CN108229031A - Consider the axial load computational length coefficient practical calculation method of both ends fixed spring hinge effect of constraint value - Google Patents
Consider the axial load computational length coefficient practical calculation method of both ends fixed spring hinge effect of constraint value Download PDFInfo
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Abstract
The present invention relates to a kind of axial load computational length coefficient practical calculation method for considering both ends fixed spring hinge effect of constraint value, the method for the invention includes the following steps：Determine the rotational stiffness of axial load bottom support bracketR a, top support rotational stiffnessR b；Calculate axial load Line stiffnessi；Calculate axial load bottom spring hinge ~ compression bar rigidity ratior aWith top spring hinge ~ compression bar rigidity ratior b；According to axial load computational length coefficient useful calculating method proposed by the present invention, the axial load computational length coefficient for considering both ends fixed spring hinge effect of constraint value is calculated.The invention has the advantages that：It can solve previous axial load computational length coefficientμThe problem of excessively simplifying processing, and causing to over-evaluate axial load ultimate bearing capacity in engineering design or experiment；Also existing method, which can be solved, cannot directly calculate axial load computational length coefficient in the case of given support stiffnessμThe problem of；Meanwhile the method for the present invention step is succinct, required parameter is small, and precision is high.
Description
Technical field
The present invention relates to Axial Compression Stability computing technique field, more particularly, to a kind of consideration both ends fixed spring hinge constraint shadow
Loud axial load computational length coefficient practical calculation method.
Background technology
The computational length of axis compression member is the important parameter for analyzing its component axial compression overall stability.No
By the calculating for the Perry formula forms that the Euler formula or multi-section design specification for applying to perfect elasticity axial load use
Formula, it is necessary first to obtain the practical computational length of axial load, then could accurately calculate axial load limit stability bearing capacity.Together
When, for Axial Compression Stability experimental study, even with hilted broadsword hinge or it is directly affixed wait bearings, compression bar both ends bearing is not yet
It is evitable to there is the rotation for being not zero, not also being infinity, translation rigidity.And the compression bar in engineering structure, then it is more difficult to
To have ideal mechanics bearing, end restraint mechanical model can be reduced to be cut with scissors by fixed spring and constrain.
Therefore, in this case, the computational length coefficient μ of axial load, can not simply be taken as 1.0,0.5 or 0.7,
According to this rough processing method, it will the ultimate bearing capacity of axial load is excessively over-evaluated, not only so that axial compression test result
Inaccuracy, while can also so that engineering design is partially dangerous.
And the μ value calculating methods that existing research obtains, the rigid-frame column being only applicable in frame structure.In actually calculating,
The Line stiffness of the crossbeam being connected with column and upper lower prop need to be solved first, the computational length coefficient of target rigid-frame column can be carried out
It solves.However, existing research calculation shows that, due to the premise of existing rigid-frame column computational length coefficient μ assume it is excessive, by existing
Method cannot directly calculate the axial load computational length coefficient μ in the case of given support stiffness.Therefore, it is necessary to propose one kind
For when preferable bearing can not achieve, i.e., end is cut with scissors by fixed spring and constrained under experimental condition, the calculating for acquiring axial load is grown
Spend coefficient practical calculation method.
Invention content
The technical issues of present invention is mainly solved in the presence of existing Axial Compression Stability computational length coefficient calculates；It provides
A kind of axial load computational length coefficient practical calculation method for considering both ends fixed spring hinge effect of constraint value.The method calculates letter
Single, required parameter is clear and definite and is easy to get, while also has higher computational accuracy, and the practical calculating of axial load can accurately be calculated
Length factor, so as to greatly improve the precision of experiment gained Axial Compression Stability ultimate bearing capacity.
The above-mentioned technical problem of the present invention is mainly what is be addressed by following technical proposals：
In the loading process of axial load, axial load, loading end are collectively formed one from the system to balance each other, in axial load
Bottom, at the support node of top, loading end has identical translation displacements Δ with axial loadaWith Δb, and the axis that axial load is born
The direction of power P also will voluntarily adjust change therewith, shown in attached drawing 1 so that axle power corner ψ meets：
Wherein, ε is the compression bar axial direction compressive strain under axle power P effects；L is compression bar geometrical length.
At this time it is considered that the translational degree of freedom of axial load both ends bearing is restricted, and rotational freedom is then by top
Spring hinge and the spring hinge of bottom end (fixed-hinged support with certain rotational stiffness) constraint, shown in attached drawing 2.Both ends are by spring hinge
Shown in the axial load mechanical model as attached drawing 3 of constraint and attached drawing 4.Then axial load is taken to be detached from body, such as attached drawing 5.
It is sheared and balanced by y directions, can established an equation：
Wherein, QxFor shearing suffered by axial load infinitesimal section bottom；dQxFor axial load infinitesimal section internal shear force increment；X is compression bar
Axis direction, dx are axial increment in axial load infinitesimal section；
As available from the above equation：
dQx=0 (3)
By equalising torque, can establish an equation：
Wherein, Mx is axial load infinitesimal section bottom institute bending moment；DMx is moment of flexure increment in axial load infinitesimal section；Dy is axis
Translation increment in compression bar infinitesimal section；P is external load；
It can thus be concluded that：
Simultaneous formula (3) and formula (5), have：
Under the premise of small deformation assumes, micro unit moment M x and compression bar curvature φ meet：
In formula, E is axial load elasticity modulus, and I is axial load the moment of inertia.
Simultaneous simultaneous formula (6) and formula (7) can obtain：
To simplify formula, setting：
Then formula (8) can be rewritten as：
Above formula is 4 rank Differential Equation with Constant Coefficients, and the general solution for easily acquiring formula (10) is：
Y=Asinkx+Bcoskx+Cx+D (11)
Formula (11) is the Flexural Equation of axial load under the spring hinge constraint of both ends.In formula, A, B, C, D are undetermined coefficient, can
It is determined according to axial load boundary condition.
Then 4 boundary condition that can obtain axial load with reference to the accompanying drawings, i.e.,：
Axial load is in x=0 positions, lateral displacement y=0；
Axial load is in x=l positions, lateral displacement y=0；
Axial load is led in x=0 positions, end corner for the single order of axial load Flexural Equation, i.e. y ' (0)；
Axial load is led in x=l positions, end corner for the single order of axial load Flexural Equation, i.e., y ' (l)；
It therefore, can row axial load boundary condition equation group：
Equation group includes 4 equations it can be seen from equation group (12), and due to θa、θbIt is unknown quantity so that side
Journey group (12) only has 2 known quantities, can not solve.
Therefore, according to bearing boundary condition, it is as follows that spring hinge stiffness equations are supplemented：
Formula (13) is further written as：
Rear two formula in equation group (12) is replaced using formula (14), can be obtained：
Equation group can be further written as in detail：
Pass through equation group (16), you can obtain every position constant in formula (11), scratched so as to obtain spring hinge axial load
Spend equation.It is the factor arrays [C]=0 of equation group have that equation group (16), which has the condition of untrivialo solution,：
Formula (17) is equal to：
[RaRbkl-(Ra+Rb)EI·k-(EI·k)2kl]sinkl
+[2RaRb+(Ra+Rb)EI·k(kl)]coskl-2RaRb=0 (18)
In above formula, variable k is the function (formula (9)) of axle power P.In view of Euler formula, computational length l0Axis pressure
Bar, when P reaches critical force PcrWhen, have：
In formula, π is pi；
Convolution (9) and formula (19), can obtain：
I.e.
Formula (21) is substituted into formula (18), formula (18) can be rewritten as to the equation containing compression bar computational length coefficient μ：
Above formula can be also further simplified.Now define compression bar Line stiffness i：
Continue definition spring hinge~compression bar rigidity and compare ra、rb：
On the equal sign both sides of formula (22), while divided by i2, formula (22) can be further simplified：
The Buckling Equation of the axial load of formula (26), as both ends spring hinge constraint, by solving the equation, you can obtain bullet
The computational length coefficient μ values of the lower axial load of spring hinge constraint.Can be seen that by formula (26), computational length coefficient μ values only with rigidity ratio
ra、rbValue it is related.
The analytic solutions of spring hinge axial load computational length coefficient μ values, it is difficult to be directly obtained, but can passed through by formula (26)
Iterative algorithm solves the μ value numerical solutions with enough accuracy, though its numerical solution can be obtained in the method, but inconvenient
And there is limitation.Therefore, it is necessary to the useful calculating method of computational length coefficient μ values is studied, in order to practical application.
Now by iterative algorithm, r is solveda、rbA large amount of calculate that value is divided into 0.05 between 0~100 range, value is grown
Factor v solution is spent, partial data is shown in Table 1.According to result of calculation, μ and r are drawn outa、rbThe three-dimension curved surface of correlativity,
As shown in attached drawing 6 and attached drawing 7.
1 computational length coefficient μ numerical solution summary sheets of table
Tables of data and surface chart show, μ values are along plane (ra=rb) symmetrically, μ value curved surfaces are sufficiently close to hyperboloid.Therefore it is fixed
Adopted fitting formula μ=g (ra,rb) be hyperbolic functions form.
It is selected through tentative calculation repeatedly, the form for taking hyperbolic functions is：
Above formula has A1,A2,A3,A4,A5,A6And A7Totally 7 unknowm coefficients.To simplify fitting formula form, and reduce unknown
Coefficient, formula (27) is merged arrangement is：
After adjustment, formula (28) only has C1,C2,C3,C4,C5And C6Totally 6 unknowm coefficients.And according to known conditions, formula (28)
Unknowm coefficient can be further reduced.
1) by g (0,0)=1.0, it can be deduced that：
Then there is C3=C6。
2) by g (∞, ∞)=0.5, it can be deduced that：
Then there is C4=2C1。
According to conditions above, formula (30) can be reduced to：
(31) are fitted using numerical fitting, the value that can obtain each coefficient is：
C1=1.259；C2=5.517；C3=21.35；C4=7.844.
The useful calculating method that computational length coefficient μ values can finally be write out as a result, is:
Formula (32) is 0.002368 relative to the standard deviation of each data in attached drawing 6, and the square value (R- of coefficient R
Square it is) 0.9997.This illustrates that carried practical fitting formula has higher precision.
Therefore, a kind of axial load computational length coefficient practical calculation method for considering both ends fixed spring hinge effect of constraint value,
It is characterized in that：
Consider that the calculation formula that both ends fixed spring cuts with scissors the axial load computational length coefficient μ of effect of constraint value is specially：
Wherein, raFor axial load bottom spring hinge~compression bar rigidity ratio, rbFor spring hinge~compression bar rigidity at the top of axial load
Than.
In the above method, axial load bottom spring hinge~compression bar rigidity compares raCompare r with top spring hinge~compression bar rigidityb's
Calculation formula is specially：
Wherein, RaFor the rotational stiffness of axial load bottom support bracket, RbFor the rotational stiffness of axial load top support, i is axis pressure
Bar Line stiffness.
In the above method, the calculation formula of axial load Line stiffness i is specially：
Wherein, l is the geometrical length of compression bar, and E is axial load elasticity modulus, and I is axial load the moment of inertia.
In the above method, axial load elastic modulus E and axial load the moment of inertia I are obtained by looking into shaped steel table.
In the above method, the rotational stiffness R of axial load bottom support bracketaWith the rotational stiffness R of axial load top supportbBy tying
Structure design primary condition is obtained or is obtained by actual measurement.
In the above method, the rotational stiffness R of axial load bottom support bracketaWith the rotational stiffness R of axial load top supportbMeter
Calculating formula is specially：
Ra=Ma/θa, Rb=Mb/θb
Wherein, Ma, MbRespectively axial load bottom end section turn moment and tip section moment of flexure；θa, θbRespectively axial load bottom end
Bearing angle of rotation degree and top bearing angle of rotation degree；Ma, Mb, θa, θbIt is obtained by structure design primary condition or by surveying
It arrives.
In the above method, the rotational stiffness R of axial load bottom support bracketaWith the rotational stiffness R of axial load top supportbPass through
The rotational stiffness detection method of axial load bearing measures, and this method further comprises the steps：
Step 1, at the top of axial load, bottom sidewall be respectively arranged multiple foil gauges, for measuring at the top of axial load, bottom
The Strain Distribution in section；Along parallel or to coincide with axial load strong axis direction arrangement at least two perpendicular below axial load top support
To displacement sensor, for measuring the vertical displacement of the head base displacement measuring points corresponding to vertical displacement sensor；In axial load
It is perpendicular for measuring along parallel or coincide with the strong axis direction of axial load and arrange at least two vertical displacement sensors above bottom support bracket
Vertical displacement to the bottom support bracket displacement measuring points corresponding to displacement sensor；
Step 2, when axial load carries, the strain data of axial load and vertical displacement data are obtained；
Step 3, axial load tip section moment M is calculatedaWith bottom end section turn moment Mb,
In formula, WxIt is axial load section around the section bending resistance resistance moment of weak axis；E is test specimen elasticity modulus；εmax,aAnd εmin,a
Maximum strain value and minimum strain value respectively in the strain distribution on sections of axial load bottom end；εmax,bAnd εmin,bRespectively axis pressure
Maximum strain value and minimum strain value in bar tip section Strain Distribution；
Step 4, axial load bottom support bracket rotational angle θ is calculatedaWith top support rotational angle θb,
In formula：v2,a, v1,aTwo of which vertical displacement sensor measures vertical respectively above axial load bottom support bracket
Displacement, DaThe horizontal distance between displacement measuring points is corresponded to for the two vertical displacement sensors；v2,b, v1,bRespectively at the top of axial load
The vertical displacement that two of which vertical displacement sensor measures below bearing, DbDisplacement is corresponded to for the two vertical displacement sensors
Horizontal distance between measuring point；
Step 5, axial load bottom support bracket rotational stiffness R is calculatedaWith rotational stiffness R at the top of axial loadb
Ra=Ma/θa, Rb=Mb/θb
In formula, Ma, MbRespectively axial load bottom end section turn moment and axial load tip section moment of flexure；θa, θbRespectively axis pressure
Bar bottom end bearing angle of rotation degree and axial load top bearing angle of rotation degree.
In the above method, in above-mentioned steps 1, the foil gauge on the side wall of axial load top is uniformly distributed and positioned at same level
On face；Foil gauge on the side wall of axial load bottom end is uniformly distributed and in same level.
In the above method, in above-mentioned steps 4, the strong axis along axial load, be arranged symmetrically according to the axial load centre of form two are chosen
The displacement that a vertical displacement sensor measures, for the calculating at axial load top, bottom support bracket rotational angle.
Therefore, the invention has the advantages that：1. can solve existing method using the method for the present invention cannot directly calculate
The problem of axial load computational length coefficient μ in the case of given support stiffness；2. it is previous right also to be reduced using the method for the present invention
Error caused by the rough computational methods of computational length coefficient μ in axial load can make the ultimate bearing capacity meter of axial load
It is more accurate to calculate result；3. calculating parameter is few needed for the method for the present invention, formula is succinct, and computational accuracy is high.
The present invention is by state natural sciences fund general project：The superpower bearing capacity feature of large-size high-strength angle steel compression bar and
Mechanism study (fund number：51378401) it subsidizes.
Description of the drawings
Fig. 1 is state diagram before mechanical model loading system deformation of the present invention；
Fig. 2 is state diagram after mechanical model loading system deformation of the present invention；
Fig. 3 is spring hinge axial load mechanical model figure of the present invention；
Fig. 4 is stress sketch after compression bar flexure of the present invention；
Fig. 5 is that compression bar infinitesimal of the present invention is detached from mechanics illustraton of model；
Fig. 6 is that the method for the present invention calculated rigidity compares ra、rbAxial load computational length factor v solution surface when being 0~100
Figure；
Fig. 7 is that the method for the present invention calculated rigidity compares ra、rbAxial load computational length factor v solution thin portion when being 0~10
Surface chart；
Fig. 8 is the embodiment of the present invention to measure the strain measuring point and displacement that the rotational stiffness of axial load end support saddle is arranged
Measuring point figure；
Fig. 9 is axial load end support saddle corner schematic diagram of the embodiment of the present invention.
In figure：X is compression bar axis direction；Y is compression bar lateral deformation direction；X-x is the weak axis of compression bar；Y-y is the strong axis of compression bar；
L is compression bar geometrical length；P is external load；O is the compression bar centre of form；ΔaFor the translation displacements value at compression bar infinitesimal a points；ΔbFor compression bar
Translation displacements value at infinitesimal b points；ψ is axle power corner；L (1- ε) is the geometrical length after compression bar is acted on by axle power；ε is axle power
Compression bar axial direction compressive strain under effect；RaFor the rotational stiffness of axial load bottom support bracket, RbRotation for axial load top support is firm
Degree；θaThe corner occurred under outer load action for axial load bottom；θbTurn for what is occurred under outer load action at the top of axial load
Angle；MaFor axial load bottom institute bending moment；MbFor institute's bending moment at the top of axial load；Mx is axial load infinitesimal section bottom institute bending moment；
QxFor shearing suffered by axial load infinitesimal section bottom；DMx is moment of flexure increment in axial load infinitesimal section；dQxTo be cut in axial load infinitesimal section
Power increment；Dx is axial increment in axial load infinitesimal section；Dy is translation increment in axial load infinitesimal section；raFor axial load bottom bullet
Spring hinge~compression bar rigidity ratio；rbFor spring hinge~compression bar rigidity ratio at the top of axial load；μ is the computational length coefficient of axial load；S-
A, S-B, S-C, S-D, S-E, S-F, S-G, S-H are the strain measuring point for being arranged in axial load end；DR-1, DR-2 are surveyed for displacement
Point；v1, v2The vertical displacement of displacement measuring points DR-1 and DR-2 are represented respectively；M is axial load end institute bending moment；D is displacement measuring points
Horizontal distance between DR-1 and DR-2；θ is bearing angle of rotation degree.
Specific embodiment
Below by embodiment, the technical solutions of the present invention will be further described.
Embodiment 1：
Using intensity as Q420, limb width is 220mm, and limb thickness is 20mm, and length 2604mm, both ends are spring fastening constraint,
The rotational stiffness R of bottom support bracketaFor 4550kNm, the rotational stiffness R of top supportbHigh strength and large specification angle steel for 500kNm is
Example, a kind of axial load computational length coefficient practical calculation method for considering both ends fixed spring hinge effect of constraint value, including following step
Suddenly：
Step 1, the rotational stiffness R of axial load bottom support bracket is specifieda, top support rotational stiffness Rb：Known by primary condition
The rotational stiffness R of its bottom support bracketaFor 4550kNm, the rotational stiffness R of top supportbFor 500kNm；
Step 2, axial load Line stiffness i calculates step：By axial load elastic modulus E and the moment of inertia I, calculated by (23) formula
Its axial load Line stiffness i；
In formula, l=2604mm；Known by inquiring shaped steel table, the elastic modulus E of the axial load is 206000MPa, the moment of inertia
I is 1592.2 × 104mm4, axial load Line stiffness i=(206000 × 1592.9 × 104)/2604=126kNm；
Step 3, axial load spring hinge~compression bar rigidity compares ra、rbCalculate step：By the rotational stiffness of axial load bottom support bracket
Ra, top support rotational stiffness RbWith axial load Line stiffness i, spring hinge~compression bar rigidity ratio is calculated by (24) and (25) formula
ra、rb；
The rotational stiffness R of known bottom support bracketaFor 4550kNm, the rotational stiffness R of top supportbFor 500kNm；Axial load
Line stiffness i is 126kNm, and bottom spring hinge~compression bar rigidity compares raFor 4550/126=36.11；Its top spring hinge~pressure
Bar rigidity compares rbFor 500/126=3.97；
Step 4, consider the axial load computational length coefficient calculating step of both ends fixed spring hinge effect of constraint value：By axial load
Spring hinge~compression bar rigidity compares ra、rb, its axial load computational length coefficient μ is calculated by (32) formula.
Known axial load bottom spring hinge~compression bar rigidity compares raCompare r for 36.11, top spring hinge~compression bar rigiditybFor
3.97, then the axial load computational length coefficient μ for considering both ends fixed spring hinge effect of constraint value are：
In the present embodiment, using the axial load computational length coefficient practicality meter for considering both ends fixed spring hinge effect of constraint value
The main calculating content and formula of calculation method include：1. the rotational stiffness R of axial load bottom support bracketa, the rotation of top support it is firm
Spend Rb；2. axial load bottom spring hinge~compression bar rigidity compares raCompare r with spring hinge~compression bar rigidity at the top of axial loadbCalculating it is public
Formula；3. consider the axial load computational length coefficient useful calculating method of both ends fixed spring hinge effect of constraint value.
Embodiment 2：
Using intensity as Q420, limb width is 220mm, and limb thickness is 20mm, and length 2604mm, both ends are spring fastening constraint,
But for the high strength and large specification angle steel for not providing practical bearing rotational stiffness, a kind of consideration both ends fixed spring hinge constraint shadow
Loud axial load computational length coefficient practical calculation method, includes the following steps：
Step 1, the rotational stiffness R of axial load bottom support bracket is specifieda, top support rotational stiffness Rb：
Step 1.1, at the top of axial load, bottom sidewall be respectively arranged 8 foil gauges, for measuring at the top of axial load, bottom
The Strain Distribution in portion section；The strong axis direction of axial load is coincided with below axial load top support and arranges 2 vertical displacement sensings
Device, for measuring the vertical displacement of the head base displacement measuring points corresponding to vertical displacement sensor；On axial load bottom support bracket
Side coincides with the strong axis direction of axial load and arranges 2 vertical displacement sensors, for measuring the bottom corresponding to vertical displacement sensor
The vertical displacement of portion's support displacement measuring point；
Step 1.2, when axial load carries, the strain data of axial load and vertical displacement data are obtained；
Step 1.3, axial load tip section moment M is calculatedaWith bottom end section turn moment Mb：
By tabling look-up it is found that the elastic modulus E of the angle steel is 206000MPa, WxFor 182160mm3.It is measured by foil gauge,
Maximum strain value ε in the strain distribution on sections of axial load bottom endmax,aIt is 5270 × 10-6, minimum strain value εmin,aIt is 108 × 10-6.Therefore：
It is measured by foil gauge, the maximum strain value ε in axial load tip section Strain Distributionmax,bIt is 684 × 10-6, it is minimum
Strain value εmin,bIt is 86 × 10-6.Therefore：
Step 1.4, axial load bottom support bracket rotational angle θ is calculatedaWith top support rotational angle θb；
In this example, the distance between upper and lower two displacement measuring points is 760mm, i.e. Da=Db=760mm, passes through displacement meter
Measure the vertical displacement v that two of which vertical displacement sensor measures above axial load bottom support bracket2,a=8.76mm, v1,a=-
8.63mm.Therefore：
The vertical displacement that two of which vertical displacement sensor measures below axial load top support is measured by displacement meter
v2,a=5.28mm, v1,a=-5.17mm.Therefore：
Step 1.5, axial load bottom support bracket rotational stiffness R is calculatedaWith rotational stiffness R at the top of axial loadb
Ra=Ma/θa=96.85/0.023kNm=4210.87kNm；
Rb=Mb/θb=11.22/0.014kNm=801.43kNm；
Step 2, axial load Line stiffness i calculates step：By axial load elastic modulus E and the moment of inertia I, calculated by (23) formula
Its axial load Line stiffness i；
In formula, l=2604mm；Known by inquiring shaped steel table, the elastic modulus E of the axial load is 206000MPa, the moment of inertia
I is 1592.2 × 104mm4, axial load Line stiffness i=(206000 × 1592.9 × 104)/2604=126kNm；
Step 3, axial load spring hinge~compression bar rigidity compares ra、rbCalculate step：By the rotational stiffness of axial load bottom support bracket
Ra, top support rotational stiffness RbWith axial load Line stiffness i, spring hinge~compression bar rigidity ratio is calculated by (24) and (25) formula
ra、rb；
The rotational stiffness R of known bottom support bracketaFor 4210.87kNm, the rotational stiffness R of top supportbFor 801.43kNm；
Axial load Line stiffness i is 126kNm, and bottom spring hinge~compression bar rigidity compares raFor 4210.87/126=33.42；Its top bullet
Spring hinge~compression bar rigidity compares rbFor 801.43/126=6.36；
Step 4, consider the axial load computational length coefficient calculating step of both ends fixed spring hinge effect of constraint value：By axial load
Spring hinge~compression bar rigidity compares ra、rb, its axial load computational length coefficient μ is calculated by (32) formula.
Known axial load bottom spring hinge~compression bar rigidity compares raCompare r for 33.42, top spring hinge~compression bar rigiditybFor
6.36, then the axial load computational length coefficient μ for considering both ends fixed spring hinge effect of constraint value are：
In the present embodiment, using the axial load computational length coefficient practicality meter for considering both ends fixed spring hinge effect of constraint value
The main calculating content and formula of calculation method include：1. the rotational stiffness R of axial load bottom support bracketa, the rotation of top support it is firm
Spend Rb；2. axial load bottom spring hinge~compression bar rigidity compares raCompare r with spring hinge~compression bar rigidity at the top of axial loadbCalculating it is public
Formula；3. consider the axial load computational length coefficient useful calculating method of both ends fixed spring hinge effect of constraint value.
Specific embodiment described herein is only an example for the spirit of the invention.Technology belonging to the present invention is led
The technical staff in domain can do various modifications or additions to described specific embodiment or replace in a similar way
In generation, however, it does not deviate from the spirit of the invention or beyond the scope of the appended claims.
Although it is used more herein：The rotational stiffness R of axial load bottom support bracketa, the rotational stiffness R of top supportb,
Axial load Line stiffness i, axial load bottom spring hinge~compression bar rigidity compare raCompare r with spring hinge~compression bar rigidity at the top of axial loadbDeng
Term, but it does not preclude the possibility of using other terms.The use of these items is only for more easily describe and explain
The essence of the present invention；Any one of the additional limitations is construed as all to disagree with spirit of the present invention.
Claims (9)
1. a kind of axial load computational length coefficient practical calculation method for considering both ends fixed spring hinge effect of constraint value, feature exist
In：
Consider that the calculation formula that both ends fixed spring cuts with scissors the axial load computational length coefficient μ of effect of constraint value is specially：
Wherein, raFor axial load bottom spring hinge~compression bar rigidity ratio, rbFor spring hinge~compression bar rigidity ratio at the top of axial load.
2. the axial load computational length coefficient practicality meter according to claim 1 for considering both ends fixed spring hinge effect of constraint value
Calculation method, it is characterised in that：
Axial load bottom spring hinge~compression bar rigidity compares raCompare r with top spring hinge~compression bar rigiditybCalculation formula be specially：
Wherein, RaFor the rotational stiffness of axial load bottom support bracket, RbFor the rotational stiffness of axial load top support, i is axial load line
Rigidity.
3. the axial load computational length coefficient practicality meter according to claim 2 for considering both ends fixed spring hinge effect of constraint value
Calculation method, it is characterised in that：
The calculation formula of axial load Line stiffness i is specially：
Wherein, l is the geometrical length of compression bar, and E is axial load elasticity modulus, and I is axial load the moment of inertia.
4. the axial load computational length coefficient practicality meter according to claim 3 for considering both ends fixed spring hinge effect of constraint value
Calculation method, it is characterised in that：
Axial load elastic modulus E and axial load the moment of inertia I are obtained by looking into shaped steel table.
5. the axial load computational length coefficient practicality meter according to claim 2 for considering both ends fixed spring hinge effect of constraint value
Calculation method, it is characterised in that：
The rotational stiffness R of axial load bottom support bracketaWith the rotational stiffness R of axial load top supportbIt is obtained by structure design primary condition
To or by actual measurement obtain.
6. the axial load computational length coefficient practicality meter according to claim 2 for considering both ends fixed spring hinge effect of constraint value
Calculation method, it is characterised in that：
The rotational stiffness R of axial load bottom support bracketaWith the rotational stiffness R of axial load top supportbCalculation formula be specially：
Ra=Ma/θa, Rb=Mb/θb
Wherein, Ma, MbRespectively axial load bottom end section turn moment and tip section moment of flexure；θa, θbRespectively axial load bottom end bearing
Rotational angle and top bearing angle of rotation degree；Ma, Mb, θa, θbIt is obtained by structure design primary condition or is obtained by actual measurement.
7. the axial load computational length coefficient practicality meter according to claim 2 for considering both ends fixed spring hinge effect of constraint value
Calculation method, it is characterised in that：
The rotational stiffness R of axial load bottom support bracketaWith the rotational stiffness R of axial load top supportbPass through the rotation of axial load bearing
Rigidity measuring method measures, and this method further comprises the steps：
Step 1, at the top of axial load, bottom sidewall be respectively arranged multiple foil gauges, for measuring at the top of axial load, bottom section
Strain Distribution；Along parallel or coincide with the strong axis direction of axial load and arrange at least two vertical positions below axial load top support
Displacement sensor, for measuring the vertical displacement of the head base displacement measuring points corresponding to vertical displacement sensor；In axial load bottom
Along parallel or coincide with the strong axis direction of axial load and arrange at least two vertical displacement sensors above bearing, for measuring vertical position
The vertical displacement of bottom support bracket displacement measuring points corresponding to displacement sensor；
Step 2, when axial load carries, the strain data of axial load and vertical displacement data are obtained；
Step 3, axial load tip section moment M is calculatedaWith bottom end section turn moment Mb,
In formula, WxIt is axial load section around the section bending resistance resistance moment of weak axis；E is test specimen elasticity modulus；εmax,aAnd εmin,aRespectively
For the maximum strain value and minimum strain value in the strain distribution on sections of axial load bottom end；εmax,bAnd εmin,bRespectively axial load top
Maximum strain value and minimum strain value in end section Strain Distribution；
Step 4, axial load bottom support bracket rotational angle θ is calculatedaWith top support rotational angle θb,
In formula：v2,a, v1,aThe vertical displacement that respectively two of which vertical displacement sensor measures above axial load bottom support bracket,
DaThe horizontal distance between displacement measuring points is corresponded to for the two vertical displacement sensors；v2,b, v1,bRespectively axial load top support
The vertical displacement that lower section two of which vertical displacement sensor measures, DbDisplacement measuring points are corresponded to for the two vertical displacement sensors
Between horizontal distance；
Step 5, axial load bottom support bracket rotational stiffness R is calculatedaWith rotational stiffness R at the top of axial loadb
Ra=Ma/θa, Rb=Mb/θb
In formula, Ma, MbRespectively axial load bottom end section turn moment and axial load tip section moment of flexure；θa, θbRespectively axial load bottom
Hold bearing angle of rotation degree and axial load top bearing angle of rotation degree.
8. the axial load computational length coefficient practicality meter according to claim 7 for considering both ends fixed spring hinge effect of constraint value
Calculation method, it is characterised in that：
In above-mentioned steps 1, the foil gauge on the side wall of axial load top is uniformly distributed and in same level；Axial load bottom end
Foil gauge on side wall is uniformly distributed and in same level.
9. the axial load computational length coefficient practicality meter according to claim 7 for considering both ends fixed spring hinge effect of constraint value
Calculation method, it is characterised in that：
In above-mentioned steps 4, the strong axis along axial load, two vertical displacement sensors being arranged symmetrically according to the axial load centre of form are chosen
The displacement measured, for the calculating at axial load top, bottom support bracket rotational angle.
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Citations (3)
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|---|---|---|---|---|
| US6745712B1 (en) * | 1999-05-28 | 2004-06-08 | Mitsubishi Denki Kabushiki Kaisha | Fully rotatable shuttle |
| CN206256738U (en) * | 2016-11-08 | 2017-06-16 | 国家电网公司华中分部 | A kind of transmission tower angle steel component reinforced structure |
| CN108009334A (en) * | 2017-11-22 | 2018-05-08 | 中国航空工业集团公司西安飞机设计研究所 | A kind of aircraft freight transport system hanger rail joint load computational methods |
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2018
- 2018-01-05 CN CN201810012001.6A patent/CN108229031A/en not_active Withdrawn
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|---|---|---|---|---|
| US6745712B1 (en) * | 1999-05-28 | 2004-06-08 | Mitsubishi Denki Kabushiki Kaisha | Fully rotatable shuttle |
| CN206256738U (en) * | 2016-11-08 | 2017-06-16 | 国家电网公司华中分部 | A kind of transmission tower angle steel component reinforced structure |
| CN108009334A (en) * | 2017-11-22 | 2018-05-08 | 中国航空工业集团公司西安飞机设计研究所 | A kind of aircraft freight transport system hanger rail joint load computational methods |
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| Title |
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| 曹珂: "高强度大规格角钢轴压稳定性能研究", 《中国博士学位论文全文数据库工程科技Ⅱ辑》 * |
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