# Application of monosymmetrical I-beams in light metal frames with variable stiffness.

UDC 624.014Introduction. One of the priorities of the capital construction industry is increasing the effectiveness of structures by improving the structural forms and methods of calculation. I-beam elements with a flexible wall have broad prospects for application: beams and cover, frame, arch system--all these structures at low values cut efforts can be made of the thin-walled profile. The efficiency of these elements caused by higher values of the inertia moments in relation to cross-sectional area due to the concentration of material in the shelves. In the overwhelming action of the bending moments it provides a significant economic benefit and achieves frame weight reducing by 30 % in compare to traditional welded sections.

Operating the light frames with thin I-beam sections has certain characteristics. First, rack and crossbars of single-span frames have quite stable distribution of internal forces (of the bending moments especially) (Fig. 1), so that it can be produced of profiles with variable stiffness. Of course, taking into account the presence of structural constraints, so-called "beam of equal resistance" is impossible in the frame elements, but to minimize the material consumption is possible by changing the cross-section. Second, there are longitudinal efforts in the columns and frame bolts except of the bending moments and leading to uneven stresses in the compressed and stretched shelves section. Because of this, the logical step is to perform asymmetric profiles, advanced compressed shelf beams (Fig. 2).

The study of variable stiffness constructions, including the frame skeletons, dedicated work by V. Katyushin [1], G. Nasser [2], O. Glitin [3], S. Bilyk [4] and etc. It should be noted that all these works study the stress-strain state, durability and strength frame structures of variable section, but, unfortunately, the results of all the studies have not been definitively formulated the calculation method for thin-walled elements with action the compression of the bend.

The aim of research is to confirm the usefulness of I-beams with flexible wall bearing as light metal skeletons of buildings universal assignment.

Materials and Methods. In order to reduce the metal consumption a frame is conventionally divided into several sections according to bending moment diagrams so that in the more compressed zone section the belt of great area was located, and in the stretched or less intense zone the lesser belt was installed (Fig. 2). The area of the shelf at length of each section is not changed.

Thus, obtained sections have smaller area compared to symmetric profiles. Additional reducing of the bending moments is provided by the displacement of axes elements of variable section. In addition, compressed shelves can lead to loss of stability, so use shelf with larger area will help improve the stiffness of frame.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

Calculations and selection of sections of the frame elements via the example frame warehouse building with span of 36 m have shown that by using monosymmetrical sections can be achieved by reducing the bearing elements weight by 10 % in compare to the symmetrical profiles of variable stiffness. Calculated load for cover of the buildings was 2.85 kN/[m.sup.2] (including snow load--1.55 kN/[m.sup.2] and own weight constructions for covering fences--1.3 kN/[m.sup.2]).

As a result of the selection section were offered such dimensions of structures:

1. Symmetric profiles:

--Comice node--the wall is 1600x6 mm, shelf is 270x14 mm;

--Flange node--the wall is 1200x6 mm, shelf is 140x14 mm.

2. Monosymmetrical profiles:

--Cornice node--the wall is 1600x6 mm, shelf is 270x14 mm (in compressed mode) and 220x12 mm (in stretched state);

--Flange node--the wall is 1200x6 mm, shelf is 140x14 mm (in compressed mode) and 100x12 mm (in stretched state).

The weight bearing structures per square meter of building area is about 19.87 kg/[m.sup.2] for symmetric profiles and 17.98 kg/[m.sup.2] for monosymmetrical profiles.

Results. Evaluate the effectiveness of the proposed constructive solution is possible by comparing the weight of the frame with the analog frame presented by V. Trofimov [5] (see Table).

Trofimov noted that using more advanced thin profiles will reduce the weight of constructions for another 5 ... 12 % compared to the structural solution proposed in [5], which we see in the table--weight frame construction symmetrical profile lighter on 15.3 %; and monosymmetrical profile on 27 %.

We showed [6 ... 9] that considering the critical work of flexible thin-walled plate of I-beams can increase the carrying capacity of structures. For these profiles is recommended to carry out checks the bearing capacity of elements of frames sections with relative eccentricity [m.sub.ef] [greater than or equal to] 15 by:

[absolute value of N/[N.sub.u]] + ([M.sub.x]/[[M.sub.u[phi]]).sup.2] + [(Q/[Q.sub.u]).sup.4] [less than or equal to] [[gamma].sub.c],

where [M.sub.x], N, Q--bending moment, longitudinal and cross section efforts of the calculation section frame;

[M.sub.u[phi]], [N.sub.u], [Q.sub.u]--limit value of bending moment, longitudinal and transverse effort under simultaneous actions in the calculation section;

[[gamma].sub.c]--coefficient of working conditions.

The critical shear stress [[tau].sub.cr] and limit value of transverse forces [Q.sub.u] are calculated using the formulas from section 22 of State Standard DBN V.2.6-198:2014 for I-beams with flexible wall.

The coefficient of working conditions [[gamma].sub.c], taking into account the complex mode of deformation elements of variable stiffness steel frame with a flexible wall, must be limited to 0,95.

Experimental studies that have been conducted by Sklyarov and Bilyk [9] found that in the supercritical phase of a flexible wall shelves work in the section there are additional strain due the actions of local bending moments. Bending moments in compressed shelves are result of deformation of walls and "settling" of shelf, which works as a beam on elastic foundation bed with variable coefficients subgrade resistance (depending on the nature of the deformation of the wall). Thus, the maximum normal stresses in the compressed zone of the frame with a flexible wall may be defined as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2)

where N, M--squeezing force and bending moment of the action of external loads;

[A.sub.red], [W.sub.red]--area and resistance moment of weakened cross section with flexible wall;

[M.sub.fc]--additional bending moment that occurs in a belt when buckling wall;

[I.sub.fc]--inertia moment of section, formed compressed shelf and part of the wall with height [h.sub.wred];

[[gamma].sub.0]--distance from the center of gravity of section of compressed zone to the brink of the belt;

[R.sub.y]--steel estimated resistance;

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]--coefficient for accounting the redistribution of loading bending moment and depends on the flexibility of the wall;

[bar.[[lambda].sub.w] = [h.sub.w]/[t.sub.w] [square root of [R.sub.y]/E--conditional flexibility of I-section wall, where [h.sub.w]--wall height, [t.sub.w]--wall thickness;

E--elastic modulus of steel;

[bar.[[lambda].sub.wu] = 12--experimentally established limit of the flexibility of the wall, where shelf does not lose stability in the plane of the wall.

To check the calculation regulations of proposed method for calculation of these structures there was conducted mathematical modeling of the frame by the software system <<LIRA-SAPR>> (Fig. 3).

[FIGURE 3 OMITTED]

Conclusions. Analysis of stress-strain state structures showed some features of the frames mono-symmetrical I-beams in compare to symmetric profiles: first, due to asymmetrical type of profile the shift of the gravity section center appears, which leads to a redistribution of internal forces in the frame, that requires to adjust rod design scheme frames after sections selecting; secondly, because of the small cross-sectional area it is difficult to ensure the stability of the plane form of bending beams, which leads to the necessity to disconnect the areas curtain beams by the constraints with smaller steps.

In a market economy and the transition from design of typical mass to individual work with a particular customer, using highly efficient steel structures is a prerequisite for preserving competitiveness as designers of metal structures and steel industry as well. The conducted research of lightweight frames designs based on monosymmetrical profiles indicates the significant prospects for their use in this area. Operations of these structures are still understudied and needs further theoretical analysis as well as series of additional experimental tests.

DOI 10.15276/opu.1.48.2016.06

[1.] [TEXT NOT REPRODUCIBLE EN ASCII].

[2.] The legacy and future of an American icon: The precast, prestressed concrete double tee / G.D. Nasser, M. Tadros, A. Sevenker, D. Nasser // PCI Journal.--2015.--Vol. 60, Issue 4.--PP. 49-68.

[3.] Permyakov, V.O. Optimum design of transverse frames containing elements of variable stiffness in frameworks of buildings / V.O. Permyakov, O.B. Glitin // B kh.: Progress in steel, composite and aluminium structures / ed. by M.A. Gizejowski, A. Kozlowski, L. Sleczka, J. Ziolko.--London: Taylor & Francis Group, 2006.--PP. 336-337.

[4.] [TEXT NOT REPRODUCIBLE EN ASCII].

[5.] [TEXT NOT REPRODUCIBLE EN ASCII].

[6.] [TEXT NOT REPRODUCIBLE EN ASCII].

[7.] [TEXT NOT REPRODUCIBLE EN ASCII].

[8.] Sklyarov, I.A. Designing of frame structures of welded double-T with variable cross section and flexible wall / I.A. Sklyarov // Proceedings of XIX International Scientific Seminar <<Perspective Directions of Innovative Development of Construction Industry and Engineering Trainings (PDDC'2014), 23-25 October 2014, Brest.--Brest: BSTU, 2014.--Vol. 1.--PP. 338-345.

[9.] [TEXT NOT REPRODUCIBLE EN ASCII].

References

[1.] Katyushin, V.V. (2005). Buildings with Steel Frames of Variable Cross Section: Calculation, Design, Construction. Moscow: Stroiizdat.

[2.] Nasser, G.D., Tadros, M., Sevenker, A., & Nasser, D. (2015). The legacy and future of an American icon: The precast, prestressed concrete double tee. PCI Journal, 60(4), 49-68.

[3.] Permyakov, V.O., & Glitin, O.B. (2006). Optimum design of transverse frames containing elements of variable stiffness in frameworks of buildings. In M.A. Gizejowski, A. Kozlowski, L. Sleczka, J. Ziolko (Eds.), Progress in Steel, Composite and Aluminium Structures (pp. 336-337). London: Taylor & Francis Group.

[4.] Bilyk, S.I. (2008). Stability calculation for steel frames made of I-beams with variable wall height. Resource-Intensive Materials, Constructions, Buildings and Structures, 16(2), 73-78.

[5.] Trofimov, V.I., & Kaminsky, A.M. (2002). Light Metal Structures of Buildings and Constructions. Moscow: ASV.

[6.] Sklyarov, I.O. (2011). On the calculation of the thin-walled I-beam in historical perspective. Resource-Intensive Materials, Constructions, Buildings and Structures, 21, 337-345.

[7.] Bilyk, S.I., & Sklyarov, I.O. (2011). Selection of design section for frames of variable stiffness with solid flexible wall. Stroitel'stvo, Materialovedenie, Mashinostroenie, 60, 16-20.

[8.] Sklyarov, I.A. (2014). Designing of frame structures of welded double-T with variable cross section and flexible wall. In Proceedings of XIX International Scientific Seminar "Perspective Directions of Innovative Development of Construction Industry and Engineering Training" (PDDC'2014) (Vol. 1, pp. 338-345). Brest: Brest State Technical University.

[9.] Sklyarov, I.O., & Bilyk, S.I. (2012). Experimental study of thin-walled frames with double-T crosssection. Resource-Intensive Materials, Constructions, Buildings and Structures, 24, 248-254.

Received February 10, 2016

Accepted March 15, 2016

I.O. Sklyarov, PhD, Assoc.Prof.

Kyiv National University of Construction and Architecture, 31 Povitroflotsky Ave., 03680 Kyiv, Ukraine; e-mail: mdk.skl@gmail.com

Table Comparing the projected weight with analogue design Calculated Weight of load on the constructions Group of floor, kN/ of frames, constructions Span, m Step, m [m.sup.2] kg/[m.sup.2] Frame analog [5] 24 6 2.4 22.92 Designed frame of 36 6 2.85 19.87 symmetrical profile Designed frame of 36 6 2.85 17.98 mono-symmetrical profile

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Author: | Sklyarov, I.O. |
---|---|

Publication: | Odes'kyi Politechnichnyi Universytet. Pratsi |

Article Type: | Report |

Date: | Mar 1, 2016 |

Words: | 1932 |

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