultaneously, define the first hole center and cut
The distance of identity distance bearing is critical distance Lc, enable M1=Mn1, M2=Mn2, solve Lc；
Step 9：When considering that with the first hole central cross-section strength failure occurs for bearing section, the name in bearing section is defined
Adopted anti-bending bearing capacity is Mn, calculate Mn。
Further, the step 2 specifically includes：
The hogging moment bearing capacity in bearing section should to the torque and girder steel that combine neutral axis of the beam by the internal force of tension reinforcement
Power forms the torque two parts for combining neutral axis of the beam：
Mm1=T (as+y1)+Pyc(y2-y1)
T=Astfst
Pyc=Asf
The resultant force of reinforcing bar, A when T is guarantee concrete and girder steel co-operation in formulastFor hogging moment area concrete slab range
Longitudinal reinforcement area of section, fstFor Steel Bar Tensile Strength design value, tensile strength design values of the f for steel, asFor longitudinal steel
Muscle cross-section centroid is to the distance on girder steel top flange surface, y1Position for girder steel tensile region pulling force is to girder steel top flange surface
Distance, y2For girder steel plasticity natural axis to the distance on girder steel top flange surface.
Further, the step 3 specifically includes：
Pure shear bearing capacity V when bearing section is only by shearing actionm1It is provided by its steel beam web plate：
Vm1=0.6fAw
A in formulawSteel beam web plate area of section for the non-hole section of honeycomb combination beam.
Further, the step 4 specifically includes：
Bearing section name anti-bending bearing capacity Mn1It is calculated using following formula：
Further, the step 5 specifically includes：
When plasticity natural axis is in girder steel and in top flange, the simple bending bearing capacity of the first hole central cross-section is：
A in formulasFor center of gravity for reinforcing bar to the distance of concrete slab bottom surface, x is combination beam plasticity natural axis to girder steel upper limb
The distance of edge top surface, deck-moldings of the H for Honeycomb Beam, bf、tfRespectively top flange width and thickness, twFor web thickness, stFor
The web height in T-shaped section；AsnRepresent the Steel Castellated Beams area of section of the first hole central cross-section, AstFor hogging moment area coagulation
The longitudinal reinforcement area of section of native plate range, fstFor Steel Bar Tensile Strength design value, f is the tensile strength design value of steel；
When plasticity natural axis is located in Steel Castellated Beams in T-shaped section, the simple bending bearing capacity of the first hole central cross-section is：
S represents T-shaped section to the area moment of Steel Castellated Beams natural axis in formula；
When plasticity natural axis is not in girder steel, the simple bending bearing capacity of the first hole central cross-section is：
Further, the step 6 specifically includes：The pure shear bearing capacity V that first hole central cross-section usesm2For girder steel
The sum of upper and lower T-shaped section shear-carrying capacity：
Vm2=∑ Vt
V in formulatFor the shear-carrying capacity in T-shaped section, can be acquired by following：
WhenWhen, then the shear-carrying capacity of the first hole central cross-section is：
WhenWhen, then the shear-carrying capacity of the first hole central cross-section is：
Vt=Vpt
In formula, λ=a0/st, a0Represent the length of the length or T-shaped section at hole along beam length direction, VptRepresent T-shaped section
The plasticity shear-carrying capacity of face web,
Further, the step 7 specifically includes：
First hole central cross-section name anti-bending bearing capacity Mn2It is calculated using following formula：
Further, in the step 9, the nominal anti-bending bearing capacity M in bearing sectionnSpecific calculating process it is as follows：
Work as L=LcWhen, M at this time2=Mn2, show that bearing section is destroyed simultaneously with the first hole central cross-section, at this time Mn
For：
Mn=Mn1；
Work as L<LcWhen, M at this time2>Mn2, represent that the first hole central cross-section first destroys, at this time MnFor：
Work as L>LcWhen, M at this time2<Mn2, represent that bearing section can first be destroyed, at this time MnFor：
Mn=Mn1。
Compared with prior art, the invention has the advantages that and effect：
Different from general combination beam, divergence ratio and the first hole spacing meeting joint effect honeycomb combination beam mechanical characteristic are born
Honeycomb combination beam under Moment is not only possible to be destroyed in the maximum section (i.e. near bearing section) of moment of flexure and shearing,
And it may be destroyed at first hole close to bearing.Therefore, for honeycomb combination beam, in addition to checking computations bearing section
Bearing capacity outside, it is also necessary to check the bearing capacity at the first hole central cross-section.The hogging moment area honeycomb group provided in the present invention
The computational methods for closing load bearing beam power consider the checking computations situation in two sections comprehensively, can obtain combining beam when honeycomb
Beam-ends bearing capacity during destruction.Simultaneously propose can predict honeycomb combination beam destroy occur position critical distance concept with
Computational methods.
Description of the drawings
Fig. 1 is the cutting schematic diagram of H-shaped steel used in the present invention.
Fig. 2 is the schematic cross-section after the cutting of H-shaped steel used in the present invention.
Fig. 3 is the welding schematic diagram of Steel Castellated Beams used in the present invention.
Fig. 4 is Steel Castellated Beams schematic cross-section used in the present invention.
Fig. 5 is the honeycomb combination working drawing of beam of the embodiment of the present invention.
Fig. 6 is the stress envelope in honeycomb combination beam support section in the present invention.
Fig. 7 is answering when the first hole of honeycomb combination beam central cross-section plasticity natural axis is located at girder steel top flange in the present invention
Power distribution map.
Fig. 8 is that the first hole of honeycomb combination beam central cross-section plasticity natural axis is located in Steel Castellated Beams T-shaped section in the present invention
Stress envelope during face.
Fig. 9 is stress distribution when the first hole of honeycomb combination beam central cross-section plasticity natural axis is located at floor in the present invention
Figure.
Figure 10 is the stress sketch of the embodiment of the present invention.
Figure 11 is the honeycomb combination beam schematic diagram under typically being acted on by hogging moment.
Specific embodiment
The present invention is described in further detail with reference to embodiment and attached drawing, but embodiments of the present invention are unlimited
In this.
Figure 11 is typically by the lower honeycomb combination beam schematic diagram of hogging moment effect, and Section A-A is bearing section in figure, B-B
Section is the first hole central cross-section, and usually in Specific construction, the Steel Castellated Beams of honeycomb combination beam are generally by H profile steel or work
Word steel is welded, specifically as depicted in figs. 1 and 2, in given divergence ratio K, beam length L0In the case of, Steel Castellated Beams are by H profile steel
Or the web of I-steel is cut along certain tooth socket shape, then dislocation is welded (see Fig. 3 and Fig. 4), meanwhile, at bearing
The real abdomen girder steel of identical size in butt welding, and at bearing set 200mm spacing steel beam web plate ribbed stiffener.Fig. 5 is final
The honeycomb combination working drawing of beam of both ends overhanging.
A kind of honeycomb combination beam bearing capacity computation method of hogging moment area provided in this embodiment, includes the following steps：
Step 1：Determine stress sketch, i.e., divergence ratio K, beam length L in design0And first hole away from branch seat spacing
From L, corresponding stress sketch (see Figure 10) are drawn, bearing section (non-hole section) is Section A-A defined in Fig. 5, the first hole
Mouthful central cross-section (hole section) is section B-B, M1And M2Respectively Section A-A and section B-B institute bending moment, Mm1And Mm2Respectively
For the simple bending bearing capacity of Section A-A and section B-B under hogging moment effect, L0Bearing is represented to the length of beam-ends, for this reality
Example is applied, right end overhanging honeycomb combination beam is defined as A ends, and left end overhanging honeycomb group beam is defined as B ends, and relevant parameter is given by table 1
Go out.
Table 1：
| K | L0(m) | L(m) | L0-L(m) | |
| A ends | 1.2 | 1.25 | 0.17 | 1.08 |
| B ends | 1.2 | 1.25 | 0.32 | 0.93 |
Step 2：Calculate the lower simple bending bearing capacity M of bearing section hogging moment effectm1For：
Mm1=T (as+y1)+Pyc(y2-y1)
T=Astfst
Pyc=Asf
The resultant force of reinforcing bar, A when T is guarantee concrete and girder steel co-operation in formulastFor hogging moment area concrete slab range
Longitudinal reinforcement area of section, fstFor Steel Bar Tensile Strength design value, tensile strength design values of the f for steel, asFor longitudinal steel
Muscle cross-section centroid is to the distance on girder steel top flange surface, y1Position for girder steel tensile region pulling force is to girder steel top flange surface
Distance, y2For girder steel plasticity natural axis to the distance on girder steel top flange surface.
Step 3：Calculate bearing section pure shear bearing capacity Vm1, the pure shear bearing capacity V in bearing sectionm1It is carried by its steel beam web plate
For：
Vm1=0.6fAw,
A in formulawSteel beam web plate area of section for the non-hole section of honeycomb combination beam.
Step 4：Calculate bearing section anti-bending bearing capacity Mn1：
Step 5：Calculate the simple bending bearing capacity M of the first hole central cross-sectionm2, specifically include：
When plasticity natural axis is in girder steel and in top flange, the simple bending bearing capacity of the first hole central cross-section is
(stress distribution is as shown in Figure 7)：
A in formulasFor center of gravity for reinforcing bar to the distance of concrete slab bottom surface, x is combination beam plasticity natural axis to girder steel upper limb
The distance of edge top surface, deck-moldings of the H for Honeycomb Beam, bf、tfRespectively top flange width and thickness, twFor web thickness, stFor
The web height in T-shaped section；AsnRepresent the Steel Castellated Beams area of section of the first hole central cross-section, AstFor hogging moment area coagulation
The longitudinal reinforcement area of section of native plate range, fstFor Steel Bar Tensile Strength design value, f is the tensile strength design value of steel；
When plasticity natural axis is located in Steel Castellated Beams in T-shaped section, the simple bending bearing capacity of the first hole central cross-section is：
S represents T-shaped section to the area moment of Steel Castellated Beams natural axis in formula；
When plasticity natural axis is not in girder steel, the simple bending bearing capacity of the first hole central cross-section is (stress distribution such as Fig. 9
It is shown)：
Step 6：Calculate the pure shear bearing capacity V of the first hole central cross-sectionm2, it is T-shaped section shearing resistance carrying above and below girder steel
The sum of power：
Vm2=∑ Vt
V in formulatFor the shear-carrying capacity in T-shaped section, can be acquired by following：
WhenWhen, then the shear-carrying capacity of the first hole central cross-section is：
WhenWhen, then the shear-carrying capacity of the first hole central cross-section is：
Vt=Vpt
In formula, λ=a0/st, a0Represent the length (or the length of T-shaped section along beam length direction) at hole, VptRepresent T-shaped
The plasticity shear-carrying capacity of section web,
Step 7：Calculate the first hole central cross-section anti-bending bearing capacity Mn2：
In the present embodiment, the step 2~step 7 uses the measured value of the strength of materials, and result of calculation is given by table 2
Go out：
Table 2：
Step 8：M is obtained according to stress sketch1With M2Relationship, wherein M1With M2Section A-A and section B-B are represented respectively
Hogging moment.It is assumed that Section A-A has destroyed, M at this time1=Mn1, result of calculation provides by table 3.
Table 3：
| Test specimen is numbered | M1/kN·m | M2/kN·m |
| A ends | 78.3 | 67.6 |
| B ends | 78.3 | 58.2 |
Step 9：Calculate critical distance Lc, consider the bearing section name anti-bending bearing capacity M after dangerouse cross-section at twon, tool
Body calculating process is as follows：
Work as L=LcWhen, M at this time2=Mn2, show that bearing section is destroyed simultaneously with the first hole central cross-section, at this time Mn
For：
Mn=Mn1；
Work as L<LcWhen, M at this time2>Mn2, represent that the first hole central cross-section first destroys, at this time MnFor：
Work as L>LcWhen, M at this time2<Mn2, represent that bearing section can first be destroyed, at this time MnFor：
Mn=Mn1。
As a result it is provided by table 4.
Table 4：
Note：M in table0Represent the measured value of bearing section turn moment when test specimen destroys.
When designing honeycomb combination beam, generally in order not to which the first hole central cross-section is made first to destroy, for more than
Test specimen, design is appropriate to the occasion to meet L >=Lc, i.e. L >=0.17m, at this time Mn=Mn1。
Have for test specimen A ends：L≈Lc、M2≈Mn2, show that nearly bearing section will occur simultaneously with the first hole central cross-section
It destroys；Have for test specimen B ends：L>Lc、M2<Mn2, show that nearly bearing section will be destroyed prior to the first hole central cross-section, two
Person is consistent with result of the test.Meanwhile beam-ends bearing capacity calculation value error compared with test value within 10%, shows bearing capacity
Formula calculated value can more accurately calculate the hogging moment bearing capacity of honeycomb combination beam, while Bearing Capacity Formula calculated value is than test value more
It is small, show that Bearing Capacity Formula calculated value is content to retain sovereignty over a part of the country complete.
The above embodiment of the present invention be only to clearly illustrate example of the present invention, and not be to the present invention
Embodiment restriction.For those of ordinary skill in the art, it can also make on the basis of the above description
Other various forms of variations or variation.There is no necessity and possibility to exhaust all the enbodiments.It is all the present invention
All any modification, equivalent and improvement made within spirit and principle etc., should be included in the protection of the claims in the present invention
Within the scope of.
Claims (8)
1. a kind of honeycomb combines negative moment of girder bearing capacity computation method, which is characterized in that including step：
Step 1：Given divergence ratio K, determines hogging moment area beam computational length L0, it is assumed that the first hole central cross-section is away from bearing distance
For L, corresponding stress sketch are drawn, M is obtained according to stress sketch1With M2Relationship, M1And M2Respectively bearing section and first
Hole central cross-section institute bending moment；
Step 2：Calculate simple bending bearing capacity M when bearing section is only acted on by hogging momentm1；
Step 3：Pure shear bearing capacity V when calculating bearing section only by shearing actionm1；
Step 4：When hogging moment is born with shearing in bearing section simultaneously, consider that shearing has weakening to its anti-bending bearing capacity, define
It is nominal anti-bending bearing capacity Mn1, calculate Mn1；
Step 5：Calculate the simple bending bearing capacity M of the first hole central cross-sectionm2；
Step 6：Calculate the pure shear bearing capacity V of the first hole central cross-sectionm2；
Step 7：When the first hole central cross-section bears hogging moment with shearing simultaneously, its nominal anti-bending bearing capacity M is calculatedn2；
Step 8：When bearing section and the first hole central cross-section destroy simultaneously, define the first hole central cross-section away from
The distance of bearing is critical distance Lc, enable M1=Mn1, M2=Mn2, solve Lc；
Step 9：When considering that with the first hole central cross-section strength failure occurs for bearing section, the name for defining bearing section resists
Curved bearing capacity is Mn, calculate Mn。
2. honeycomb according to claim 1 combines negative moment of girder bearing capacity computation method, which is characterized in that the step 2
It specifically includes：
The hogging moment bearing capacity in bearing section is by the internal force of tension reinforcement to the combination torque of neutral axis of the beam and girder steel stress pair
The torque two parts for combining neutral axis of the beam are formed：
Mm1=T (as+y1)+Pyc(y2-y1)
T=Astfst
Pyc=Asf
The resultant force of reinforcing bar, A when T is guarantee concrete and girder steel co-operation in formulastFor the vertical of hogging moment area concrete slab range
To area of reinforcement, fstFor Steel Bar Tensile Strength design value, tensile strength design values of the f for steel, asIt is cut for longitudinal reinforcement
The face centre of form is to the distance on girder steel top flange surface, y1For girder steel tensile region pulling force position to girder steel top flange surface away from
From y2For girder steel plasticity natural axis to the distance on girder steel top flange surface.
3. honeycomb according to claim 1 combines negative moment of girder bearing capacity computation method, which is characterized in that the step 3
It specifically includes：
Pure shear bearing capacity V when bearing section is only by shearing actionm1It is provided by its steel beam web plate：
Vm1=0.6fAw
A in formulawSteel beam web plate area of section for the non-hole section of honeycomb combination beam.
4. honeycomb according to claim 1 combines negative moment of girder bearing capacity computation method, which is characterized in that the step 4
It specifically includes：
Bearing section name anti-bending bearing capacity Mn1It is calculated using following formula：
5. honeycomb according to claim 1 combines negative moment of girder bearing capacity computation method, which is characterized in that the step 5
It specifically includes：
When plasticity natural axis is in girder steel and in top flange, the simple bending bearing capacity of the first hole central cross-section is：
A in formulasFor center of gravity for reinforcing bar to the distance of concrete slab bottom surface, x is combination beam plasticity natural axis to girder steel top flange top
The distance on surface, deck-moldings of the H for Honeycomb Beam, bf、tfRespectively top flange width and thickness, twFor web thickness, stIt is T-shaped section
The web height in face；AsnRepresent the Steel Castellated Beams area of section of the first hole central cross-section, AstFor hogging moment area concrete slab model
The longitudinal reinforcement area of section enclosed, fstFor Steel Bar Tensile Strength design value, f is the tensile strength design value of steel；
When plasticity natural axis is located in Steel Castellated Beams in T-shaped section, the simple bending bearing capacity of the first hole central cross-section is：
S represents area moment of the T-shaped section to Steel Castellated Beams natural axis in formula；
When plasticity natural axis is not in girder steel, the simple bending bearing capacity of the first hole central cross-section is：
6. honeycomb according to claim 1 combines negative moment of girder bearing capacity computation method, which is characterized in that the step 6
It specifically includes：The pure shear bearing capacity V of first hole central cross-sectionm2For the sum of section shear-carrying capacity T-shaped above and below girder steel：
Vm2=∑ Vt
V in formulatFor the shear-carrying capacity in T-shaped section, can be acquired by following：
WhenWhen, then the shear-carrying capacity of the first hole central cross-section is：
WhenWhen, then the shear-carrying capacity of the first hole central cross-section is：
Vt=Vpt
In formula, λ=a0/st, a0Represent the length of the length or T-shaped section at hole along beam axis direction, VptRepresent T-shaped section abdomen
The plasticity shear-carrying capacity of plate,
7. honeycomb according to claim 1 combines negative moment of girder bearing capacity computation method, which is characterized in that the step 7
It specifically includes：
First hole central cross-section name anti-bending bearing capacity Mn2It is calculated using following formula：
8. honeycomb according to claim 1 combines negative moment of girder bearing capacity computation method, which is characterized in that the step 9
In, the nominal anti-bending bearing capacity M in bearing sectionnSpecific calculating process it is as follows：
Work as L=LcWhen, M at this time2=Mn2, show that bearing section is destroyed simultaneously with the first hole central cross-section, at this time MnFor：
Mn=Mn1；
Work as L<LcWhen, M at this time2>Mn2, represent that the first hole central cross-section first destroys, at this time MnFor：
Work as L>LcWhen, M at this time2<Mn2, represent that bearing section can first be destroyed, at this time MnFor：
Mn=Mn1。
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| CN109507040A (en) * | 2018-12-12 | 2019-03-22 | 中国航空工业集团公司西安飞机设计研究所 | A kind of honeycomb sandwich construction panel compression stress appraisal procedure |
| CN109885925A (en) * | 2019-02-15 | 2019-06-14 | 河海大学 | A kind of calculation method of assembled PEC combination beam bearing capacity |
| CN110990922A (en) * | 2019-11-27 | 2020-04-10 | 江南大学 | Method for calculating bending resistance bearing capacity of cross-section beam under action of negative bending moment |
| CN113137005A (en) * | 2021-04-28 | 2021-07-20 | 浙江工业大学 | Partially-coated honeycomb steel-concrete composite beam and manufacturing method thereof |
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| CN109507040A (en) * | 2018-12-12 | 2019-03-22 | 中国航空工业集团公司西安飞机设计研究所 | A kind of honeycomb sandwich construction panel compression stress appraisal procedure |
| CN109507040B (en) * | 2018-12-12 | 2021-03-26 | 中国航空工业集团公司西安飞机设计研究所 | Honeycomb sandwich structure panel compression stress assessment method |
| CN109885925A (en) * | 2019-02-15 | 2019-06-14 | 河海大学 | A kind of calculation method of assembled PEC combination beam bearing capacity |
| CN109885925B (en) * | 2019-02-15 | 2022-08-26 | 河海大学 | Method for calculating bearing capacity of assembled PEC (reinforced concrete) composite beam |
| CN110990922A (en) * | 2019-11-27 | 2020-04-10 | 江南大学 | Method for calculating bending resistance bearing capacity of cross-section beam under action of negative bending moment |
| CN110990922B (en) * | 2019-11-27 | 2024-02-27 | 江南大学 | Bending-resistant bearing capacity calculation method for section beam under hogging moment effect |
| CN113137005A (en) * | 2021-04-28 | 2021-07-20 | 浙江工业大学 | Partially-coated honeycomb steel-concrete composite beam and manufacturing method thereof |
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