CN103984863A - Stability detection method of adjustable stand-alone steel support under upper-end translation boundary conditions - Google Patents

Abstract

The invention discloses a stability detection method of an adjustable stand-alone steel support under upper-end translation boundary conditions, comprising the following steps of (1) taking off the stand-alone steel support formed by a lower section of externally-sleeved steel pipe and an upper section of internally-inserted steel pipe; (2) determining parameters of the lower pipe and the upper pipe of the steel support, wherein the formula of a critical load value calculated by a computational formula or through a computer is as follows: pcr=u<2>EIx/H<2>, and a length coefficient miu is further obtained, wherein miu=Pi/u. According to the stability detection method of the adjustable stand-alone steel support under the upper-end translation boundary conditions, the blank of stability detection for the adjustable stand-alone steel support under the upper-end translation boundary conditions of a lower-end simply support is filled. The stability detection method of the adjustable stand-alone steel support under the upper-end translation boundary conditions can be applied to actual engineering material selection and construction, is simple and reliable, and has important practical application values.

Description

The Detection of Stability method of adjustable independent type steel support under upper end translation boundary condition

Technical field

The present invention relates to a kind of steel construction Detection of Stability method, relate in particular to the Detection of Stability method of adjustable independent type steel support under upper end translation boundary condition.

Background technology

Steel construction, due to advantages such as its intensity are high, quality is light, mechanical property is good, is widely used at building field.

The independent steel being connected to form by hypomere outer steel pipe and epimere interpolation steel for steel pipes pin supports, support more and more as residential housing slab form, the lower end steel plate of this support is supported on ground, upper end steel plate be supported on the master of template stupefied on, bearing height can be in 1.8m～4.0m left and right adjusting, very easy to use.

Due to this support in use, upper-lower section steel tube section once stepped appearance changes, and becomes rigidity support so be called single-order, and its 4stability determination is difficult to find, especially the assay method of freely-supported upper end in lower end under can translation, the particularly removable boundary condition that can not rotate also do not have at present.The present invention has carried out having completed the boundary condition 4stability determination of upper end translation just under this background technology.

Summary of the invention

Technical matters to be solved by this invention is to provide a kind of steel stability of strutting system detection method, the Detection of Stability method of adjustable independent type steel support under a kind of upper end translation boundary condition is especially provided, fill up the blank of the independent steel stability of strutting system detection technique of hypomere outer steel pipe and epimere interpolation steel pipe composition, there is simple, reliable advantage, there is popularizing value.

Technical matters to be solved by this invention is achieved through the following technical solutions:

The Detection of Stability method of adjustable independent type steel support under upper end translation boundary condition, comprises the following steps:

(1) the independent steel of the section of taking off outer steel pipe and epimere interpolation steel pipe composition supports;

(2) measure described steel and support upper pipe outer diameter D _s, thickness of pipe t _s, variable height H _s, upper pipe perforate spacing, aperture d; Lower pipe outer diameter D _x, thickness of pipe t _x, uniform height H _x;

The cross section property numerical value of pipe, lower pipe gross cross-sectional in mensuration: the long-pending A of upper tube section _s, moment of inertia I _s, cross section mould W _s, turning radius i _s; Lower tube section amasss A _x, moment of inertia I _x, section modulus W _x, turning radius i _x;

Further obtain described steel pipe support overall height H=H _s+ H _x, pipe moment of inertia ratio I up and down _x/ I _sdefinite value and H _x/ H _svariate;

(3) computing formula or the following formula that calculates by computing machine, critical force (payload values) formula that hypomere steel pipe moment of inertia is expressed:

$p_{\mathrm{cr}}=\frac{u^2{\mathrm{EI}}_x}{H^2},$ Can further obtain length factor $\mathrm{\&mu;}=\frac{\mathrm{\&pi;}}{u}.$

Wherein: p _crfor critical load value, H is that steel supports overall height, H _xfor lower pipe height, H _sfor upper pipe height, p is that steel supports end face load, and E is steel elastic modulus, I _s, I _xbe respectively upper, lower tube moment of inertia.

Detection of Stability method of the present invention, described step also further comprises: become in order to measure single order other stability of complicated boundary condition more that rigidity supports;

Described step also further comprises: described method also can become in order to measure second order the stability of the multiple boundary condition of rigidity support.

Described step also further comprises: described critical load and the moment of inertia of measuring compression member, and carry out critical load and the moment of inertia comparison of the change rigidity axle center compression member of different pressures, different length or different-diameter, thereby obtain the different Compression Stability performance that this steel supports, finally supply practical engineering application.

The present invention adopts technique scheme to have following technique effect:

1. the invention provides the Detection of Stability method of adjustable independent type steel support under a kind of practicality, simple, reliable lower end freely-supported upper end translation boundary condition, filled up the Detection of Stability blank of adjustable independent type steel support under upper end translation boundary condition.

2. this method is simple, and the steel type that only need to need according to job design, selects, and can obtain its critical load value by above-mentioned detection method and step, thereby provides reliable basis for estimation for bridge, subway work selection.

3. the present invention calculates the stability of lower end freely-supported, upper end translation boundary condition, significant to engineering application.

Brief description of the drawings

One of the existing adjustable independent type steel support structural shape in Fig. 1-1 schematic diagram

Two schematic diagram of the existing adjustable independent type steel support structural shape of Fig. 1-2

Three schematic diagram of the existing adjustable independent type steel support structural shape in Fig. 1-3

The single-order of Fig. 2-1 steel supporting deformation of the present invention front lower end freely-supported upper end translation becomes rigidity and supports calculation diagram

The single-order of Fig. 2-2 steel supporting deformation of the present invention posterior end freely-supported upper end translation becomes rigidity and supports calculation diagram

Fig. 3 the present invention is adjustable independent type steel support structure example structure figure

Embodiment

Embodiment 1

The Detection of Stability method of adjustable independent type steel support under upper end translation boundary condition as shown in Fig. 1-1, Fig. 1-2, Fig. 1-3, Fig. 2-1, Fig. 2-2, Fig. 3, comprises the following steps: the independent steel of the section of taking off outer steel pipe and epimere interpolation steel pipe composition supports; Measure described steel and support upper pipe outer diameter D _s, thickness of pipe t _s, variable height H _s, upper pipe perforate spacing, aperture d; Lower pipe outer diameter D _x, thickness of pipe t _x, uniform height H _x, height H value range is got 1.71～3.0m;

The cross section property numerical value of pipe, lower pipe gross cross-sectional in mensuration: the long-pending A of upper tube section _s, moment of inertia I _s, cross section mould W _s, turning radius i _s; Lower tube section amasss A _x, moment of inertia I _x, section modulus W _x, turning radius i _x;

Further obtain described steel pipe support overall height H=H _s+ H _x, pipe moment of inertia ratio I up and down _x/ I _sdefinite value and H _x/ H _svariate;

Process and concrete steps thereof that the following stable formula that further uses computing formula or calculate by computing machine obtains:

The balance differential equation of setting up lower upper lower tube section shown in Fig. 3 is as follows: (p, y ₁, y ₂, x as shown in Figure 3)

Balance differential equation is as follows:

${\mathrm{EI}}_s\frac{d^2{y}_1}{{\mathrm{dx}}_1^2}=-{\mathrm{py}}_1---\left(1\right)$

${\mathrm{EI}}_x\frac{d^2{y}_2}{{\mathrm{dx}}_2^2}=-{\mathrm{py}}_2---\left(2\right)$

In formula: E is steel elastic modulus, I _s, I _xbe respectively upper and lower steel pipe moment of inertia

Introduce mark: $k_1^2=\frac{p}{{\mathrm{EI}}_S},k_2^2=\frac{p}{{\mathrm{EI}}_X},$

Equation (1) and (2) are rewritten as:

$y_1^{\&prime;\&prime;}+k_1^2{y}_1=0---\left(3\right)$

$y_{21}^{\&prime;\&prime;}+k_2^2{y}_2=0---\left(4\right)$

The solution of equation (3), (4) formula:

y ₁＝A ₁cosk ₁x ₁+B ₁sink ₁x ₁ (5)

y ₂＝A ₂cosk ₂x ₂+B ₂sink ₂x ₂ (6)

Boundary condition: work as x ₂=0 o'clock, y ₂=0 (a)

x ₁＝H _s,y′＝0 (b)

x ₁＝0,x ₂＝H _x,y ₁＝y ₂ (c)

x ₁＝0,x ₂＝H _x,y′ ₁＝y′ ₂ (d)

Obtained by (a) and (6): A ₂=0, y ₂=B ₂sink ₂x, y' ₂=B ₂k ₂cosk ₂x

Ask first order derivative to obtain to (5) formula: y '=-A ₁k ₁sink ₁x+B ₁k ₁cosk ₁x ， And tries to achieve the substitution of (b) formula:

-A ₁k ₁sink ₁H _s+B ₁k ₁cosk ₁H _s＝0 (7)

Derived by (c) condition: A ₁-B ₂sink ₂h _x=0 (8)

Derived by (d) condition: B ₁k ₁-B ₂k ₂cosk ₂h _x=0 (9)

Simultaneous equations (7), (8), (9) obtain:

$\left\{\begin{array}{c}-A_1{k}_1\sin k_1{H}_s+B_1{k}_1\cos k_1{H}_s=0\\ A_1-B_2\sin k_2{H}_x=0\\ B_1{k}_1-B_2{k}_2\cos k_2{H}_x=0\end{array}\right.---\left(10\right)$

Obtain thus the determinant of coefficient:

$\left|\begin{array}{ccc}-k_1\sin k_1{H}_s& k_1\cos k_1{H}_S& 0\\ 1& 0& -\sin k_2{H}_x\\ 0& k_1& -k_2\cos k_2{H}_x\end{array}\right|=0---\left(11\right)$

(11) formula of expansion obtains: $k_1{k}_2\cos k_1{H}_s\&times;\cos k_2{H}_x-k_1^2\sin k_1{H}_s\&times;\sin k_2{H}_x=0$

Same divided by k ₁cosk ₁h _s× cosk ₂h _x: k ₂-k ₁tg (k ₁h _s) × tgk ₂h _x=0

Simplify to obtain stability equations: $1-\frac{k_1}{k_2}\mathrm{tg}\left(k_1{H}_s\right)\&times;\mathrm{tg}\left(k_2{H}_x\right)=0---\left(12\right)$

Equation (12) is transcendental equation, generally solves with calculation method, and the root of trying to achieve equation (12) just obtains the Critical Stability power value of this problem.For solving equation (12), also need it to simplify.

If 1-α=H _s(because H=H _x+ H _s), equation (12) is rewritten as:

Need only known n and α value, try to achieve the u value of equation (13) with regard to available trial and error procedure, also just try to achieve critical force value.Because: $u^2=k_2^2{H}^2,$ And $k_2^2=\frac{p}{{\mathrm{EI}}_x},$ $p=\frac{u^2{\mathrm{EI}}_x}{H^2},$ As long as the u that we try to achieve is minimum value, the p calculating is also minimum value, desired Critical Stability power value that Here it is:

Above formula is the Calculation on Critical Force formula of expressing by hypomere steel pipe moment of inertia, also can use the moment of inertia of epimere steel pipe instead and express.Be not difficult to try to achieve computational length coefficient

For the stability equations of other boundary condition, also can try to achieve by above-mentioned similar approach.

Embodiment 2

As Fig. 1-1, Fig. 1-2, Fig. 1-3, Fig. 2-1, Fig. 2-2, Fig. 3, the Detection of Stability method practice of adjustable independent type steel support under a kind of upper end translation boundary condition:

If epimere outer diameter of steel pipes D _s=48mm, thickness of pipe t _s=3.0mm, height H _sfor 1.07m, Hs is variable height, lower pipe outer diameter D _x=60mm, thickness of pipe t _x=3.0mm, height H _xfor 1.50m is constant.Support can be used height H=1.71～3.0m.Critical force value p when H=3.0m is calculated in examination _cr.According to calculating, I _s=107831mm ⁴, I _x=218780mm ⁴,

$n=\frac{k_1}{k_2}=\sqrt{\frac{{\mathrm{EI}}_x}{{\mathrm{EI}}_s}}=\sqrt{\frac{218780}{107831}}=1.4244,\mathrm{\&alpha;}=\frac{H_x}{H}=\frac{1.5}{3.0}=0.5$

By n=1.4244, α=0.5 substitution equation (13):

1-1.4244tg(0.7122u)×tg(0.5u)＝0 (15)

Described: the angle in (15) formula is that radian is unit

Solve the u value in (15) formula with trial and error procedure below.

If: 1-1.4244tg (0.7122u) × tg (0.5u)=M

Trial and error procedure solves table

Item	u	M
			1	1.100000	0.130141205
2	1.118000	0.0894232
			3	1.156000	-0.0024066504
4	1.154000	0.002635744753
			5	1.155600	-0.00139624184
6	1.155040	0.000016707664
			7	1.155048	-0.00000346402
8	1.155046	0.000001578932
			9	1.155047	-0.00000094254

Table note: requirement determines whether to need to continue to calculate according to counting accuracy, and the 9th M value in this example is very little, so get the value of the 9th inferior u value for finally asking.

Critical Stability power:

$p_{\mathrm{cr}}=\frac{u^2{\mathrm{EI}}_x}{H^2}=\frac{1.155047^2\&times;206000\&times;218780}{{3000}^2}=6680.8N=6.68\mathrm{kN}$

Computational length coefficient: can try to achieve corresponding Critical Stability power according to different α values, the stability of expressing this support with number table, for practical engineering application.

The inventive method can be used for solving single order and become the stable problem of other boundary condition that rigidity supports, also can be with the stable problem that becomes the multiple boundary condition that rigidity supports to solve second order.

Claims (6)

1. the Detection of Stability method of adjustable independent type steel support under upper end translation boundary condition, comprises the following steps:

(1) the independent steel of the section of taking off outer steel pipe and epimere interpolation steel pipe composition supports;

(2) measure described steel and support upper pipe outer diameter D _s, thickness of pipe t _s, variable height H _s, upper pipe perforate spacing, aperture d; Lower pipe outer diameter D _x, thickness of pipe t _x, uniform height H _x;

The cross section property numerical value of pipe, lower pipe gross cross-sectional in mensuration: the long-pending A of upper tube section _s, moment of inertia I _s, cross section mould W _s, turning radius i _s; Lower tube section amasss A _x, moment of inertia I _x, section modulus W _x, turning radius i _x;

Further obtain described steel pipe support overall height H=H _s+ H _x, pipe moment of inertia ratio I up and down _x/ I _sdefinite value and H _x/ H _svariate;

(3) apply critical force (payload values) formula that following a kind of computing formula or the hypomere steel pipe calculating by computing machine or epimere steel pipe moment of inertia are expressed:

can further obtain length factor

Wherein: wherein: p _crfor critical load value, H is that steel supports overall height, H _xfor lower pipe height, H _sfor upper pipe height, p is that steel supports end face load, and E is steel elastic modulus, I _s, I _xbe respectively upper, lower tube moment of inertia.

2. the Detection of Stability method of adjustable independent type steel support under translation boundary condition in upper end according to claim 1, described bearing height H is 1.8m～4.0m.

3. the Detection of Stability method of adjustable independent type steel support under translation boundary condition in upper end according to claim 1 and 2, described step also further comprises: described method becomes the stability of the boundary condition of rigidity support in order to measure single order.

4. the Detection of Stability method of adjustable independent type steel support under translation boundary condition in upper end according to claim 1 and 2, described step also further comprises: described method becomes the stability of the boundary condition of rigidity support in order to measure second order.

5. the Detection of Stability method of adjustable independent type steel support under translation boundary condition in upper end according to claim 1 and 2, described step also further comprises: described critical load and the moment of inertia of measuring compression member, critical load and the moment of inertia of the change rigidity axle center compression member to different pressures, different length or different-diameter compare, obtain the different Compression Stability that this steel supports, for practical engineering application.

6. the Detection of Stability method of adjustable independent type steel support under translation boundary condition in upper end according to claim 1 and 2, described step also further comprises: the stability under lower end freely-supported, upper end translation boundary condition is calculated, for practical engineering application.