RU2656297C1 - Wedge-shaped curce-closed profile - Google Patents

Abstract

FIELD: construction.

SUBSTANCE: invention relates to construction and can be used as rod elements at development of bearing structures of buildings and structures of various purposes. In the particular case, these can be the rod elements of the chords of run-through and non-run-through coatings. In curved-closed profile with joint in the middle of one of faces, where each part of docked face has extension in form of an I-shaped rib, cross section of profile is given wedge shape with flat face edge and feather of two identical cylindrical faces joined together to form rib. In this case, each of arcs of cylindrical faces is quarter of circle radius of which is half the size of plane face and is equal to edge size.

EFFECT: technical result of proposed solution is the same stability (uniform stability) of curved-enclosed profiles from plane and in plane of structure, as well as increase in load capacity, decrease in construction height.

1 cl, 8 dwg

Description

The invention relates to the field of construction and can be used as bar elements in the development of load-bearing structures of buildings and structures for various purposes. In the particular case, these may be the core elements of the belts of trusses of run-and-drive-free coatings.

Known core elements, a multifaceted cross-section of which is formed by bending along the length of both edges of the sheet blank (strip) in the opposite directions with the formation of gussets along the entire length of the profile and closing its cross section by installing coupling bolts. Such sections are recommended as truss belts with gratings made of galvanized steel profiles [Salakhutdinov MA, Kuznetsov I.L., Sayanov S.F. Steel trusses with belts from pipes of multifaceted cross-section. - Proceedings of KG ASU, 2016, No. 4 (38). - S.236-242, Fig. 2, c]. The use of sections with a gusset along the entire length is rational in non-stop coatings, when stability from the truss plane is ensured by laying and fastening the profiled flooring directly along the upper belts. Here, the sections under consideration are sufficiently developed in the truss plane to provide effective resistance to the combined action of bending moments and compressive forces. For run coatings, sections that are equally stable both from the plane and in the truss plane are more preferable. Therefore, in such cases, a multifaceted section with a gusset needs additional elaboration.

Another well-known technical solution is a frame T-shaped profile with one edge, made of a continuous strip. The profile is made with a lower horizontal shelf, a hollow upper reinforcing capsule-shaped extension and a vertical rib extending upward from the shelf to the extension. To minimize lateral eccentricity, the rib is made in the form of a single layer of a strip and is formed with a pair of vertically spaced offsets. Displacements occupy most of the single rib layer in the nominal mid-plane of the profile, which divides the flange and expansion in half [Rakhil MM, Likhayn J. J. Ml., Lalond P. Frame T-profile with one rib made from one strip . - Patent RU No. 2481442, 05/10/2013, bull. No. 13]. Such a profile is rational enough to be used as a suspended ceiling run. However, its shape and bearing capacity limit the possibility of using coatings and other supporting structures in trusses.

Closest to the proposed (adopted as a prototype) is a technical solution, which is a bent closed profile made in a cross section of a square or rectangular shape with a joint approximately in the middle of one of the faces. Each part of the face on which the joint is located has a continuation in the form of a G- or I-shaped rib [Levin E.V. Bent closed profile. - Patent RU No. 98155, 10/10/2010, bull. No. 28]. Such a profile effectively competes with I-beams. However, as a rod element, equally stable both from the plane and in the plane of the supporting structure, it requires some refinement.

The technical result of the proposed solution is the same stability (equidistance) of bent closed profiles from the plane and in the plane of the structure, as well as an increase in the resources of the bearing capacity, a decrease in the building height.

The specified technical result is achieved by the fact that in a bent closed profile with a joint in the middle of one of the faces, where each part of the joined face has an extension in the form of an I-shaped rib, the cross-section of the profile is given a wedge-shaped shape with a flat edge and a feather of two identical cylindrical faces interconnected to form a rib. Moreover, each of their arcs of cylindrical faces is a quarter of a circle, the radius of which is two times smaller than the size of the flat face and as many times the size of the rib.

The proposed bent closed (bent closed) profiles have a fairly universal technical solution, the implementation of which for their manufacture can be used as gear mounts, as well as welded, bolted or riveted joints. If in this case the radius of the arcs of cylindrical faces is two times smaller than the size of the flat face and is equal to the same size as the size of I-shaped ribs, then such profiles are equally stable, that is, they have the same stability from the plane and in the plane of the supporting structure. The equal stability of the wedge-shaped bent closed profiles contributes to the effectiveness of their use in the belts of roof trusses and trusses of run-through coatings. With regard to truss belts of non-chromed coatings, it is rational to lengthen the dimensions of the rib parts of double thickness of bent closed profiles depending on the values of jointly acting bending moments and compressive forces, developing their calculated cross section in the force plane of the supporting structure and while preserving the already defined ratios of sizes of tubular parts of single thickness.

For the manufacture of wedge-shaped bent-closed profiles without welded, bolted or riveted joints, it is advisable to select the parameters of the serrated longitudinal edges of their sheet blanks (strips) so that to form the edges of two blanks at once with one zigzag cut. At the same time, production costs will be minimal, which will reduce additional costs. In addition, the bends of the gear mounts of bent closed profiles increase the thickness of the collapse, which can contribute to a certain increase in the bearing capacity of the joints of thin-walled elements, working mainly on shear [Kuznetsov I.L., Fakhrutdinov A.F., Ramazanov P.P. The results of experimental studies of the work of compounds of thin-walled elements in shear. - Vestnik MGSU, 2016, No. 12. - S. 34-43].

The proposed technical solution is illustrated by graphic materials, where in FIG. 1 shows a cross section of a wedge-shaped bent closed profile with an I-shaped rib optimized by the criterion of equidistance; in FIG. 2 - section wedge-shaped bent closed profile with an I-shaped rib, elongated by 1 size; in FIG. 3 - section wedge-shaped bent closed profile with an I-shaped rib, elongated by 2 sizes; in FIG. 4 - section wedge-shaped bent closed profile with an I-shaped rib, elongated by 3 sizes; in FIG. 5 shows a fragment of a wedge-shaped bent closed profile with an optimized axonometric section; in FIG. 6 shows a design diagram of a cross section of a cylindrical face in the form of a quarter of a circular ring; in FIG. 7 is a design diagram of a cross section of a pen (i.e., a wedge-shaped bent-closed profile without a pick and without a rib); in FIG. 8 is a design diagram of a cross section of a wedge-shaped bent closed profile without a rib.

In order to derive the reduced aspect ratio of a wedge-shaped bent closed profile with the same stability from the plane and in the plane of the supporting structure, as well as to quantify its bearing capacity, it is advisable to calculate the moments of inertia of the section I _X and I _Y relative to the main central axes and equate them to each other. In this case, it is permissible to carry out computational calculations along the midline of a thin-walled section without taking into account the angular curves of a wedge-shaped bent closed profile, and also without taking into account numerical values containing the thicknesses raised to the second and third degree (t ² , t ³ ) [Marutyan A.S. Optimization of structures from tubular (bent-welded) profiles of square (rectangular) and rhombic sections. - Structural mechanics and calculation of structures, 2016, No. 1. - S. 30-38].

The section of a wedge-shaped bent-closed profile can be considered as a figure that includes two rectangles (a pick and a rib), as well as two halves of two round half-rings. In turn, a thin-walled ring sector with an angular parameter α = 45 ° = π / 4 = 0.785 [Material Resistance Reference / Ed. G.S. Pisarenko. - Kiev: Naukova Dumka, 1988. - S. 68-69]:

y _c = Rsinα / α = R × 0.7071 / 0.785 = 0.9008R;

I _X = (2α + sin2α-4 (sinα) ² / α) R ³ t / 2 =

= (2 × 0.785 + 1-4 × 0.7071 ² / 0.785) R ³ t / 2 = 0.011115tR ³ ;

I _Y = ((2α-sin2α) R ³ t / 2 = (2 × 0.785-1) R ³ t / 2 = 0.285tR ³ ;

A = 2αRt = 2 × 0.785 × 0.5Rt = 1.57tR,

where y _c , I _X , I _Y , A are respectively the ordinate of the center of gravity of the section, the moment of inertia of the section relative to the xx axis, the moment of inertia of the section relative to the yy axis, the sectional area of the half ring half;

R is the radius of the half ring in its midline;

t is the wall thickness.

The symmetric arrangement of paired halves of round half rings forms an integral part of a wedge-shaped bent-closed profile in the form of its feather (without a pick and without a rib):

- overall height

H = R;

- overall width

U = 2R;

- cross-sectional area

A = 2 × 1.57tR = 3.14tR;

- ordinate of the center of gravity of the section relative to the upper edge

y _s = 0.36304R;

- moments of inertia

I _X = 2 (0.011115tR ³ × 0.5 + 0.285tR ³ × 0.5) = 0.296115tR ³ ;

I _Y = 2 (0.285tR ³ × 0.5 + 0.011115tR ³ × 0.5 + 1.57tR (0.36304R) ² ) = 0.709961tR ³ ;

I _X / I _Y = 0.4170862,

where (sin45 °) ² = (cos45 °) ² = 0.5;

0,363047R - distance from the ordinate axis of a single arc to the ordinate axis in a pair layout.

The attachment of the pick in the form of a horizontal face to the considered pen forms the tubular part of the wedge-shaped bent closed profile (without rib):

- overall height

H = R;

- overall width

U = 2R;

- cross-sectional area

A = tR (3.14 + 2) = 5.14tR;

- ordinate of the center of gravity of the section relative to the upper edge

y _c = R (2 × 0.36304 / 5.14) = 0.14126R;

- moments of inertia

I _X = tR ³ (2 (0.36304-0.14126) ² + 0.296115 + 3.14 × 0.14126 ² ) = 0.4571441tR ³ ;

I _Y = tR ³ (2 ³ × / 12 + 0,709961) = 1,3766276tR ³

I _X / I _Y = 0.3320753.

As can be seen, the axial moments of inertia of the cross section of the tubular part of the wedge-shaped bent closed profile are three times different. To nullify this difference, the pipe part of the profile under consideration must be developed in the direction of the ordinate axis due to the rib part of double thickness, using the method of phased approximations equating I _X and I _Y to each other.

Wedge-shaped bent-closed profiles optimized according to the criterion of equilibrium stability have the following cross-sectional characteristics:

- overall height

H = 3V;

- overall width

U = 4V;

- cross-sectional area

A = 12.28tV;

- ordinate of the center of gravity of the section relative to the upper face

y _c = 0.7785V;

- moments of inertia

I _X = 10.904203tV ³ ;

I _Y = 11.01302tV ³ ;

I _X / I _Y = 10.904203 / 11.01302 = 0.990119≈1

with relative error

100 (11.01302-10.904203) / (11.01302 ... 10.904203) = 0.988 ... 0.998%;

- moments of resistance

W _{X, max} = 10.904203tV ³ / (0.7785V) = 14.006683tV ² ;

W _{X, min} = 10.9004203tV ³ / (3V-0.7785V) = 4.9084866tV ² ;

W _Y = 11.01302tV ³ / (4V / 2) = 5.50651tV ² ;

- radii of inertia

i _X = V (10.9004203 / 12.28) ^1/2 = 0.9423186V;

i _Y = V (11.01302 / 12.28) ^1/2 = 0.9470088V;

i _X / i _Y = 0.9423186 / 0.9470088 = 0.995119≈l

with relative error

100 (0.9470088-0.9423186) / (0.9470088 ... 0.9423186) = 0.495 ... 0.498%,

where V is the size of the gusset (rib part) of the cross section V = 0.5R.

With the combined action of bending moments and compressive forces that take place in the belts of trusses of drive-free coatings, it is rational to develop wedge-shaped bent-closed profiles in the force planes of the supporting structures. To this end, it is advisable to take the obtained ratios of the parameters of the I-shaped rib, the flat and cylindrical faces of an equally stable cross section as the base ones, so that in relation to each design case, the section height is developed successively by one rib size.

Then, if you increase the height by 1 size of the rib part and repeat all the calculations, then the wedge-shaped bent-closed profiles will have the following cross-sectional characteristics:

- overall height

H = 4V;

- overall width

U = 4V;

- cross-sectional area

A = 14.28tV;

- ordinate of the center of gravity of the section relative to the upper face

y _c = 1.1596V;

- moments of inertia

I _X = 23.719464tV ³ , I _Y = 11.01302tV ³ ;

- moments of resistance

W _{X, max} = 20.454867tV ² , W _{X, min} = 8.3507477tV ² , W _Y = 5.50651tV ² ;

- radii of inertia

i _X = l, 2888082V, i _Y = 0.8781912V.

If we develop the height by 2 sizes of the rib part, then the wedge-shaped bent-closed profiles will have the following cross-sectional characteristics:

- overall height

H = 5V;

- overall width

U = 4V;

- cross-sectional area

A = 16.28tV;

- ordinate of the center of gravity of the section relative to the upper face

y _c = 1,570V;

- moments of inertia

I _X = 41.958704tV ³ ; I _Y = 11.01302tV ³ ;

- moments of resistance

W _{X, max} = 26.725289tV ² , W _{X, min} = 12.232858tV ² , W _Y = 5.50651tV ² ;

- radii of inertia

i _X = 1.605402V, i _Y = 0.8224812V.

If we develop the height by 3 sizes of the rib part, then the wedge-shaped bent-closed profiles will have the following cross-sectional characteristics:

- overall height

H = 6V;

- overall width

U = 4V;

- cross-sectional area

A = 18.28tV

- ordinate of the center of gravity of the section relative to the upper face

y _c = 2.0V;

- moments of inertia

I _X = 71.227173tV ³ , I _Y = 11.01302tV ³ ;

- moments of resistance

W _{X, max} = 35.613586tV ² , W _{X, min} = 17.806793tV ² , W _Y = 5.50651tV ² ;

- radii of inertia

i _X = 1.9739436V, i _Y = 0.7761847V.

To compare wedge-shaped bent closed profiles (new technical solution) with the prototype, the panel of the upper truss belt made of steel of class C255 with a design length of 3 m in the plane, as well as internal forces N = 412/2 = 206 kN and M = 16, was adopted as the basic object. 7/2 = 8.35 kN⋅m, reduced by 2 times in proportion to the prototype [Salakhutdinov MA, Kuznetsov I.L., Sayanov S.F. Steel trusses with belts from pipes of multifaceted cross-section. - Proceedings of KSASU, 2016, No. 4 (38). - S. 237].

The prototype is represented by a bent closed profile with parameters a = 120 mm, b = 120 mm, c = 120 mm, d = 120 mm, with a thickness of t = 2 mm and the following cross-sectional characteristics:

- overall height

H = 242 mm;

- overall width

U = 120 mm;

- cross-sectional area

A = 16.8 cm ² ;

- ordinate of the center of gravity of the section relative to the upper face

y _c = 121 mm;

- moments of inertia

I _X = 1114 cm ⁴ ,

I _Y = 247 cm ⁴ ;

- moments of resistance

W _X = 1114 / 12.1 = 92.07 cm ³ ,

W _Y = 247/6 = 41.17 cm ³ ;

- radii of inertia

i _X = (1114 / 16.8) ^1/2 = 8.143 cm,

i _Y = (247 / 16.8) ^1/2 = 3.834 cm.

Then the calculated voltage from the combined action of internal forces in the section of the panel from the profile of the prototype will be:

σ = N / (ϕ A) + M / W _X = 20600 / (0.908⋅16.8) + 83 500 / 92.07 = 1350.4 + 906.9 =

= 2257.3 kgf / cm ² = 0.945R _y ,

where the design flexibility of the panel is λ = l / i _X = 300 / 8.143 = 36.84; conditional (reduced) panel flexibility λ * = λ (R _y / E) ^1/2 = 36.84 (2400/2100000) ^1/2 = 1.245 <2.5; design resistance of steel of class C255 R _y = 2400 kgf / cm ² ; modulus steel E = 2100000 kgf / cm ^2; coefficient of longitudinal bending ϕ = 1-0,066 (λ *) ^3/2 = 1-0,066 (1,245) ^3/2 = 0,908.

The new technical solution is represented by a wedge-shaped bent closed profile, equally stable from the plane and in the plane, with the following parameters:

- cross-sectional area

A = 12.28tV = 16.8 cm ² ;

- calculated rib size

V = A / (12.28t) = 16.8 / (12.28 × 0.2) = 6.8403905≈6.84 cm;

- overall height

H = 3V = 3 × 6.64 = 20.52 cm;

- overall width

U = 4V = 4 × 6.64 = 27.36 cm;

- ordinate of the center of gravity of the section relative to the upper face

y _c = 0.7785 × 6.64 = 5.32494 cm;

- moments of inertia

I _X = 10.904203 × 0.2 × 6.84 ³ = 697.89843 cm ⁴ ,

I _Y = 11.01302 × 0.2 × 6.84 ³ = 704.86301 cm ⁴ ;

- moments of resistance

W _{X, max} = 14.006683 × 0.2 × 6.84 ² = 131.06221 cm ³ ,

_{W X, min = 4,9084866 × 0,2} × 6,84 cm ² = 45.929298 ³

W _Y = 5.50651 × 0.2 × 6.84 ² = 51.525075 cm ³ ;

- radii of inertia

i _X = 0.9423186 × 6.84 = 6.445 cm,

i _Y = 0.9470088 × 6.84 = 6.478 cm.

Then, the calculated voltage from the combined action of internal forces in the section of the panel from an equally stable profile according to the new technical solution will be:

σ = N / (φA) + M / W X, max = 20600 / (0,870 × 16,8) + 83500 / 131.062214 = 1409.4 + 637.1 = 2046.5 kgf / cm ² _y = 0,853R ,

where the design flexibility of the panel is λ = 300 / 6.445 = 46.55; panel conditional flexibility λ * = 46.55 (2400/2100000) ^1/2 = l, 574 <2.5; the coefficient of longitudinal bending ϕ = 1-0,066 (λ *) ^3/2 = 1-0,066 (1,574) ^3/2 = 0,870.

As you can see, the calculated voltage in the new technical solution was 100 (0.945-0.870) / (0.945 ... 0.870) = 7.9 ... 8.6% lower than in the prototype. At the same time, the overall height dimension of the prototype is 100 (242-205.2) / (242 ... 205.2) = 15.2 ... 17.3% more than the new solution.

The cross-sectional characteristics in the new solution were calculated using formulas obtained by the method of stepwise approximations, therefore, their repeated (test) calculation along the midline of a thin-walled section, including taking into account numerical values containing thicknesses raised to the second and third degree (t ² , t ³ ):

- ordinate of the center of gravity of the section relative to the upper face

y _c = H-y _n = 20.52-15.1943 = 5.3257 cm

with relative error

100 (5.3257-5.32494) / (5.3257 ... 5.32494) = 0.01425%,

where y _n - the distance from the center of gravity of the section to the lower edge,

y _n = (0.2 × 27.36 × 20.52 + 2 × 4.29552 (20.52-0.36304 × 13.68) +

+ 2 × 0.2 × 6.84 × 6.84 / 2) + 2 × 12.516 × 6.258)) / 16.8 =

= 15.1943 cm,

R = 2V = 2 × 6.84 = 13.68 cm,

A _R = 1.57tR = 1.57 × 0.2 × 13.68 = 4.29552 cm ² ,

20.52-0.36304 × 13.68 = 15.553613 cm - the distance from the center of gravity of the cross section of the cylindrical face to the lower edge,

6.84 / 2 = 3.42 cm - the distance from the center of gravity of the rib section to the lower edge;

- moment of inertia about the x-x axis

I _X = 0.2 ³ × 27.36 / 12 + 0.2 × 27.36 × 5.3257 ² +

+2 (5.69112 × 0.5 + 145.92615 × 0.5 + 4.29552 (5.3257-0.36304 × 13.68) ² +

+2 (0,2 × 6,84 ^3/12 + 0,2 × 6,84 (20,52-5,3257-6,84 / 2) ²⁾ =

= 697.90386 cm ⁴ ,

with relative error

100 (697.90386-697.89843) / (697.90386 ... 697.89843) = 0.0123%,

where I _XR = 0.011115tR ³ = 0.011115 × 0.2 × 13.68 ³ = 5.69112 cm ⁴ ,

I _YR = 0.285tR ³ = 0.285 × 0.2 × 13.68 ³ = 145.92615 cm ⁴ ;

- moment of inertia about the y-axis

I _Y = 0,2 × 27,36 ^3/12 +

+2 (145.92615 × 0.5 + 5.69112 × 0.5 + 4.29552 (0.36304 × 13.68) ² +

+2 (0.2 ³ × 6.84 / 12 + 0.2 × 6.84 (0.2 / 2) ² ) =

= 704.89948 cm ⁴ ,

with relative error

100 (704.89948-704.86301) / (704.89948 ... 704.86301) = 0.0052%.

As you can see, the test results allow us to conclude that the above calculations do not require adjustment, and their error is quite acceptable for practical calculations.

Thus, the obtained comparison results confirm the prospects, rationality and effectiveness of the use of wedge-shaped bent closed profiles in the supporting structures, as well as the correctness of its calculated parameters. At the same time, the universality of their technical solution, if necessary, allows having a section optimized according to the criterion of equilibrium stability and starting from it as a base one, to select derivatives, but the most optimal design sections, according to the parameters specified by the project. It seems that in the future, similarly and in tune with bent-welded profiles (GSP), the proposed wedge-shaped bent-closed profiles can be abbreviated as GBZ.

Claims (1)

A bent closed profile with a joint in the middle of one of the faces, where each part of the joined face has an extension in the form of an I-shaped rib, characterized in that the cross-section of the profile is given a wedge-shaped shape with a flat edge and a feather made of two identical cylindrical faces interconnected with the formation of an edge, with each of the arcs of cylindrical faces being a quarter of a circle whose radius is two times smaller than the size of the flat face and is equal to the same size as the size of the rib.

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