RU2714033C1 - H-shaped folded closed profile with perforated flange - Google Patents

Abstract

FIELD: construction.SUBSTANCE: invention relates to construction and can be used as structural elements of bearing structures of buildings. In H-shaped folded closed profile of two walls and one flange formed of two perforated elements of U-shape, attached to walls by means of tooth closures of longitudinal edges of vertical sections and mutually resting on horizontal sections, perforated elements throughout the horizontal sections are provided with cutouts with toothed edge closure along the entire perimeter of each of said cuts. At that, when width of cuts is 0.2…0.8 of profile width, ratio of its overall dimensions is equal to 1/1.809…1/1.771, and with no cuts, this ratio is equal to 1/1.810.EFFECT: technical result of the invention is overall stability of H-shaped folded closed profiles, their uniform stability from the plane and in the plane of the bearing structure.1 cl, 11 dwg, 1 tbl

Description

The proposed technical solution relates to the field of construction and can be used as core elements in the development of load-bearing structures of buildings and structures for various purposes. In particular, these can be elements of racks, columns, trusses, girders, crossbars, beams, frames, frames.

Known steel composite beam I-section, in which the upper and lower zones, as well as the vertical wall forms a pair of bent thin-walled profiles. The flat sections of these profiles for the formation of a vertical wall are interconnected by bends of stamped studs, mutually entering into the formed holes from the stamping. The longitudinal edges of the horizontal sections of the same paired profiles for the formation of tubular (cavity) belts are bent to contact the opposite face and connected by welding [Zamaliev FS, Zamaliev EF, Zamaliev E.F. Steel composite beam. - Patent No. 176505, 01/22/2018, bull. No. 3]. However, welded joints limit the minimum thickness of the welded elements and do not allow the use of galvanized steel, which provides high resistance to corrosion. The use of stamped studs and their holes is accompanied by a certain increase in additional costs.

Another well-known technical solution is a multi-span supporting structure (beam), including a tubular (hollow) profile of two curved walls and two flat belts (upper and lower). Both walls are welded to the belts and, being concave inward, are connected by tie rods in the zone of their contact, which gives the hollow profile of the structure an I-shaped outline [Veselov V.V., Fedorov A.M. Multi-span carrier beam. - Patent No. 176462, 01/19/2018, bull. No. 2]. As in the previous case, welding limits the minimum thickness of the elements being welded and does not allow the use of galvanized steel, and the tie rods and their holes cause a certain increase in additional costs.

One more technical solution is known (adopted as an analogue) in the form of an I-beam with a perforated wall, consisting of individual elements interconnected by vertical stiffeners by welding. In the spans, the wall elements are made of corrugated profile, the guides of which diverge from the center of the element with a hole in the shape of a circle. The hole is located in the center, obtained by a cutout and provided with edges reinforced with a collar from sheet metal [Kholopov I.S., Lukin A.O., Valkaev P.P. Metal I-beam. - Patent No. 147433, 10/10/2014, bull. No. 31]. However, here, welded joints limit the minimum thickness of the welded elements and do not allow the use of galvanized steel.

Closest to the proposed (adopted as a prototype) is a technical solution, which is an I-beam bent closed profile of two flat belts and two walls of an arcuate shape, concave inward. The walls are attached to the belts by means of gear closures of the longitudinal edges and are mutually supported in the area of their contact. In the cross section, the walls have the shape of round half rings, the diameter of which is equal to the width of the belts. The I-beam bent closed profile can be performed with shelves thicker than the walls, as well as bistal ones with a design resistance of the shelves greater than the walls [Marutyan AS I-beam bent closed profile. - Patent No. 2680560, 02.22.2019, bull. No. 6]. Such a profile, having a compact cross-sectional shape with equal dimensions in width and height, is quite effective in resisting longitudinal loads applied centrally and with eccentricities, which is typical for such core elements as columns and columns. However, for the structural layout of the uprights and columns, it is preferable that such cross-sectional shapes provide them with equal stability from the plane and in the plane of the supporting structure. In such cases, the beam I-beams are replaced by wide-shelf ones, and the wide-beam ones, in turn, are replaced by columned ones. However, in columned I-beams, the moments of inertia of their sections relative to the main central axes differ by two to three times. With the decrease of this difference to zero, the I-shaped contours of the profiles are transformed into H-shaped. In relation to the H-shaped bent closed perforation profiles of their shelves (instead of walls), additional functionality can be given in the form of forming cutouts of various shapes with serrated edges along the entire perimeter of each of these cutouts. Such closures can provide the necessary connections of the composite section without welded, bolted or riveted joints and, like an analog, strengthen the edges of the perforated wall cutouts. The indicated study with the reformatting of I-shaped bent closed profiles into the same profiles of H-shaped configurations with perforated shelves, supplemented by optimization of design parameters, can help expand the field of their rational use.

The technical result of the proposed solution is sufficient local (local) and overall stability of H-shaped bent closed profiles, their equidistance from the plane and in the plane of the supporting structure, expanding the field of rational use, as well as reducing additional costs and consumption of structural material.

The specified technical result is achieved in that in an H-shaped bent closed profile of two walls (vertical faces) and one shelf (horizontal face) of two perforated elements of a p-shaped (channel) shape, attached to the walls by means of serrated closures of the longitudinal edges of the vertical sections and mutually supported along horizontal sections, perforated elements along the entire horizontal sections are provided with cutouts with serrated edges along the entire perimeter of each of these cuts. Moreover, when the width of the cuts is 0.2 ... 0.8 of the width of the profile, the ratio of its overall dimensions is 1 / 1.809 ... 1 / 1.771 times, and in the absence of cuts this ratio is 1 / 1.810.

The proposed H-shaped bent-closed profile has a fairly universal technical solution, with the implementation of which sheet blanks of the same and different thickness can be used for its manufacture, both with gear locks, and with welded, bolted or riveted joints. For the manufacture of 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 so that they form the edges of two blanks 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]. In addition, the bends of the gear mounts ensure the preservation of local (local) stability and the cross-sectional shape of thin-walled elements to the limit state, which allows you to calculate not reduced sections, but net sections [Bely G.I. To the determination of reduced sections of the core elements of light steel thin-walled structures. - Bulletin of Civil Engineers, 2017, No. 6. - S. 33-37]. It should be added that the bends of the gear mounts distributed evenly over the walls and shelves throughout the H-shaped bent-closed profile retain its integrity and monolithic to a greater extent than the contact zones with friction of the seam-type connection in the rectangular beam profile with the ends attached to the hooks, which allowed us to consider the cross section of the beam monolithic [Yakovleva E.L., Atavin I.V., Kazakova Yu.D., Maksudov I.Kh. Strength characteristics of thin-walled elements. - Construction of unique buildings and structures, 2017, No. 12 (63). - S. 125-139]. Moreover, in some cases, to reduce the additional costs, the integrity of the composite section of the bent closed profile is quite achievable due to the use of a similar zone of contact with friction without perforation of its shelf.

The proposed technical solution is illustrated by graphic materials, where

FIG. 1 shows a top view (or bottom) of an H-shaped bent closed profile with rectangular cutouts of a perforated shelf;

FIG. 2 is a top view (or bottom) of an H-shaped bent closed profile with round cutouts of a perforated shelf;

FIG. 3 is a top view (or bottom) of an H-shaped bent closed profile with hexagonal cutouts of a perforated shelf;

FIG. 4 is a top view (or bottom) of an H-shaped bent closed profile with rhombic cutouts of a perforated shelf;

FIG. 5 is a top view (or bottom) of an H-shaped bent closed profile with oval cutouts of a perforated shelf;

FIG. 6 is a side view of an H-shaped bent closed profile with a perforated shelf;

FIG. 7 is a cross-sectional view of an H-shaped bent closed profile within one of the cutouts of its perforated shelf;

FIG. 8 is a design diagram of a cross section of an H-shaped bent closed profile within one of the cutouts of its perforated shelf;

FIG. 9 is a perspective view of a fragment of an H-shaped bent closed profile with rectangular cut-outs of its perforated shelf in a disassembled form;

FIG. 10 is a perspective view of a fragment of an H-shaped bent closed profile with a continuous shelf without cutouts in an unassembled form;

FIG. Figure 11 shows graphs of changes in the main design parameters of an H-shaped bent closed profile depending on the growth of the relative width b / U of the cutouts of its perforated shelf.

The H-shaped bent closed profile with a perforated shelf according to the proposed technical solution consists of two pairs of sheet blanks (strips or molding strips). The external pair of blanks 1 of a flat cross-sectional shape after the closure of the bent profile is located vertically. The inner pair of blanks 2 has rectangular cuts, 3 - round cuts, 4 - hexagonal cuts, 5 - rhombic cuts, 6 - oval cuts. The inner pair of blanks 7 is made without cutouts. The inner pair of blanks (2, 3, 4, 5, 6, and 7) has a p-shaped (channel) cross-sectional shape with two angular curves of three flat faces: vertical - walls and horizontal - shelves. Shelves can be perforated with cutouts of different shapes or solid without cutouts. All blanks are made along the entire length with serrated longitudinal edges, the teeth of which are staggered relative to each other and mutually bent in grooves between themselves after closing a bent profile. Perforated blanks of inner pairs 2, 3, 4, 5, and 6 are additionally made with the same serrated edges along the entire perimeter of each of the cutouts. The teeth of these edges are exactly the same in relation to each other in a checkerboard pattern and mutually bent in grooves between each other after closing a bent profile.

To quantify the resources of the bearing capacity of an I-shaped bent closed profile with a perforated wall, it is advisable to calculate the area, as well as the moments of inertia of its cross section I _x and I _y relative to the main central axes. Here, it is obvious that the cross section of such a profile can be considered a composite figure, including two pairs of vertical rectangles of dimensions t × V forming the side walls, as well as one pair of horizontal rectangles of size t × U with cutouts of dimensions t × b (0 <b <U) or without cutouts (b = 0) forming a perforated shelf. In this case, it is permissible to carry out computational calculations along the midline of a thin-walled section without taking into account angular curves and without taking into account numerical values containing the thicknesses raised to the second and third degree (t ² , t ³ ) [Marutyan AS 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 estimated cross-sectional area of the H-shaped bent closed profile is the sum of the calculated cross-sectional areas of four rectangular wall elements and two rectangular elements of a perforated shelf (at b = 0, b is the width of the cut):

A = 4tV + 2tU = 2tU (2 / n + 1),

where from

U = {A / t) / (1 / (2 (2 / n + 1))) and V = (A / t) / (1 / (2 (n + 2))),

where n is the ratio of the smaller (horizontal) size to the larger (vertical), n = U / V;

t and A are the thickness and total area of strips (sheet blanks or formed strips, respectively), t = const and A = const.

Moment of inertia of a section of an I-beam bent closed profile relative to the central axis xx:

I _x = 4tV ^{3/12 3} = tU / (3n ^3).

The moment of inertia of the cross-section of the I-beam bent closed profile relative to the central axis yy:

I _y = 2tU ^3/12 + 4tV (0,5U) ² = tU ³ (1 / n + 1/6).

It is appropriate to test the formulas obtained on the basis of standard HP rolling profiles (wide-shelf bearing piles), in which the walls and shelves have the same thickness [Shaped steel and commercial profiles: Product Catalog. - ArcelorMittal, 2014-1. - S. 94-95]. Its main results are more clearly presented in tabular form, from which it can be seen that these formulas are correct enough to continue numerical calculations with their application.

If the values of the axial moments of inertia of the section are equated to each other, then an equation of the third degree will take place:

I _x -I _y = 0;

1 / (3n ³ ) - (1 / n + 1/6) = 0;

n ³ + 6n ² -2 = 0;

n ₁ = -5.9433809; n ₂ = -0.6090937; n ₃ = 0.5524746.

Practical application has the third value of the variable n, when the calculated profile is a core element, equally stable from the plane and in the plane of the supporting structure:

I _x = tU ³ / (3n ³ ) = tU ³ / (3 × 0.5524746 ³ ) = 1.9767042tU ³ ,

I _y = tU ³ (1 / n + 1/6) = tU ³ (1 / 0.5524746 + 1/6) = 1,9767045tU ³

with error

100 (1.9767045-1.9767042) / (1.9767045 ... 1.9767042) = 0.00001% ≈0.

All further numerical calculations are more obvious in comparison with the corresponding calculated parameters adopted as reference (100 percent) values, when the shelves and wall of the bent-closed I-beam profile from the prototype have the same thickness (k = 1):

A = 2tU (1.57 + k) = 2tU (1.57 + 1) = 5.14tU;

U = V = (A / t) / 5.14 = 0.1945525A / t (100%);

I _x = tU ³ (0.3925 + 0.5k) = t (0.1945525A / t) ³ (0.3925 + 0.5 × 1) = 0.0065722A ³ / t ² (100%);

I _y = tU ³ (0.1774670 + 0.1666666k) = t (0.1945525A / t) ³ (0.1774670 + 0.1666666 × 1) = 0.0025341A ³ / t ² (100%);

W _x = 2I _x / V = 2 (0.0065722A ³ / t ² ) / (0.1945525A / t) = 0.0675622A ² / t (100%);

W _y = 2I _y / U = 2 (0.0025341A ³ / t ² ) / (0.1945525A / t) = 0.0260505A ² / t (100%);

i _x = (I _x / A) ^1/2 = ((0.0065722A ³ / t ² ) / A) ^1/2 = 0.0810691A / t (100%);

i _y = (I _y / A) ^1/2 = ((0.0025341A ³ / t ² ) A) ^1/2 = 0.0503398A / t (100%),

where t and A are, respectively, the thickness and total area of the strips (sheet blanks or formed strips), t = const and A = const.

H-shaped bent closed profile, equally stable from the plane and in the plane of the supporting structure, without cutouts in the shelf has the following calculated parameters:

b / U = 0;

n = U / V = 0.5524746 = 1 / 1.8100379≈1.810;

U = (A / t) / (1 / (2 (2 / n + 1))) = (A / t) / (1 / (2 (2 / 0.5524746 + 1))) = 0.1082233A / t (55.63%);

V = (A / t) / (1 / (2 (n + 2))) = (A / t) / (1 / (2 (0.5524746 + 2))) = 0.1958882A / t (100, 7%);

I _x = tU ³ / (3n ³ ) = t (0.1082233A / t) ³ / (3 × 0.5524746 ³ ) = 0.0025054A ³ / t ² (38.12%);

I _y = tU ³ (1 / n + 1/6) = t (0.1082233A / t) ³ (1 / 0.5524746 + 1/6) = 0.0025054A ³ / t ² (98.87%);

W _x = I _x / y _max = 2I _x / V = 2 (0.0025054A ³ / t ² ) / (0.1958882A / t) = 0.0255798A ² / t (37.87%);

W _y = I _y / x _max = 2I _y / U = 2 (0.0025054A ³ / t ² ) / (0.1082233A / t) = 0.0463005A ² / t (177.7%);

i _x = (I _x / A) ^1/2 = ((0.0025054A ³ / t ² ) / A) ^1/2 = 0.0500539A / t (61.74%);

i _y = (I _y / A) ^1/2 = ((0.0025054A ³ / t ² ) / A) ^1/2 = 0.0500539A / t (99.43%).

The H-shaped bent closed profile, equally stable from the plane and in the plane of the supporting structure, with cutouts in the perforated shelf at b = 0.1U has the following calculated parameters:

b / U = 0.1;

I _x = tU ³ / (3n ³ ).

I _y = tU ³ (1 / n + 1/6)) - 2t (0,1U) ^3/12 = tU ³ (1 / n + 0,1665);

1 / (3n) ³ - (1 / n + 0.1665) = 0;

n ³ + 6.006006n ² -2.0020018 = 0;

n ₁ = -5.9494457; n ₂ = -0.6090572; n ₃ = 0.5524969;

n = U / V = 0.5524969 = 1 / 1.8099649≈1.810;

U = (A / t) / (1 (2 (2 / n + 1))) = (A / t) / (1 / (2 (2 / 0.5524969 + 1))) = 0.1082267A / t (55.63%);

V = (A / t) / (1 / (2 (n + 2))) = (A / t) / (1 / (2 (0.5524969 + 2))) = 0.1958865A / t (100, 7%);

I _x = tU ³ / (3n ³ ) = t (0.1082267A / t) ³ / (3 × 0.5524969 ³ ) = 0.0025053A ³ / t ² (38.12%);

I _y = tU ³ (1 / n + 0.1665) = t (0.1082267A / t) ³ (1 / 0.5524969 + 0.1665) = 0.0025053A ³ / t ² (98.87%);

W _x = I _x / y _max = 2I _x / V = 2 (0.0025053A ³ / t ² ) / (0.1958865A / t) = 0.0255790A ² / t (37.86%);

W _y = I _y / x _max = 2I _y / U = 2 (0.0025053A ³ / t ² ) / (0.1082267A / t) = 0.0462972A ² / t (177.7%);

i _x = (I _x / A) ^1/2 = ((0.0025053A ³ / t ² ) / A) ^1/2 = 0.0500529A / t (61.74%);

i _y = (I _y / A) ^1/2 = ((0.0025053A ³ / t ² ) / A) ^1/2 = 0.0500529A / t (99.43%).

The H-shaped bent closed profile, equally stable from the plane and in the plane of the supporting structure, with cutouts in the perforated shelf at b = 0.2U has the following calculated parameters:

b / U = 0.2;

I _x = tU ³ / (3n ³ ).

I _y = tU ³ (1 / n + 1/6) -2t (0,2U) ^3/12 = tU ³ (1 / n + 0,1653333);

1 / (3n ³ ) - (1 / n + 0.1653333) = 0;

n ³ + 6.0483883n ² -2.0161292 = 0;

n ₁ = -5.9922396; n ₂ = -0.60088023; n ₃ = 0.5526535;

n = U / V = 0.5526535 = 1 / 1.8994520≈1.809;

U = (A / t) / (1 / (2 (2 / n + 1))) = (A / t) / (1 / (2 (2 / 0.5526535 + 1))) = 0.1082507A / t (55.63%);

V = (A / t) / (1 / (2 (n + 2))) = (A / t) / (1 / (2 (0.5526535 + 2))) = 0.1958744A / t (100, 7%);

I _x = tU ³ / (3n ³ ) = t (0.1082507A / t) ³ / (3 × 0.5526535 ³ ) = = 0.0025050A ² / t ² (38.12%);

I _y = tU ³ (1 / n + 0.1653333) = t (0.1082507A / t) ³ (1 / 0.5526535 + 0.1653333) = 0.0025050A ³ / t ² (98.85%);

W _x = I _x / y _max = 2I _x / V = 2 (0.0025050A ³ / t ² ) / (0.1958744A / t) = 0.0255776A ² / t (37.86%);

W _y = I _y / x _max = 2I _y / U = 2 (0.0025050A ³ / t ² ) / (0.1082507A / t) = 0.0462814A ² / t (177.7%);

i _x = (I _x / A) ^1/2 = ((0.0025053A ³ / t ² ) / A) ^1/2 = 0.0500529A / t (61.74%);

i _y = (I _y / A) ^1/2 = ((0.0025053A ³ / t ² ) / A) ^1/2 = 0.0500529A / t (99.42%).

An H-shaped bent closed profile, equally stable from the plane and plane of the supporting structure, with cutouts in the perforated shelf b = 0.3U has the following calculated parameters:

b / U = 0.3;

I _x = tU ³ / (3n ³ ).

I _y = tU ³ (1 / n + 1/6) -2t (0,3U) ^3/12 = tU ³ (1 / n + 0,1621666);

1 / (3n ³ ) - (1 / n + 0.1621666) = 0;

n ³ + 6.1664979n ² -2.055499 = 0;

n ₁ = -6.1114645; n ₂ = -0.6081131; n ₃ = 0.5530796;

n = U / V = 0.5530796 = 1 / 1.8080580≈1.808;

U = (A / t) / (1 / (2 (2 / n + 1))) = (A / t) / (1 / (2 (2 / 0.5530796 + 1))) = 0.1083161A / t (55.67%);

V = (A / t) / (1 / (2 (n + 2))) = (A / t) / (1 / (2 (0.5530796 + 2))) = 0.1958417A / t (100, 7%);

I _x = tU ³ / (3n ³ ) = t (0.1083161A / t) ³ / (3 × 0.5530796 ³ ) = 0.0025037A ³ / t ² (38.10%);

I _y = tU ³ (1 / n + 0.1621666) = t (0.1083161A / t) ³ (1 / 0.5530796 + 0.1621666) = 0.0025037A ³ / t ² (98.80%);

W _x = I _x / y _max = 2I _x / V = 2 (0.0025037A ³ / t ² ) / (0.1958417A / t) = 0.0255686A ² / t (37.84%);

W _y = I _y / x _max = 2I _y / U = 2 (0.0025037A ³ / t ² ) / (0.1083161A / t) == 0.0462295A ² / t (177.5%);

i _x = (I _x / A) ^1/2 = ((0.0025037A ³ / t ² ) / A) ^1/2 = 0.0500369A / t (61.72%);

i _y = (I _y / A) ^1/2 = ((0.0025037A ³ / t ² ) / A) ^1/2 = 0.0500369A / t (99.40%).

The H-shaped bent closed profile, equally stable from the plane and in the plane of the supporting structure, with cutouts in the perforated shelf at b = 0.4U has the following calculated parameters:

b / U = 0.4;

I _x = tU ³ / (3n ³ ).

I _y = tU ³ (1 / n + 1/6) -2t (0,4U) ^3/12 = tU ³ (1 / n + 0,1560);

1 / (3n ³ ) - (1 / n + 0.1560) = 0;

n ³ + 6.4102564n ² -2.1367519 = 0;

n ₁ = -6.3573879; n ₂ = -0.6067825; n ₃ = 0.5539140;

n = U / V = 0.5539140 = 1 / 1.8053344≈1.805;

U = (A / t) / (1 / (2 (2 / n + 1))) = (A / t) / (1 / (2 (2 / 0.5539140 + 1))) = 0.1084441A / t (55.74%);

V = (A / t) / (1 / (2 (n + 2))) = (A / t) / (1 / (2 (0.5539140 + 2))) = 0.1957778A / t (100, 6%);

I _x = tU ³ / (3n ³ ) = t (0.1084441A / t) ³ / (3 × 0.5539140 ³ ) = 0.0025012A ³ / t ² (38.06%);

I _y = tU ³ (1 / n + 0.1560) = t (0.1084441A / t) ³ (1 / 0.5539140 + 0.1560) = 0.0025012A ³ / t ² (98.70%);

W _x = I _x / y _max = 2I _x / V = 2 (0.0025012A ³ / t ² ) / (0.1957778A / t) = 0.0255514A ² / t (37.84%);

W _y = I _y / x _max = 2I _y / U = 2 (0.0025012A ³ / t ² ) / (0.1084441A / t) = 0.0461288A ² / t (177.1%);

i _x = (I _x / A) ^1/2 = ((0.0025012A ³ / t ² ) / A) ^1/2 = 0.0500119A / t (61.69%);

i _y = (I _y / A) ^1/2 = ((0.0025012A ³ / t ² ) / A) ^1/2 = 0.0500119A / t (99.35%).

The H-shaped bent closed profile, equally stable from the plane and in the plane of the supporting structure, with cutouts in the perforated shelf at b = 0.5U has the following calculated parameters:

b / U = 0.5;

I _x = tU ³ / (3n ³ ).

I _y = tU ³ (1 / n + 1/6) -2t (0,5U) ^3/12 = tU ³ (1 / n + 0,1458333);

1 / (3n ³ ) - (1 / n + 0.1458333) = 0;

n ³ + 6.8571444n ² -2.2857145 = 0;

n ₁ = -6,8078264; n ₂ = -0.60046211; n ₃ = 0.5553032;

n = U / V = 0.5553032 = 1 / 1.800810≈1.801;

U = (A / t) / (1 / (2 (2 / n + 1))) = (A / t) / (1 / (2 (2 / 0.5553032 + 1))) = 0.1086570A / t (55.85%);

V = (A / t) / (1 / (2 (n + 2))) = (A / t) / (1 / (2 (0.5553032 + 2))) = 0.1956714A / t (100, 6%);

I _x = tU ³ / (3n ³ ) = t (0.1086570A / t) ³ / (3 × 0.5553032 ³ ) = 0.0024972A ³ / t ² (38.06%);

I _y = tU ³ (1 / n + 0.1458333) = t (0.1086570A / t) ³ (1 / 0.5553032 + 0.1458333) = 0.0024972A ³ / t ² (98.54%);

W _x = I _x / y _max = 2I _x / V = 2 (0.0024972A ³ / t ² ) / (0.1956714A / t) = 0.0255244A ² / t (37.78%);

W _y = I _y / x _max = 2I _y / U = 2 (0.0024972A ³ / t ² ) / (0.1086570A / t) = 0.0459648A ² / t (176.4%);

i _x = (I _x / A) ^1/2 = ((0.0024972A ³ / t ² ) / A) ^1/2 = 0.0499719A / t (61.64%);

i _y = (I _y / A) ^1/2 = ((0.0024972A ³ / t ² ) / A) ^1/2 = 0.0499719A / t (99.27%).

The H-shaped bent closed profile, equally stable from the plane and in the plane of the supporting structure, with cutouts in the perforated shelf at b = 0.6U has the following calculated parameters:

b / U = 0.6;

I _x = tU ³ / (3n ³ ).

I _y = tU ³ (1 / n + 1/6) -2t (0,6U) ^3/12 = tU ³ (1 / n + 0,1306666);

1 / (3n ³ ) - (1 / n + 0.1306666) = 0;

n ³ + 7.6530651n ² -2.5510214 = 0;

n ₁ = -7,6090037; n ₂ = -0.6014691; n ₃ = 0.5574077;

n = U / V = 0.5574077 = 1 / 1.7940189≈1.794;

U = (A / t) / (1 / (2 (2 / n + 1))) = (A / t) / (1 / (2 (2 / 0,5574077 + 1))) = 0.1089790A / t (56.02%);

V = (A / t) / (1 / (2 (n + 2))) = (A / t) / (1 / (2 (0.5574077 + 2))) = 0.1955103A / t (100, 5%);

I _x = tU ³ / (3n ³ ) = t (0.1089790A / t) ³ / (3 × 0.5574077 ³ ) = 0.0024909A ³ / t ² (37.90%);

I _y = tU ³ (1 / n + 0.1306666) = t (0.1089790A / t) ³ (1 / 0.5574077 + 0.1306666) = 0.0024909A ³ / t ² (98.30%);

W _x = I _x / y _max = 2I _x / V = 2 (0.0024909A ³ / t ² ) / (0.1955103A / t) = 0.0254810A ² / t (37.71%);

W _y = I _y / x _max = 2I _y / U = 2 (0.0024909A ³ / t ² ) / (0.1089790A / t) = 0.0457133A ² / t (175.5%);

i _x = (I _x / A) ^1/2 = ((0.0024909A ³ / t ² ) / A) ^1/2 = 0.0499089A / t (61.56%);

i _y = (I _y / A) ^1/2 = ((0.0024909A ³ / t ² ) / A) ^1/2 = 0.0499089A / t (99.14%).

The H-shaped bent closed profile, equally stable from the plane and in the plane of the supporting structure, with cutouts in the perforated shelf at b = 0.7U has the following calculated parameters:

b / U = 0.7;

I _x = tU ³ / (3n ³ ).

I _y = tU ³ (1 / n + 1/6) -2t (0,7U) ^3/12 = tU ³ (1 / n + 0,10950);

1 / (3n ³ ) - (1 / n + 0.10950) = 0;

n ³ + 9.13242n ² -3.0441397 = 0;

n ₁ = -9,6090037; n ₂ = -0.5972073; n ₃ = 0.5604114;

n = U / V = 0.5604114 = 1 / 1.7844033≈1.784;

U = (A / t) / (1 / (2 (2 / n + 1))) = (A / t) / (1 / (2 (2 / 0.5604114 + 1))) = 0.1094377A / t (56.25%);

V = (A / t) / (1 / (2 (n + 2))) = (A / t) / (1 / (2 (0.5604114 + 2))) = 0.1952810A / t (100, 4%);

I _x = tU ³ / (3n ³ ) = t (0.1094377A / t) ³ / (3 × 0.5604114 ³ ) == 0.0024821A ³ / t ² (37.77%);

I _y = tU ³ (1 / n + 0.10950) = t (0.1094377A / t) ³ (1 / 0.5604114 + 0.10950) = 0.0024821A ³ / t ² (97.95%);

W _x = I _x / y _max = 2I _x / V = 2 (0.0024821A ³ / t ² ) / (0.1952810A / t) = 0.0254208A ² / t (37.63%);

W _y = I _y / x _max = 2I _y / U = 2 (0.0024821A ³ / t ² ) / (0.1094377A / t) = 0.0453609A ² / t (174.1%);

i _x = (I _x / A) ^1/2 = ((0.0024821A ³ / t ² ) / A) ^1/2 = 0.0498206A / t (61.45%);

i _y = (I _y / A) ^1/2 = ((0.0024821A ³ / t ² ) / A) ^1/2 = 0.0498206A / t (98.97%).

The H-shaped bent closed profile, equally stable from the plane and in the plane of the supporting structure, with cutouts in the perforated shelf at b = 0.8U has the following calculated parameters:

b / U = 0.8;

I _x = tU ³ / (3n ³ ).

I _y = tU ³ (1 / n + 1/6) -2t (0,8U) ^3/12 = tU ³ (1 / n + 0,0813333);

1 / (3n ³ ) - (1 / n + 0.0813333) = 0;

n ³ + 12.296087n ² -4.0983619 = 0;

n ₁ = -12.267855; n ₂ = -0.5917668; n ₃ = 0.5645352;

n = U / V = 0.5645352 = 1 / 1.7713687≈1.771;

U = (A / t) / (1 / (2 (2 / n + 1))) = (A / t) / (1 / (2 (2 / 0.5645352 + 1))) = 0.1100657A / t (56.57%);

V = (A / t) / (1 / (2 (n + 2))) = (A / t) / (1 / (2 (0.5645352 + 2))) = 0.1949669A / t (100, 2%);

I _x = tU ³ / (3n ³ ) = t (0,1100657A / t) ³ / (3 × 0.05.5645352 ³ ) = 0.0024702A ³ / t ² (37.59%);

I _y = tU ³ (1 / n + 0.0813333) = t (0.1100657A / t) ³ (1 / 0.5645352 + 0.0813333) = 0.0024702A ³ / t ² (97.48%);

W _x = I _x / y _max = 2I _x / V = 2 (0.0024821A ³ / t ² ) / (0.1949669A / t) = 0.0253396A ² / t (37.51%);

W _y = I _y / x _max = 2I _y / U = 2 (0.0024821A ³ / t ² ) / (0.1100657A / t) = = 0.0448859A ² / t (172.3%);

i _x = (I _x / A) ^1/2 = ((0.0024702A ³ / t ² ) / A) ^1/2 = 0.0497011A / t (61.31%);

i _y = (I _y / A) ^1/2 = ((0.0024702A ³ / t ² ) / A) ^1/2 = 0.0497011A / t (98.73%).

The H-shaped bent closed profile, equally stable from the plane and in the plane of the supporting structure, with cutouts in the perforated shelf at b = 0.9U has the following calculated parameters:

b / U = 0.9;

I _x = tU ³ / (3n ³ ).

I _y = tU ³ (1 / n + 1/6) -2t (0,9U) ^3/12 = tU ³ (1 / n + 0,0451666);

1 / (3n ³ ) - (1 / n + 0,0451666) = 0;

n ³ + 22.140254n ² -7.3800839 = 0;

n ₁ = -22.125178; n ₂ = -0.5851341; n ₃ = 0.5700581;

n = U / V = 0.5700581 = 1 / 1.7542071≈1.754;

U = (A / t) / (1 / (2 (2 / n + 1))) = (A / t) / (1 / (2 (2 / 0.5700581 + 1))) = 0.1109037A / t (57.0%);

V = (A / t) / (1 / (2 (n + 2))) = (A / t) / (1 / (2 (0.5700581 + 2))) = 0.1945480A / t (100, 0%);

I _x = tU ³ / (3n ³ ) = t (0,1109037A / t) ³ / (3 × 0.5700581 ³ ) = 0.0024543A ³ / t ² (37.34%);

I _y = tU ³ (1 / n + 0.0451666) = t (0.1109037A / t) ³ (1 / 0.5700581 + 0.0451666) = 0.0024543A ³ / t ² (96.85%);

W _x = I _x / y _max = 2I _x / V = 2 (0.0024543A ³ / t ² ) / (0.1945480A / t) = 0.0252307A ² / t (37.34%);

W _y = I _y / x _max = 2I _y / U = 2 (0,0024543A ³ / t ² ) / (0,1109037A / t) = 0,044260A ² / t (169.9%);

i _x = (I _x / A) ^1/2 = ((0.0024543A ³ / t ² ) / A) ^1/2 = 0.0495408A / t (61.11%);

i _y = (I _y / A) ^1/2 = ((0.0024543A ³ / t ² ) / A) ^1/2 = 0.0495408A / t (98.41%).

The H-shaped bent closed profile, equally stable from the plane and in the plane of the supporting structure, with cutouts in the perforated shelf at b = 0.95U has the following calculated parameters:

b / U = 0.95;

I _x = tU ³ / (3n ³ ).

I _y = tU ³ (1 / n + 1/6) -2t (0,95U) ^3/12 = tU ³ (1 / n + 0,0237708);

1 / (3n ³ ) - (1 / n + 0,0237708) = 0;

n ³ + 42.06842n ² -14.022805 = 0;

n ₁ = -42.060493; n ₂ = -0.5813815; n ₃ = 0.5734549;

n = U / V = 0.5734549 = 1 / 1.7438162≈1.744;

U = (A / t) / (1 / (2 (2 / n + 1))) = (A / t) / (1 / (2 (2 / 0.5734549 + 1))) = 0.1114173A / t (57.27%);

V = (A / t) / (1 / (2 (n + 2))) = (A / t) / (1 / (2 (0.5734549 + 2))) = 0.1942913A / t (99, 87%);

I _x = tU ³ / (3n ³ ) = t (0.1114173A / t) ³ / (3 × 0.5734549 ³ ) = 0.0024447A ³ / t ² (37.20%);

I _y = tU ³ (1 / n + 0.0237708) = t (0.1114173A / t) ³ (1 / 0.5734549 + 0.0237708) = 0.0024447A ³ / t ² (96.47%);

W _x = I _x / y _max = 2I _x / V = 2 (0.0024447A ³ / t ² ) / (0.1942913A / t) = 0.0251653A ² / t (37.25%);

W _y = I _y / x _max = 2I _y / U = 2 (0.0024447A ³ / t ² ) / (0.1114173A / t) = 0.0438836A ² / t (168.5%);

i _x = (I _x / A) ^1/2 = ((0.0024447A ³ / t ² ) / A) ^1/2 = 0.0494439A / t (60.99%);

i _y = (I _y / A) ^1/2 = ((0.0024447A ³ / t ² ) / A) ^1/2 = 0.0494439A / t (98.22%).

The results obtained and their comparison show that the proposed bent closed profile has equal stability with respect to both main central axes. It is more compact than the prototype in one of the orthogonal directions. In this direction, the stiffness of the prototype is more approximately proportional to the difference in the degree of compactness.

The main results of numerical calculations can be more clearly represented in graphical form, from which it is obvious that the calculated parameters over the entire interval of the relative width of the cutouts of the perforated shelf from b / U = 0 to b / U = 0.95 change almost linearly. The absolute values of changes in such parameters are comparatively small.

Of practical importance is the further refinement of the design characteristics of the proposed profiles with the addition of gear mounts instead of welded, bolted or riveted joints. To do this, in the considered profiles, it is necessary to select the sizes of the gear fastening elements (teeth), which should be at least 1/10 of the overall cross-sectional size [SP 260.1325800.2016. Thin-walled steel structures made of cold-formed galvanized profiles and corrugated sheets. Design rules. - M., 2016. - S. 16, formula (7.2)]. In this case, this size is 0.1U, where U is the width of the bent flange profile.

The noted parameter of the gear mounts limits the boundary values of the width of the cutouts of the perforated shelf and allows you to summarize the given ratios of the overall dimensions of the bent-closed profile:

in the absence of cutouts

b = 0 and n = U / V = 0.5524746 = 1 / 1.8100379≈1.810;

with minimal cutouts

b _min = 0.2U and n = U / V = 0.5526535 = 1 / 1.8094520≈1.809;

at maximum cutouts

b _max = 0.8U and n = U / V = 0.5645352 = 1 / 1.7713687≈1.771.

In the calculation calculations, the parameter of the gear mounts (the size of the teeth) will be reflected in a 12-fold way (8-fold in the prototype), since the H-shaped bent-closed profile has a composite section of 4 sheet blanks (strips or molding strips) with longitudinal edges of the gear shape, from of which 2 perforated blanks are additionally provided with the same serrated edges along the entire perimeter of each of the cutouts.

In the general case, for 0 <b <U

n is U / V;

A = 2tU (2 / n + 1);

A _gross = A + ΔA = 2tU (2 / n + 1) + 12 × 0,1tU = 2tU (2 / n + 1,6).

In particular (boundary) cases

at b = 0

n = U / V = 0.5524746 = 1 / 1.8100379≈1.810;

A = 2tU (2 / 0.5524746 + 1) = 9.2401518tU;

A _gross = A + ΔA = 9.2401518tU + 8 × 0.1tU = 10.040151tU;

A / A _gross = 9.2401518 / 10.040151 = 0.920320;

with b _min = 0.2U

n = U / V = 0.5526535 = 1 / 1.8994520≈1.809;

A = 2tU (2 / 0.5526535 + 1) = 9.2378080tU;

A _gross = A + ΔA = 9.2378080tU + 12 × 0.1tU = 10.437808tU;

A / A _gross = 9.2378080 / 10.437808 = 0.9850333;

at b _max = 0.8U

n = U / V = 0.5645352 = 1 / 1.7713687≈1.771.

A = 2tU (2 / 0.5645352 + 1) = 9.0854748tU

A _gross = A + ΔA = 9.0854748tU + 12 × 0.1tU = 10.285474tU;

A / A _gross = 9.0854748 / 10.285474 = 0.8833306.

The found values of the A / A ratio of the _gross H-shaped bent closed profiles with perforated shelves exceed the similar ratios of the prototype (I-beam bent closed profile with h / V = 0 and A / A _gross = 0.8561151 ... 0.8653198) and are approximately in the same range as the reduction coefficient of the core elements of light steel thin-walled structures (LSTK):

ρ = A _red / A,

where A _red is the estimated area of the reduced (effective) section, A is the estimated area of the full section.

So, in relation to continuous bent profiles of C-shaped and channel sections ρ = 0.694 ... 0.950 [Recommendations for the design, manufacture and installation of enclosing and supporting structures from steel bent profiles of increased rigidity. - M.: TSNIIPSK them. N.P. Melnikova, 1999 .-- S. 10-11, tab. 2].

The implementation of an H-shaped bent closed profile with a perforated shelf can be shown using an example with a base object in the form of a composite profile of two bent sigma profiles with a section size of 300 × 80 × 20.5 × 2 mm, the geometric characteristics of which are: for a full section

A = 20.03 cm ² (100%);

n = U / V == 160/300 = 0.5333333 = 1 / 1.875;

I _x = 2510.05 cm ⁴ (100%); W _x = 167.34 cm ³ (100%);

i _x = (2510.05 / 20.03) ^1/2 = 11.194 cm (100%);

I _y = 226.88 cm ⁴ (100%); W _y = 28.36 cm ³ (100%);

i _y = (226.88 / 20.03) ^1/2 = 3.366 cm (100%);

for effective cross section

A = 11.63 cm ² (100%);

n = U / V == 160/300 = 0.5333333 = 1 / 1.875;

I _x = 753.25 cm ⁴ (100%); W _x = 32.70 cm ³ (100%);

i _x = (753.25 / 11.63) ^1/2 = 8.048 cm (100%);

I _y = 143.42 cm ⁴ (100%); W _y = 17.93 cm ³ (100%);

i _y = (143.42 / 11.63) ^1/2 = 3.512 cm (100%),

where the calculated parameters of the effective cross section are determined during compression with bending without taking into account the initial geometric imperfections [Korsun ND, Prostakishina DA Analysis of the VAT of a composite section of thin-walled profiles, taking into account the initial geometric imperfections. - Academic Bulletin UralNIIproekt RAASN, 2018, No. 4. - S. 83-88].

The new technical solution in the first version is represented by an H-shaped bent closed profile with a shelf without cutouts (b / U = 0), the geometric characteristics of which at V = 300 mm are: for a full section

b = 0 for n = U / V == 0.5524746;

U = nV = 0.5524746 × 300 = 165.74238≈166 mm;

t = A / (9.2401518U) = 20.03 / (9.2401518 × 16.6) = 0.1305851 cm, t = 1.3 mm;

A = 9.2401518 × 0.13 × 16.6 = 19.940 cm ² (99.55%);

I _x = I _y = 0,0025054A ^3/2 = 0,0025054 × 19,940 ³ / 0.13 ² = 1175.35 cm ⁴ (46.83% and 518.0%);

i _x = i _y = (1175.35 / 19.940) ^1/2 = 7.678 cm (68.59% and 228.1%);

W _x = 1175.35 / 15.0 = 78.357 cm ³ (46.82%);

W _y = 1175.35 / 8.30 = 141.608 cm ³ (499.3%);

for effective cross section

b = 0 for n = U / V = 0.5524746;

U = nV = 0.5524746 × 300 = 165.74238≈166 mm;

t = A _gross / (10.040151U) = 20.03 / (10.040151 × 16.6) = 0.1201801 cm, t = 1.2 mm;

A = 9.2401518 × 0.12 × 16.6 = 18.406 cm ² (158.3%);

I _x = I _y = 0.0025054A ³ / t ² ), 0025054 × 18.406 ³ / 0.12 ² = 1084.91 cm ⁴ (144.0% and 765.5%);

i _x = i _y = (1084.91 / 18.406) ^1/2 = 7.677 cm (95.27% and 218.6%);

W _x = 1084.91 / 15.0 = 72.327 cm ³ (221.2%);

W _y = 1084.91 / 8.30 = 130.71 cm ³ (729.0%),

where the thickness values (t = 1.3 mm and t = 1.2 mm) are adopted according to GOST 19904-90 “Cold-rolled sheet metal. Assortment ”, which reduces additional costs.

The new technical solution in the second embodiment is represented by an H-shaped bent closed profile with minimal cutouts of the perforated shelf (b _min / U = 0.2), the geometric characteristics of which at V = 300 mm are:

for full cross section

b _min = 0.2U at n = U / V = 0.5526535;

U = nV = 0.5526535 × 300 = 165.79605≈166 mm;

b _min = 0.2 × 166 = 33.2 mm;

t = A (9.2378080U) = 20.03 / (9.2378080 × 16.6) = 0.1306182 cm, t = 1.3 mm;

A = 9.2378080 × 0.13 × 16.6 = 19.9352 cm ² (99.53%);

I _x = I _y = 0.0025050A ³ / t ² = 0.0025050 × 19.9352 ³ / 0.13 ² = 1174.31 cm ⁴ (46.78% and 517.6%);

i _x = i _y = (1174.31 / 19.9352) ^1/2 = 7.675 cm (68.56% and 228.0%);

W _x = 1174.31 / 15.0 = 78.287 cm ³ (46.78%);

W _y = 1174.31 / 8.30 = 141.483 cm ³ (498.9%);

for effective cross section

b _min = Q, 2U at n = U / V = 0.5526535;

U = nV = 0.5526535 × 300 = 165.79605≈166 mm;

b _min = 0.2 × 166 = 33.2 mm;

t = A _gross / (10.437808U) = 20.03 / (10.437808 × 16.6) = 0.1156015 cm, t = 1.1 mm;

A = 9.2378080 × 0.11 × 16.6 = 16.8682 cm ² (145.04%);

I _x = I _y = 0.0025050A ³ / t ² = 0.0025050 × 16.8682 ³ / 0.11 ² = 993.639 cm ⁴ (131.9% and 692.8%);

i _x = i _y = (993.639 / 16.8682) ^1/2 = 7.675 cm (95.37% and 218.5%);

W _x = 993.639 / 15.0 = 66.243 cm ³ (202.6%);

W _y = 993.639 / 8.30 = 119.716 cm ³ (667.7%),

where the thickness values (t = 1.3 mm and t = 1.1 mm) are adopted according to GOST 19904-90 “Cold-rolled sheet metal. Assortment ”, which reduces additional costs.

A new technical solution in the third embodiment is represented by an H-shaped bent closed profile with maximum perforated shelf cutouts (b _max / U = 0.8), the geometric characteristics of which at V = 300 mm are:

for full cross section

b _max = 0.8U at n = U / V = 0.5645352;

U = nV = 0.5645352 × 300 = 169.36056≈169 mm;

b _max = 0.8 × 169 = 135.2 mm;

t = A / (9.0854748U) = 20.03 / (9.0854748 × 16.9) = 0.1304507 cm, t = 1.3 mm;

A = 9.0854748 × 0.13 × 16.9 = 19.961 cm ² (99.65%);

I _x = I _y = 0.0024702A ³ / t ² = 0.0024702 × 19.961 ³ / 0.13 ² = 1162.50 cm ⁴ (46.31% and 512.4%);

i _x = i _y = (1162.50 / 19.961) ^1/2 = 7.631 cm (68.17% and 226.7%);

W _x = 1162.50 / 15.0 = 77.50 cm ³ (46.31%);

W _y = 1162.50 / 8.45 = 137.574 cm ³ (485.1%);

for effective cross section

b _max = 0.8U at n = U / V = 0.5645352;

U = nV = 0.5645352 × 300 = 169.36056≈169 mm;

b _max = 0.8 × 169 = 135.2 mm;

t = A _gross (10.285474U) = 20.03 / (10.285474 × 16.9) = 0.1152311 cm, t = 1.1 mm;

A = 9.0854748 × 0.11 × 16.9 = 16.890 cm ² (145.2%);

I _x = I _y = 0.0024702A ³ / t ² = 0.0024702 × 16.890 ³ / 0.11 ² = 983.639 cm ⁴ (130.6% and 685.8%);

i _x = i _y = (983.639 / 16.890) ^1/2 = 7.631 cm (68.17% and 226.7%);

W _x = 983.639 / 15.0 = 65.576 cm ³ (200.5%);

W _y = 983.639 / 8.45 = 116.407 cm ³ (649.2%),

where the thickness values (t = 1.3 mm and t = 1.1 mm) are adopted according to GOST 19904-90 “Cold-rolled sheet metal. Assortment ”, which reduces additional costs.

As can be seen, the obtained results of computational calculations and their comparison confirm the rationality and effectiveness of the prospective use of an H-shaped bent closed profile with a perforated shelf in load-bearing elements that provide strength resistance to compression with bending.

Claims (1)

H-shaped bent closed profile of two walls (vertical faces) and one shelf (horizontal face) of two perforated elements of a p-shaped (channel) shape, attached to the walls by means of serrated closures of the longitudinal edges of the vertical sections and mutually supported along the horizontal sections, characterized in that the perforated elements along the entire length of the horizontal sections are provided with cutouts with serrated locking edges along the entire perimeter of each of these cutouts, while when the width of the cuts is 0.2 ... 0.8 of the width of the profile, the ratio of its overall dimensions is 1 / 1.809 ... 1 / 1.771, and in the absence of cutouts, this ratio is 1 / 1.810.

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