CN104933309A - Method for calculating buckling load of rod to be tested with elastic constraints at two ends - Google Patents

Abstract

The invention discloses a method for calculating the buckling load of a rod to be tested with elastic constraints at the two ends. The buckling stress of the rod to be tested (1) does not exceed the proportional limit of a material of which the rod to be tested is made. The method is characterized by comprising the following steps: S1, acquiring the material parameters of the rod to be tested (1); S2, calculating the column-end rotational constraint rigidity parameter alpha of the rod to be tested (1) through a formula according to the material parameters of the rod to be tested (1); and S3, calculating the buckling load of the rod to be tested (1) through a formula according to data in the step 1 and the step 2. Through adoption of the method for calculating the buckling load of the rod to be tested with elastic constraints at the two ends, calculated results are accurate. Compared with the prior art, the method for calculating the buckling load of the rod to be tested with elastic constraints at the two ends is easy for calculation, and rapid to use.

Description

A kind ofly calculate the method treating the buckling load of measuring staff that two ends have elastic restraint

Technical field

The present invention relates to engineering design technology field, particularly relate to and a kind ofly calculate the method treating the buckling load of measuring staff that two ends have elastic restraint.

Background technology

In the stability analysis of colonnette, for the rotational restraint of styletable, be usually assumed to be perfect rigidity or completely free.But in Practical Project, styletable rotational restraint is difficult to meet this assumed condition, is generally between the two, i.e. elastic restraint against rotation state.

Therefore, wish a kind of technical scheme to overcome or at least alleviate at least one above-mentioned defect of prior art.

Summary of the invention

The object of the present invention is to provide and a kind ofly calculate the method treating the buckling load of measuring staff that two ends have an elastic restraint and overcome or at least alleviate at least one above-mentioned defect of prior art.

For achieving the above object, the invention provides and a kind ofly calculate the method treating the buckling load of measuring staff that two ends have elastic restraint.Described in the method treating the buckling load of measuring staff that described calculating two ends have an elastic restraint, method comprises the steps: step 1: the material parameter treating measuring staff described in acquisition; Step 2: according to the described material parameter treating measuring staff, by treating the styletable rotational restraint parameter alpha of measuring staff described in formulae discovery; Step 3: according to the data in described step 1 and described step 2, treat the buckling load of measuring staff according to formulae discovery.

Preferably, the parameter in described step 1 comprises: the length L treating measuring staff, the tensile modulus of elasticity E of bar material to be measured; Treat the minimum bend moment of inertia I of the xsect of measuring staff; Styletable rotational restraint K _m, wherein, above-mentioned parameter can be obtained by test.

Preferably, described step 2 adopts following formula to calculate:

$\mathrm{\α}=\frac{E\·I}{K_M\·L},$ Wherein,

α is styletable rotational restraint parameter, and E is the tensile modulus of elasticity of bar material to be measured; I is the minimum bend moment of inertia of the xsect treating measuring staff, and L is the length treating measuring staff; K _mfor styletable rotational restraint.

Preferably, described step 3 adopts following formula to calculate:

wherein, P _crfor treating the buckling load of measuring staff, α is styletable rotational restraint parameter, and E is the tensile modulus of elasticity of bar material to be measured; I is the minimum bend moment of inertia of the xsect treating measuring staff, and L is the length treating measuring staff; K _mfor styletable rotational restraint.

What the calculating two ends in the present invention had an elastic restraint treats that the result that the method for the buckling load of measuring staff calculates is accurate, and relative to prior art, the method treating the buckling load of measuring staff that calculating two ends of the present invention have elastic restraint calculates simple, uses quick.

Accompanying drawing explanation

Fig. 1 is the structural representation treating measuring staff according to an embodiment of the invention.

Reference numeral:

1

Treat measuring staff

Embodiment

For making object of the invention process, technical scheme and advantage clearly, below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is further described in more detail.In the accompanying drawings, same or similar label represents same or similar element or has element that is identical or similar functions from start to finish.Described embodiment is the present invention's part embodiment, instead of whole embodiments.Be exemplary below by the embodiment be described with reference to the drawings, be intended to for explaining the present invention, and can not limitation of the present invention be interpreted as.Based on the embodiment in the present invention, those of ordinary skill in the art, not making the every other embodiment obtained under creative work prerequisite, belong to the scope of protection of the invention.Below in conjunction with accompanying drawing, embodiments of the invention are described in detail.

In describing the invention; it will be appreciated that; term " " center ", " longitudinal direction ", " transverse direction ", "front", "rear", "left", "right", " vertically ", " level ", " top ", " end " " interior ", " outward " etc. instruction orientation or position relationship be based on orientation shown in the drawings or position relationship; be only the present invention for convenience of description and simplified characterization; instead of instruction or imply indication device or element must have specific orientation, with specific azimuth configuration and operation, therefore can not be interpreted as limiting the scope of the invention.

Calculating two ends of the present invention have the method treating the buckling load of measuring staff of elastic restraint, wherein, treat that the buckling stress of measuring staff 1 is no more than the proportional limit of bar material to be measured, what these calculating two ends had an elastic restraint treats that the method for the buckling load of measuring staff comprises the steps:

Step 1: obtain the material parameter treating measuring staff 1; Particularly, this parameter comprises: the length L treating measuring staff, the tensile modulus of elasticity E of bar material to be measured; Treat the minimum bend moment of inertia I of the xsect of measuring staff; Styletable rotational restraint K _m, wherein, above-mentioned parameter can be obtained by test.

Step 2: according to the material parameter treating measuring staff 1, treats the styletable rotational restraint parameter alpha of measuring staff 1 by formulae discovery; Particularly, following formula is adopted to calculate:

$\mathrm{\α}=\frac{E\·I}{K_M\·L},$ Wherein,

α is styletable rotational restraint parameter, and E is the tensile modulus of elasticity of bar material to be measured; I is the minimum bend moment of inertia of the xsect treating measuring staff, and L is the length treating measuring staff; K _mfor styletable rotational restraint.

Step 3: according to the data in step 1 and step 2, treats the buckling load of measuring staff 1 according to formulae discovery.Particularly, following formula is adopted to calculate:

wherein, P _crfor treating the buckling load of measuring staff, α is styletable rotational restraint parameter, and E is the tensile modulus of elasticity of bar material to be measured; I is the minimum bend moment of inertia of the xsect treating measuring staff, and L is the length treating measuring staff; K _mfor styletable rotational restraint.

Be elaborated further method of the present invention by way of example below, be understandable that, this elaboration does not form any limitation of the invention.

Fig. 1 is the structural representation treating measuring staff according to an embodiment of the invention.Fig. 2 is the schematic diagram data treating the buckling load that measuring staff utilizes method of the present invention to try to achieve shown in Fig. 1.

See Fig. 1, as shown in Figure 1 treat measuring staff, its design parameter is as follows:

Two fulcrum beams of two ends elastic restraint against rotation, length L=500mm, xsect is the filled circles of diameter d=10mm, the tensile modulus of elasticity E=196000MPa of material, Poisson ratio μ=0.3, K _m=962113Nmm/rad.

$\mathrm{\α}=\frac{E\·I}{K_M\·L}=\frac{E\·\frac{\mathrm{\π}}{64}{d}^4}{K_M\·L}=\frac{196000\×\frac{\mathrm{\π}}{64}\×{10}^4}{962113\×500}=0.1999$

$P_{cr}=\frac{{\mathrm{\π}}^{2}E\·I}{L^2}(1+\frac{3}{1+7\mathrm{\α}})=\frac{{\mathrm{\π}}^2\×196000\×\frac{\mathrm{\π}}{64}\×{10}^4}{{500}^2}(1+\frac{3}{1+7\×0.1999})=8534.5N$

Obtaining this buckling of bar load to be measured by test measurement is: P=8702N.

Can find out, the data that the present invention tries to achieve are relative to experimental data, basically identical.

Finally it is to be noted: above embodiment only in order to technical scheme of the present invention to be described, is not intended to limit.Although with reference to previous embodiment to invention has been detailed description, those of ordinary skill in the art is to be understood that: it still can be modified to the technical scheme described in foregoing embodiments, or carries out equivalent replacement to wherein portion of techniques feature; And these amendments or replacement, do not make the essence of appropriate technical solution depart from the spirit and scope of various embodiments of the present invention technical scheme.

Claims (4)

1. calculate the method treating the buckling load of measuring staff that two ends have elastic restraint, wherein, described in treat that the buckling stress of measuring staff (1) is no more than the proportional limit of bar material to be measured, it is characterized in that, described method comprises the steps:

Step 1: the material parameter treating measuring staff (1) described in acquisition;

Step 2: according to the described material parameter treating measuring staff (1), by treating the styletable rotational restraint parameter alpha of measuring staff (1) described in formulae discovery;

Step 3: according to the data in described step 1 and described step 2, treat the buckling load of measuring staff (1) according to formulae discovery.

2. calculating two ends as claimed in claim 1 have the method treating the buckling load of measuring staff of elastic restraint, and it is characterized in that, the parameter in described step 1 comprises: the length L treating measuring staff, the tensile modulus of elasticity E of bar material to be measured; Treat the minimum bend moment of inertia I of the xsect of measuring staff; Styletable rotational restraint K _m, wherein, above-mentioned parameter can be obtained by test.

3. calculating two ends as claimed in claim 2 have the method treating the buckling load of measuring staff of elastic restraint, and it is characterized in that, described step 2 adopts following formula to calculate:

$\mathrm{\α}=\frac{E\·I}{K_M\·L},$ Wherein,

α is styletable rotational restraint parameter, and E is the tensile modulus of elasticity of bar material to be measured; I is the minimum bend moment of inertia of the xsect treating measuring staff, and L is the length treating measuring staff; K _mfor styletable rotational restraint.

4. calculating two ends as claimed in claim 1 have the method treating the buckling load of measuring staff of elastic restraint, and it is characterized in that, described step 3 adopts following formula to calculate:

wherein, P _crfor treating the buckling load of measuring staff, α is styletable rotational restraint parameter, and E is the tensile modulus of elasticity of bar material to be measured; I is the minimum bend moment of inertia of the xsect treating measuring staff, and L is the length treating measuring staff; K _mfor styletable rotational restraint.