ArticlePDF Available

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

Article

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

Abstract

The article is devoted to effectiveness of using of monosymmetrical I-beams with flexible wall frame structures of variable section, features of their calculation and design. Aim: The aim of research is to confirm the feasibility of I-beams with flexible wall bearing as light metal skeletons for buildings of the 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. The resulting sections have smaller area in compare to symmetric profiles. Additional reduce bending moments provided as a result of displacement of elements axes with variable cross section. Results: The calculations and selection of sections of the frame have shown that it can be achieved the reducing of bearing elements weight by 10% compared to the symmetrical profiles of variable stiffness due to using monosymmetrical sections. The effectiveness of the proposed constructive solution is confirmed by compare of the projected weight frame construction with existing analogue. The symmetrical frame profile is 15.3% lighter; the monosymmetrical frame profile is 27% lighter. Conclusions: Analysis of stress-strain state structures shown: first, through asymmetrical profile there is a shifting of the center of gravity section, which leads to a redistribution of internal forces in the frame; secondly, because of the small cross-sectional area of the stretched zones more difficult to ensure the stability of the plane form of bending beams, which leads to the necessity to disconnect areas curtain beams by constraints of smaller steps.
Праці Одеського політехнічного університету, 2016. Вип. 1(48) ISSN 2076-2429 (print)
ISSN 2223-3814 (online)
МАШИНОБУДУВАННЯ. ТЕХНОЛОГІЯ МЕТАЛІВ. МАТЕРІАЛОЗНАВСТВО
30
DOI 10.15276/opu.1.48.2016.06
©2016 The Authors. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
UDC 624.014
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
APPLICATION OF MONOSYMMETRICAL I-BEAMS
IN LIGHT METAL FRAMES WITH VARIABLE STIFFNESS
І.О. Скляров. Застосування моносиметричних двотаврових перерізів у легких сталевих рамах змінної жорсткості. Стат-
тя присвячена дослідженню ефективності використання моносиметричних двотаврів з гнучкою стінкою в рамних конструкціях
змінного перерізу, особливостям їх розрахунку і конструювання. Мета: Метою дослідження є підтвердження доцільності застосу-
вання двотаврів з гнучкою стінкою як легких несучих металевих каркасів будівель універсального призначення. Матеріали і
методи: Для зменшення витрат металу рама умовно розбивається на кілька окремих ділянок відповідно до епюри згинальних
моментів так, щоб у стиснутій або більш напруженій зоні перерізу було розташовано пояс з більшою площею, а у розтягнутій або
менш напруженій полиці пояс з меншою площею. Отримані таким чином перерізи мають меншу площу порівняно з симетрич-
ними профілями. Додаткове зменшення згинальних моментів забезпечується також внаслідок зміщення осей елементів змінного
перерізу. Результати: Проведені розрахунки і підбір перерізів елементів рами показали, що шляхом використання моносиметрич-
них перерізів можна досягти зменшення маси несучих елементів на 10 % порівняно з симетричними профілями змінної жорсткості.
Ефективність запропонованого конструктивного рішення підтверджується порівнянням маси спроектованої рамної конструкції з
існуючим аналогом рама симетричного профілю легша на 15,3 %, моносиметричного профілю на 27 %. Висновки: Аналіз
напружено-деформованого стану конструкцій показав: по-перше, через несиметричність профілю відбувається зміщення центра
ваги перерізу, що призводить до перерозподілу внутрішніх зусиль у рамі; по-друге, через малу площу перерізу розтягнутих поли-
чок складніше забезпечити стійкість плоскої форми згину ригелів, що призводить до необхідності розкріпляти карнизні ділянки
ригелів вязями з меншим кроком.
Ключові слова: моносиметричні двотаври, тонкостінні конструкції, рами змінного перерізу, легкі сталеві конструкції.
I.O. Sklyarov. Application of monosymmetrical I-beams in light metal frames with variable stiffness. The article is devoted to
effectiveness of using of monosymmetrical I-beams with flexible wall frame structures of variable section, features of their calculation and
design. Aim: The aim of research is to confirm the feasibility of I-beams with flexible wall bearing as light metal skeletons for buildings of
the 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. The resulting sections have smaller area in compare to symmetric profiles. Addi-
tional reduce bending moments provided as a result of displacement of elements axes with variable cross section. Results: The calculations
and selection of sections of the frame have shown that it can be achieved the reducing of bearing elements weight by 10 % compared to the
symmetrical profiles of variable stiffness due to using monosymmetrical sections. The effectiveness of the proposed constructive solution is
confirmed by compare of the projected weight frame construction with existing analogue. The symmetrical frame profile is 15.3 % lighter;
the monosymmetrical frame profile is 27 % lighter. Conclusions: Analysis of stress-strain state structures shown: first, through asymmetrical
profile there is a shifting of the center of gravity section, which leads to a redistribution of internal forces in the frame; secondly, because of
the small cross-sectional area of the stretched zones more difficult to ensure the stability of the plane form of bending beams, which leads to
the necessity to disconnect areas curtain beams by constraints of smaller steps.
Keywords: monosymmetrical I-beams, thin-walled structures, variable cross section frame, lightweight steel structures.
Introduction. One of the priorities of the capital construction industry is increasing the effecti-
veness 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 mo-
ments 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
ISSN 2076-2429 (print) Odes’kyi Politechnichnyi Universytet. Pratsi, Issue 1(48), 2016
ISSN 2223-3814 (online)
MACHINE BUILDING. PROCESS METALLURGY. MATERIALS SCIENCE
31
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 addi-
tion, compressed shelves can lead to loss of stability, so use shelf with larger area will help improve
the stiffness of frame.
a b
Fig. 1. The principle of design of variable stiffness elements:
a
bending moment diagrams, b
rational design of variable stiffness frame
3
3
2
21 1
3
3 2
2
1
1
Fig. 2. Steel two-hinges frame with variable stiffness with monosymmetrical I-beam and flexible wall
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/m2 (including snow load
1.55 kN/m2 and own weight constructions for covering fences 1.3 kN/m2).
As a result of the selection section were offered such dimensions of structures:
1. Symmetric profiles:
Праці Одеського політехнічного університету, 2016. Вип. 1(48) ISSN 2076-2429 (print)
ISSN 2223-3814 (online)
МАШИНОБУДУВАННЯ. ТЕХНОЛОГІЯ МЕТАЛІВ. МАТЕРІАЛОЗНАВСТВО
32
Cornice node — the wall is 1600×6 mm, shelf is 270×14 mm;
Flange node — the wall is 1200×6 mm, shelf is 140×14 mm.
2. Monosymmetrical profiles:
Cornice node — the wall is 1600×6 mm, shelf is 270×14 mm (in compressed mode) and
220×12 mm (in stretched state);
Flange node — the wall is 1200×6 mm, shelf is 140×14 mm (in compressed mode) and
100×12 mm (in stretched state).
The weight bearing structures per square meter of building area is about 19.87 kg/m2 for
symmetric profiles and 17.98 kg/m2 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).
Table
Comparing the projected weight with analogue design
Group of constructions Span, m Step, m Calculated load on the
floor, kN/m2
Weight of construc-
tions of frames, kg/m2
Frame analog [5] 24 6 2.4 22.92
Designed frame of sym-
metrical profile 36 6 2.85 19.87
Designed frame of mono-
symmetrical profile 36 6 2.85 17.98
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 mef 15 by:
24
x
c
uu u
NM Q
NM Q
ϕ
⎛⎞
⎛⎞
++γ
⎜⎟
⎜⎟
⎜⎟
⎝⎠
⎝⎠ , (1)
where Mx, N, Q — bending moment, longitudinal and cross section efforts of the calculation
section frame;
M
uφ, Nu, Qu — limit value of bending moment, longitudinal and transverse effort under simulta-
neous actions in the calculation section;
γс — coefficient of working conditions.
The critical shear stress τcr and limit value of transverse forces Qu are calculated using the formu-
las from section 22 of State Standard DBN V.2.6-198:2014 for I-beams with flexible wall.
The coefficient of working conditions γс, 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 super-
critical 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:
0
fсc
yc
red red fc
Mk
NM уR
AW І
Σ
σ= + + ≤ γ, (2)
where N, M — squeezing force and bending moment of the action of external loads;
ISSN 2076-2429 (print) Odes’kyi Politechnichnyi Universytet. Pratsi, Issue 1(48), 2016
ISSN 2223-3814 (online)
MACHINE BUILDING. PROCESS METALLURGY. MATERIALS SCIENCE
33
A
red, Wred — area and resistance moment of weakened cross section with flexible wall;
M
fс — additional bending moment that occurs in a belt when buckling wall;
I
fc — inertia moment of section, formed compressed shelf and part of the wall with height hwred;
y
0 — distance from the center of gravity of section of compressed zone to the brink of the belt;
R
y — steel estimated resistance;
1, 9;
,9
w
cw
w
wu
k
λ>
=λλ≤
λ
coefficient for accounting the redistribution of loading bending moment
and depends on the flexibility of the wall;
y
w
w
w
R
h
tE
λ= — conditional flexibility of I-section wall, where hw — wall height, tw — wall
thickness;
Е — elastic modulus of steel;
12
wu
λ= — 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).
Fig. 3. Finite element model with flew 36 m with welded monosymmetrical I-beam with flexible wall
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 competitive-
ness 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.
Праці Одеського політехнічного університету, 2016. Вип. 1(48) ISSN 2076-2429 (print)
ISSN 2223-3814 (online)
МАШИНОБУДУВАННЯ. ТЕХНОЛОГІЯ МЕТАЛІВ. МАТЕРІАЛОЗНАВСТВО
34
Література
1. Катюшин, В.В. Здания с каркасами из стальных рам переменного сечения: расчет, проектирова-
ние, строительство / В.В. Катюшин. — М.: Стройиздат, 2005. — 655 с.
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 // В кн.: Progress in steel, composite and al-
uminium structures / ed. by M.A. Giżejowski, A. Kozłowski, L. Ślęczka, J. Ziółko. — London: Taylor
& Francis Group, 2006. — PP. 336 — 337.
4. Білик, С.І. Методика розрахунку на стійкість сталевих рам із двотаврів зі змінною висотою
стінки / С.І. Білик // Ресурсоекономні матеріали, конструкції, будівлі та споруди. — 2008. —
Вип. 16, Ч. 2. — С. 73 — 78.
5. Трофимов, В.И. Легкие металлические конструкции зданий и сооружений. Разработка конструк-
ций, исследование, расчет, изготовление, монтаж / В.И. Трофимов, А.М. Каминский. — М.:
АСВ, 2002. — 575 с.
6. Скляров, І.О. Питання розрахунку тонкостінних двотаврів у історичному аспекті / І.О. Скляров //
Ресурсоекономні матеріали, конструкції, будівлі та споруди. — 2011. — Вип. 21. — С. 337 — 345.
7. Білик, С.І. Вибір розрахункового перерізу в рамах змінної жорсткості з суцільною гнучкою
стінкою / С.І. Білик, І.О. Скляров // Строительство, материаловедение, машиностроение. — 2011.
Вып. 60. — С. 16 — 20.
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 Training»
(PDDC’2014), 23–25 October 2014, Brest. — Brest: BSTU, 2014. — Vol. 1. — PP. 338 — 345.
9. Скляров, І.О. Експериментальні дослідження тонкостінних рамних двотаврів / І.О. Скляров,
С.І. Білик // Ресурсоекономні матеріали, конструкції, будівлі та споруди». — 2012. — Вип. 24. —
С. 248 — 254.
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. Giżejowski, A. Kozłowski, L. Ślęczka, J. Ziółko
(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. Re-
source-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 cross-
section. Resource-Intensive Materials, Constructions, Buildings and Structures, 24, 248 — 254.
Received February 10, 2016
Accepted March 15, 2016
ResearchGate has not been able to resolve any citations for this publication.
Article
This paper traces the origin and development of the double tee, emphasizing the influence it has had on the precast, prestressed concrete industry. It reviews the advantages and diverse applications of double tees, primarily in North America. The major features of the double tee are discussed, especially in relation to parking structures. The paper summarizes the results of selected studies conducted at several universities. It discusses the northeast extreme tee (NEXT), the 16 ft (4.8 m) wide Mega-Tee, and the bulb double tee. Examples of future possibilities of double tees using high-strength concrete, self-consolidating concrete, and large-diameter prestressing strands are explored. It is concluded that the future of the double tee, with all its enhancements and ongoing research, is promising.
Здания с каркасами из стальных рам переменного сечения: расчет, проектирование
  • В В Катюшин
Катюшин, В.В. Здания с каркасами из стальных рам переменного сечения: расчет, проектирование, строительство / В.В. Катюшин. -М.: Стройиздат, 2005. -655 с.
Методика розрахунку на стійкість сталевих рам із двотаврів зі змінною висотою стінки / С.І. Білик // Ресурсоекономні матеріали, конструкції, будівлі та споруди
  • С І Білик
Білик, С.І. Методика розрахунку на стійкість сталевих рам із двотаврів зі змінною висотою стінки / С.І. Білик // Ресурсоекономні матеріали, конструкції, будівлі та споруди. -2008. -Вип. 16, Ч. 2. -С. 73 -78.
Легкие металлические конструкции зданий и сооружений. Разработка конструкций, исследование, расчет, изготовление
  • В И Трофимов
Трофимов, В.И. Легкие металлические конструкции зданий и сооружений. Разработка конструкций, исследование, расчет, изготовление, монтаж / В.И. Трофимов, А.М. Каминский. -М.: АСВ, 2002. -575 с.
Питання розрахунку тонкостінних двотаврів у історичному аспекті / І.О. Скляров // Ресурсоекономні матеріали, конструкції, будівлі та споруди
  • І О Скляров
Скляров, І.О. Питання розрахунку тонкостінних двотаврів у історичному аспекті / І.О. Скляров // Ресурсоекономні матеріали, конструкції, будівлі та споруди. -2011. -Вип. 21. -С. 337 -345.
Вибір розрахункового перерізу в рамах змінної жорсткості з суцільною гнучкою стінкою
  • С І Білик
Білик, С.І. Вибір розрахункового перерізу в рамах змінної жорсткості з суцільною гнучкою стінкою / С.І. Білик, І.О. Скляров // Строительство, материаловедение, машиностроение. -2011. -Вып. 60. -С. 16 -20.
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 Training
  • I A Sklyarov
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 Training» (PDDC'2014), 23-25 October 2014, Brest. -Brest: BSTU, 2014. -Vol. 1. -PP. 338 -345.
Buildings with Steel Frames of Variable Cross Section: Calculation, Design, Construction
  • V V Katyushin
Katyushin, V.V. (2005). Buildings with Steel Frames of Variable Cross Section: Calculation, Design, Construction. Moscow: Stroiizdat.
Optimum design of transverse frames containing elements of variable stiffness in frameworks of buildings
  • V O Permyakov
  • O B Glitin
Permyakov, V.O., & Glitin, O.B. (2006). Optimum design of transverse frames containing elements of variable stiffness in frameworks of buildings. In M.A. Giżejowski, A. Kozłowski, L. Ślęczka, J. Ziółko (Eds.), Progress in Steel, Composite and Aluminium Structures (pp. 336 ⎯ 337). London: Taylor & Francis Group.
Stability calculation for steel frames made of I-beams with variable wall height
  • S I Bilyk
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.