RU2641333C1 - Curved closed profile - Google Patents

Abstract

FIELD: construction.

SUBSTANCE: in the curved closed profile of rectangular section with a hinge in the middle of one of the long sides, where each part of an aligned edge is continued in the form of I-shaped rib, the size of short edges is half the size of the I-shaped ribs and three times smaller than the long edges.

EFFECT: same stability of the curved closed profiles from the plane and in the plane of the supporting structure, reduction of additional costs.

2 cl, 21 dwg

Description

The proposed technical solution 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 KSASU, 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 of one strip . - Patent 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 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.

In the above technical solutions, including the prototype, the bearing capacity of bent closed (bent closed) profiles is ensured by the use of welded, bolted or riveted joints in their manufacture, which causes a certain increase in additional costs.

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 supporting structure, as well as reducing additional costs.

The specified technical result is achieved by the fact that in a bent closed profile of rectangular section with a joint in the middle of one of the long faces, where each part of the joined face has an extension in the form of an I-shaped rib, the size of the short faces is half the size of the I-shaped ribs and three times smaller than the length of the long edges. For the manufacture of a bent closed profile without welded, bolted or riveted joints, its sheet blank is 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 each other after closing the bent profile along I-shaped ribs.

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 the size of the short edges is two times smaller than the size of the I-shaped ribs and three times smaller than the size of the long edges, then these profiles are equally stable, that is, they have the same stability from the plane and in the plane of the supporting structure. The equidistance of 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 net cross-section in the force plane of the supporting structure and preserving the already defined ratios of the sizes of long and short tubular faces parts of single thickness.

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 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 drawings, where in FIG. 1 shows a section of bent closed profiles optimized by the criterion of equidistance (the dashed line indicates the midline of the calculated section); in FIG. 2 is a design diagram of a section of bent closed profiles; in FIG. 3 - section bent closed profiles with gear fastening, optimized by the criterion of equidistance; in FIG. 4 - cross section of bent closed profiles with gear fastening after crimping, optimized according to the criterion of equidistance; in FIG. 5 shows a scan of a sheet blank with serrated longitudinal edges for bent closed profiles with an optimized cross-section (the dotted line indicates the midline of the calculated net cross-section); in FIG. 6 - fragment bent closed profile with optimized cross-section; in FIG. 7 is a fragment of a bent closed profile with an optimized cross section when it is closed along I-shaped ribs; in FIG. 8 is a fragment of a bent closed profile with an optimized cross section and gear mount; 9 is a fragment of a bent closed profile with an optimized cross section and gear fastening after crimping; in FIG. 10 shows a cross section of bent closed profiles with I-shaped ribs elongated by 1 size of short faces; in FIG. 11 is a section of bent closed profiles with I-shaped ribs elongated by 2 sizes of short faces; in FIG. 12 is a section of bent-closed profiles with I-shaped ribs elongated by 3 sizes of short faces; in FIG. 13 is a section of bent closed profiles with I-shaped ribs elongated by 4 sizes of short faces; FIG. 14 shows a section of bent-closed profiles with gear fastening and I-shaped ribs elongated by 1 size of short faces; in FIG. 15 is a section of bent-closed profiles with gear fastening and I-shaped ribs elongated by 2 sizes of short faces; in FIG. 16 is a section of bent-closed profiles with gear fastening and I-shaped ribs elongated by 3 sizes of short faces; in FIG. 17 is a section of bent-closed profiles with gear fastening and I-shaped ribs elongated by 4 sizes of short faces; in FIG. Figure 18 shows a section of bent-closed profiles with gear fastening after crimping and I-shaped ribs elongated by 1 size of short faces; in FIG. 19 is a section of bent-closed profiles with gear fastening after crimping and I-shaped ribs elongated by 2 sizes of short faces; in FIG. 20 is a section of bent-closed profiles with gear fastening after crimping and I-shaped ribs elongated by 3 sizes of short faces; in FIG. 21 is a section of bent-closed profiles with gear fastening after crimping and I-shaped ribs elongated by 4 sizes of short faces.

The proposed bent closed profiles, by analogy with the prototype, can be formed in 5 ... 10 passes, depending on the yield strength and elongation of the material. At the same time, in the passage of “bending of the side walls” in the opposite direction to the bending of these walls, instead of the walls themselves, the serrated longitudinal edges of the formed strips are bent. After the formation of closed (tubular) parts of single thickness and rib parts of double thickness, the teeth of the longitudinal edges are missing in the grooves between themselves in a plane orthogonal to the ribs and short faces of the bent closed profiles. Next, with the bending of the teeth parallel to the I-shaped ribs, gear fastenings are closed, which can be crimped for greater reliability.

To derive the reduced aspect ratio of the 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 cross 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 the bent closed profile, and also without taking into account the 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].

In a first approximation, the cross section of the bent closed profile can be represented as composite of the tubular part of a single thickness and the rib part of a double thickness:

A = A _t + A _I = 2 t ( U + V ) +2 t ( U - V ) = 4 tU = 4 nVt ,

where A is the estimated net cross-sectional area of the closed profile;

And _t - the estimated area of the tubular part, And _t 2 t ( U + V );

A _I - estimated area of the rib part, A _I = 2 t ( U - V );

U is the size of the long edge of the profile, equal to its dimensions in height and width, U = H ;

V is the size of the short face of the profile;

n is the ratio of the size of the long face to the size of the short face, 1≤ n = U / V.

The ordinate of the center of gravity of the section relative to the upper face of the bent closed profile is:

y _c = (2 tV ( n + 1) V / 2 + 2 tV ( n -1) V ( n + 1) / 2) / (4 nVt ) = V ( n + 1) / 4.

The moment of inertia of the section relative to the x-axis:

I _X = tV ³ (1 + 3 n) / 6 + 2 tV (n +1) V ² ((n +1) / 4-1 / 2) ² + tV ³ (n -1) ^3/6 +

+2 tV ( n -1) V ² (( n +1) / 2- ( n +1) / 4) ² =

= tV ³ ((5/12) n ³ - (1/2) n ² + (3/4) n ).

The moment of inertia of the section about the y-y axis:

I _Y = n ³ tV ^3/6 + n ² tV ^3/2 = tV ³ ((1/6) n ³ - (1/2) n ^2).

Then the equation is obtained:

I _X - I _Y = 0;

((5/12) n ³ - (1/2) n ² + (3/4) n ) - ((1/6) n ³ - (1/2) n ² ) = 0;

n ² -4 n + 3 = 0; n ₁ = 1; n ₂ = 3.

Obviously, for n ₁ = 1, the bent-closed profile transforms into a square tube, and for n ₂ = 3, the size of the short faces is two times smaller than the size of I-shaped ribs and three times smaller than the size of long faces.

Thus, bent-closed profiles optimized by the criterion of equal stability have the following cross-sectional characteristics:

- overall height dimension H = 3.0 V ;

- overall dimension in width U = 3.0 V ;

- net cross-sectional area A = 12.0 tV ;

- the ordinate of the center of gravity of the section relative to the upper face y _c = V ;

- moments of inertia I _X = I _Y = 9.0 tV ³ ;

- moments of resistance W _{X, max} = 9.0 tV ² , W _{X, min} = 4,50 tV ² , W _Y = 6,0 tV ² ;

- radii of inertia i _x = i _y = 0.86603 V.

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 bent closed profiles in the force planes of load-bearing structures. To this end, it is advisable to take the obtained ratio of the sizes of the ribs, long and short faces of an equally stable cross-section as the base so that for each design case, to develop the section height successively by one size of short faces.

Then, if you increase the height by 1 size of the short edges and repeat all the calculations, then the bent-welded profiles will have the following cross-sectional characteristics:

- overall height dimension H = 4.0 V ;

- overall dimension in width U = 3.0 V ;

- net cross-sectional area A = 14.0 tV ;

- the ordinate of the center of gravity of the section relative to the upper face y _with = 1,357 V ;

- moments of inertia I _X = 19.88 tV ³ , I _Y = 9.0 tV ³ ;

- moments of resistance W _{X, max} = 14.65 tV ² , W _{X, min} = 7.522 tV ² , W _Y = 6.0 tV ² ;

- radii of inertia i _X = 1,192 V , i _Y = 0,8018 V.

If you develop the height by 2 sizes of short edges, then bent-welded profiles will have the following cross-sectional characteristics:

- overall height dimension H = 5.0 V ;

- overall dimension in width U = 3.0 V ;

- net cross-sectional area A = 16.0 tV ;

- the ordinate of the center of gravity of the section relative to the upper face at _c = 1.750 V ;

- moments of inertia I _X = 37.33 tV ³ , I _Y = 9.0 tV ³ ;

- moments of resistance W _{X, max} = 21.33 tV ² , W _{X, min} = 11.49 tV ² , W _Y = 6.0 tV ² ;

- radii of inertia i _X = 1,528 V , i _Y = 0,750 V.

If you develop the height by 3 sizes of short edges, then bent-welded profiles will have the following cross-sectional characteristics:

- overall height dimension H = 6.0 V ;

- overall dimension in width U = 3.0 V ;

- net cross-sectional area A = 18.0 tV

- the ordinate of the center of gravity of the cross section relative to the upper face at _a = 2,60 V;

- moments of inertia I _X = 62.50 tV ³ , I _Y = 9.0 tV ³ ;

- moments of resistance W _{X, max} = 28.85 tV ² , W _{X, min} = 16.31 tV ² , W _Y = 6.0 tV ² ;

- radii of inertia i _X = 1,863 V , i _Y = 0,7071 V.

If you develop the height by 4 sizes of short edges, then bent-welded profiles will have the following cross-sectional characteristics:

- overall height dimension H = 7.0 V ;

- overall dimension in width U = 3.0 V ;

- net cross-sectional area A = 20.0 tV ;

- the ordinate of the center of gravity of the cross section relative to the upper face at _a = 2,60 V;

- moments of inertia I _X = 89.87 tV ³ , I _Y = 9.0 tV ³ ;

- moments of resistance W _{X, max} = 28.85 tV ² , W _{X, min} = 16.31 tV ² , W _Y = 6.0 tV ² ;

- radii of inertia i _X = 2,120 V , i _Y = 0,6708 V.

To compare bent closed profiles (new technical solution) with the prototype, the panel of the upper truss belt made of steel of class C255, with an estimated 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 [Salakhutdinov M.A., 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], reduced by 2 times in proportion to the prototype.

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 dimension H = 242 mm;

- overall width U = 120 mm;

- net cross-sectional area A = 16.8 cm ² ;

- the ordinate of the center of gravity of the section relative to the upper face y _with = 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 = 0.945 R _y ,

where the estimated 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 of elasticity of 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 bent closed profile, equally stable from the plane and in the plane, with the following parameters:

- net cross-sectional area A = 12.0 tV = 16.8 cm ² ;

- overall dimension of the short face V = A / (12.0 t ) = 16.8 / (12⋅0.2) = 7.0 cm;

- overall height dimension H = 3.0 V = 3.0–7.0 = 21.0 cm;

- overall width dimension U = 3.0 V = 3.0–7.0 = 21.0 cm;

- the ordinate of the center of gravity of the section relative to the upper face y _c = V = 7.0 cm;

- moments of inertia I _X = I _Y = 9.0 tV ³ = 9.0⋅0.2⋅7.0 ³ = 617.4 cm ⁴ ;

- moments of resistance W _{X, max} = 9.0 tV ² = 9.0⋅0.2⋅7.0 ² = 88.2 cm ³ ;

W _{X, mim} = 4.50 tV ² = 4.5⋅0.2⋅7.0 ² = 44.1 cm ³ ; W _Y = 6.0 tV ² = 6.0⋅0.2⋅7.0 ² = 58.8 cm ³ ;

- radii of inertia i _X = i _Y = 0.86603 V = 0.86603⋅7.0 = 6.062 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 / (ϕ A ) + M / W _{X, max} = 20600 / (0.857⋅16.8) + 83 500 / 88.2 = 1430.8 + 946.7 =

= 2377.4 kgf / cm ² = 0.991 R _y ,

where the design flexibility of the panel is λ = 300 / 6.062 = 49.49; panel conditional flexibility λ * = 49.49 (2400/2100000) ^1/2 = 1.673 <2.5; the coefficient of longitudinal bending ϕ = 1-0,066 (λ *) ^3/2 = 1-0,066 (1,673) ^3/2 = 0,857.

As you can see, the calculated voltage in the new technical solution was 100 (0.991-0.945) / (0.991 ... 0.945) = 4.6 ... 4.9% higher than in the prototype. This can be explained by the fact that the overall height of the prototype is 100 (242-211) / (242 ... 211) = 12.9 ... 14.7% more than the new solution.

In the above calculation, we used the formulas of an equidistant bent closed profile obtained as a result of computational calculations of the first approximation. Therefore, it is interesting to test them by calculation in a second approximation, presenting the calculated cross-sectional diagram of the same profile in the form of a complex figure made up of rectangular elements:

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

y _c = 0.2 (21⋅0.1 + 2⋅7⋅3.6 + 2⋅10.5⋅7.1 + 2⋅14⋅14.1) / 16.8 = 7.1 cm

with an error of 100 (7.1-7.0) / (7.1 ... 7.0) = 1.41 ... 1.43%;

- moments of inertia

I _X = 21⋅0.2 ³ ⋅1 / 12 + 21⋅0.2⋅7 ² + 2⋅7 ³ ⋅0.2⋅1 / 12 + 2⋅7⋅0.2⋅3.5 ² +2 ⋅10.5⋅0.2 ³ ⋅1 / 12 +

+ 2⋅10.5⋅0.2⋅0 ² + 2⋅0.2⋅14 ³ ⋅1 / 12 + 2⋅0.2⋅14⋅7 ² =

= 617.428 cm ⁴

with an error of 100 (617.428-617.4) / (617.428 ... 617.4) = 0.00453%;

I _Y = 21 ³ ⋅0.2 ³ ⋅1 / 12 + 2⋅7⋅0.2 ³ ⋅1 / 12 + 2⋅7⋅0.2⋅10.5 ² + 2⋅10.5 ³ ⋅0, 2⋅1 / 12 +

+ 2⋅10.5⋅0.2⋅5.25 ² + 2⋅0.2 ³ ⋅14⋅1 / 12 + 2⋅0.2⋅14⋅0.1 ² =

= 617.484 cm ⁴

with an error of 100 (617.484-617.4) / (617.484 ... 617.4) = 0.0136%;

- moments of resistance

W _{X, max} = 617.428 / 7.1 = 86.962 cm ³

with an error of 100 (88.2-86.962) / (88.2 ... 86.962) = 1.401 ... 1.424%;

W _{X, min} = 617.428 / (21-7.1) = 44.419 cm ³

with an error of 100 (44.419-44.1) / (44.419 ... 44.1) = 0.718 ... 0.723%;

W _Y = 617.484 / 10.5 = 58.808 cm ³

with an error of 100 (58.808-58.8) / (58.808 ... 58.8) = 0.0136%;

- radii of inertia

i _X = (617.428 / 16.8) ^1/2 = 6.0623 cm

with an error of 100 (6.0623-6.062) / (6.0623 ... 6.062) = 0.00494%;

i _Y = (617.484 / 16.8) ^1/2 = 6.0626 cm

with an error of 100 (6.0626-6.062) / (6.0626 ... 6.062) = 0.00989%.

The obtained results of the test calculation confirm the quite acceptable accuracy of the formulas used with the accepted assumptions of the first approximation. Therefore, the performed calculation calculations can not be adjusted.

To continue comparing the new technical solution with the prototype, the cross-section of the bent-closed profile must be developed in the plane of the truss, extending its rib part by 1 size of the short face of the tubular part:

- net cross-sectional area A = 14.0 tV = 16.8 cm ² ;

- the overall size of the short face V = A / (14.0 t ) = 16.8 / (14⋅0.2) = 6.0 cm;

- overall height dimension H = 4.0 V = 4.0–7.0 = 24.0 cm;

- overall width dimension U = 3.0 V = 3.0–6.0 = 18.0 cm;

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

y _c = 1.357 = 1.375⋅ 6.0 = 8.143 cm;

- moments of inertia I _X = 19.88 tV ³ = 19.88⋅0.2⋅6.0 ³ = 858.82 cm ⁴ ;

I _Y = 9.0 tV ³ = 9.0-0.2-6.0 ³ = 388.80 cm ⁴ ;

- moments of resistance W _{X, max} = 14.65 tV ² = 14.65⋅0.2⋅6.0 ² = 105.48 cm ³ ;

W _{X, min} = 7.522 tV ² = 7.522⋅0.2⋅6.0 ² = 54.16 cm ³ ; W _Y = 6.0 tV ² = 6.0⋅0.2⋅6.0 ² = 43.20 cm ³ ;

- radii of inertia i _X = 1,192 V = 1,192-6,0 = 7,152 cm;

i _Y = 0.8018 V = 0.8018-6.0 = 4.811 cm.

Then, the calculated stress from the combined action of internal forces in the section of the panel from the profile with a height developed by 1 size of a short face, according to a new technical solution, will be:

σ = N / (ϕ A ) + M / W _{X, max} = 20600 / (0.886⋅16.8) + 83 500 / 105.48 = 1384.0 + 791.6 =

= 2175.6 kgf / cm ² = 0.907 R _y ,

where the design flexibility of the panel is λ = 300 / 7.152 = 41.95; panel conditional flexibility λ * = 41.95 (2400/2100000) ^1/2 = l, 418 <2.5; the coefficient of longitudinal bending ϕ = 1-0.066 (λ *) ^3/2 = 1-0.066 (1.418) ^3/2 = 0.886.

As you can see, the calculated voltage in the new technical solution was 100 (0.945-0.907) / (0.945 ... 0.907) = 4.02 ... 4.19% lower than in the prototype. In this case, the overall height dimension of the prototype is 100 (242-241) / (242 ... 241) = 0.413 ... 0.415% more than the new solution.

Thus, a comparison of bent closed profiles with the prototype confirms their promise for use in load-bearing structures. Therefore, it is advisable to continue comparing the new technical solution with its prototype, adding to the bent closed profiles gear fastenings instead of welded, bolted or riveted joints. To do this, in the considered equidistant profile, it is necessary to select the sizes of the tooth fastening elements (teeth), which should be at least 1/10 of the shelf (horizontal side) or wall (vertical side) of the bent profile [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 0.1⋅2 V = 0.1⋅2⋅70 = 14 mm, where 2 V = 2⋅70 = 140 mm is the size of the rib part of the bent closed profile. Assuming a certain margin in the near future, the size of the gear fastening elements can be rounded up to 20 mm.

Taking into account the gear fastening, the bent-closed profile, equally stable from the plane and in the plane, will have the following characteristics of the cross section:

- net cross-sectional area A ₁ = 12.0 tV = 16.8-2⋅2.0⋅0.2 = 16.0 cm ² ;

- the overall size of the short face V = A ₁ / (12.0 t ) = 16.0 / (12⋅0.2) = 6.667 cm;

- overall height dimension H = 3.0 V = 3.0–6.667 = 20.001 cm;

- overall width dimension U = 3.0 V = 3.0–6.767 = 20.001 cm;

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

y _c = V = 6.667 cm;

- moments of inertia I _X = I _Y = 9.0 tV ³ = 9.0⋅0.2⋅6.667 ³ = 533.41 cm ⁴ ;

- moments of resistance W _{X, max} = 9.0 tV ² = 9.0⋅0.2⋅6.667 ² = 80.01 cm ³ ;

W _{X, min} = 4.50 tV ² = 4.5⋅0.2⋅6.667 ² = 40.004 cm ³ ; W _Y = 6.0 tV ² = 6.0⋅0.2⋅6.667 ² = 53.34 cm ³ ;

- radii of inertia i _X = i _Y = 0.86603 V = 0.86603-6.667 = 5.774 cm.

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

σ = N / (ϕ A ₁ ) + M / W _{X, max} = 20600 / (0.846⋅16.0) + 83 500 / 80.01 = 1521.9 + 1043.6 =

= 2565.5 kgf / cm ² = 1.069 R _y ,

where the design flexibility of the panel is λ = 300 / 5.774 = 51.96; panel conditional flexibility λ * = 51.96 (2400/2100000) ^1/2 = 1.757 <2.5; the coefficient of longitudinal bending ϕ = 1-0,066 (1,757) ^3/2 = 0,846.

As you can see, the surge in the new technical solution amounted to 6.9%. In this case, the overall height dimension of the prototype is 100 (242-202.01) / (242 ... 202.01) = 16.5 ... 19.8% more than the new solution.

To continue comparing the new technical solution with the prototype, the cross-section of the bent-closed profile with gear fastening must be developed in the plane of the truss, extending its rib part by 1 size of the short face of the tubular part:

- net cross-sectional area A ₁ = 14.0 tV = 16.0 cm ² ;

- the overall size of the short face V = A ₁ / (14.0 t ) = 16.0 / (14⋅0.2) = 5.714 cm;

- overall height dimension H = 4.0 V = 4.0-5.714 = 22.856 cm;

- overall width dimension U = 3.0 V = 3.0–5.714 = 17.142 cm;

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

y _c = 1.357 = 1.375-5.714 = 7.857 cm;

- moments of inertia I _X = 19.88 tV ³ = 19.88⋅0.2⋅5.714 ³ = 741.77 cm ⁴ ;

I _Y = 9.0 tV ³ = 9.0⋅0.2⋅5.714 ³ = 335.81 cm ⁴ ;

- moments of resistance W _{X, max} = 14.65 tV ² = 14.65⋅0.2⋅5.714 ² = 95.66 cm ³ ;

W _{X, min} = 7.522 tV ² = 7.522⋅0.2⋅5.714 ² = 49.12 cm ³ ; W _Y = 6.0 tV ² = 6.0⋅0.2⋅5.714 ² = 36.18 cm ³ ;

- radii of inertia i _X = 1,192 V = 1,192⋅5,714 = 6.811 cm;

i _Y = 0.8018 V = 0.8018⋅5.714 = 4.5815 cm.

Then, the calculated stress from the combined action of internal forces in the section of the panel from the profile with gear mount and height developed by 1 size of a short face, according to a new technical solution, will be:

σ = N / (ϕ A ₁ ) + M / W _{X, max} = 20600 / (0.8801⋅16.0) + 83 500 / 95.66 = 1462.9 + 872.9 =

= 2335.8 kgf / cm ² = 0.973 R _y ,

where the design flexibility of the panel is λ = 300 / 6.811 = 44.05; panel conditional flexibility λ * = 44.05 (2400/2100000) ^1/2 = 1.489 <2.5; coefficient of longitudinal bending ϕ = 1-0.066 (1.489) ^3/2 = 0.8801.

As you can see, the calculated voltage in the new technical solution was 100 (0.973-0.945) / (0.973 ... 0.945) = 2.88 ... 2.96% higher than in the prototype. The overall height dimension of the prototype is 100 (242-230.56) / (242 ... 230.56) = 4.73 ... 4.96% more than the new solution.

The obtained comparison results confirm the rationality of bent closed profiles with toothed mounts and without toothed mounts. Of practical interest here is the cross-section of a bent-closed profile with a gear mount developed in the plane of the truss due to the lengthening of its rib part by 2 sizes of the short face of the tubular part:

- net cross-sectional area A ₁ = 16.0 tV = 16.0 cm ² ;

- the overall size of the short face V = A ₁ / (16.0 t ) = 16.0 / (16⋅0.2) = 5.0 cm;

- overall height dimension H = 5.0 V = 5.0 ⋅ 5.0 = 25.0 cm;

- overall width dimension U = 3.0 V = 3.0 ⋅ 5.0 = 15.0 cm;

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

y _c = 1.750 = 1.750⋅5.0 = 8.75 cm;

- moments of inertia I _X = 37.33 tV ³ = 37.33⋅0.2⋅5.0 ³ = 922.25 cm ⁴ ;

I _Y = 9.0 tV ³ = 9.0⋅0.2⋅5.0 ³ = 225.0 cm ⁴ ;

- moments of resistance W _{X, max} = 21.33 tV ² = 21.33⋅0.2⋅5.0 ² = 106.65 cm ³ ;

W _{X, min} = 11.49 tV ² = 11.49⋅0.2⋅5.0 ² = 57.45 cm ³ ; W _Y = 6.0 tV ² = 6.0⋅0.2⋅5.0 ² = 30.0 cm ³ ;

- radii of inertia i _Х = 1,528 V = 1,528⋅5,0 = 7.64 cm;

i _Y = 0.750 V = 0.750⋅5.0 = 3.75 cm.

Then, the calculated voltage from the combined action of internal forces in the section of the panel from the profile with a gear mount and height developed by 2 sizes of a short face, according to a new technical solution, will be:

σ = N / (ϕ A ₁ ) + M / W _{X, max} = 20600 / (0.899⋅16.0) + 83 500 / 106.65 = 1432.15 + 782.9 =

= 2215.1 kgf / cm ² = 0.923 R _y ,

where the design flexibility of the panel is λ = 300 / 7.64 = 39.27; panel conditional flexibility λ * = 39.27 (2400/2100000) ^1/2 = 1.328 <2.5; coefficient of longitudinal bending ϕ = 1-0.066 (1.328) ^3/2 = 0.899.

As you can see, the calculated voltage in the new technical solution was 100 (0.945-0.923) / (0.945 ... 0.923) = 2.33 ... 2.38% lower than in the prototype. Moreover, the overall height dimension of the prototype is 100 (252-242) / (252 ... 242) = 3.97 ... 4.13% less than the new solution.

Thus, the obtained comparison results confirm the prospectivity, rationality and effectiveness of the use of bent closed profiles in the supporting structures, both without gear mounts and with gear mounts. In the latter case, as shown by numerical comparisons of the new technical solution and its prototype, the weakening of the calculated net section of the proposed bent closed profiles due to the serrated longitudinal edges with a thickness of t = 2.0 mm of their strips (sheet blanks or formed strips) was A ₁ / A = 16.0 / 16.8 = 0.9524. This attenuation is noticeably less than the corresponding attenuation from a metric thread: D ₁ / D = (1.567 ... 1.729) / 2.0 = 0.7835 ... 0.8645, where D is the outer diameter of the thread, D = 2.0 mm, D ₁ - the inner diameter of the thread, D ₁ = 1.567 mm with a pitch of 0.4 mm, D ₁ = 1.729 mm with a pitch of 0.25 mm [GOST 24705-2004. Thread metric. The main sizes. - M .: Standartinform, 2005. - S. 6]. If in the metric thread the “excess” metal in the form of shavings is disposed of as scrap, then in the new technical solution, minimizing metal waste and reducing additional costs, with one zigzag cut you can get jagged longitudinal edges of two sheet blanks for bent closed profiles at once. Moreover, 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 from the basic one, according to the parameters specified by the project, select the derived sections in one or two steps. It seems that in the future, similarly and in tune with bent-welded profiles (GSP), the proposed bent-closed profiles can be abbreviated as GZP.

Claims (2)

1. The bent closed profile of a rectangular section with a joint in the middle of one of the long faces, where each part of the joined face has a continuation in the form of an I-shaped rib, characterized in that the size of the short faces is half the size of the I-shaped ribs and three times smaller the size of the long edges. 2. The bent closed profile according to claim 1, characterized in that its sheet blank is 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 each other after closing the bent profile along I-shaped ribs .

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