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Sidostabiltet för limträbågar

Persson, David (2010) VSM820
Structural Mechanics
Civil Engineering (M.Sc.Eng.)
Abstract (Swedish)
Limträbågar med lång spännvidd har ofta ett väldigt högt och slankt tvärsnitt. Detta medför risk för vippningsinstabilitet. En jämnsymmetrisk belastning av bågen ställer oftast inte till något problem, men då bågen belastas osymmetriskt uppkommer stora böjmoment som ökar risken för instabilitet markant.

Raka balkar som belastas med punktlaster eller utbredda laster får ett tryck i balkens överkant. Ett sådant tryck medför precis som för fallet då en pelare är tryckt en viss instabilitetsrisk. Detta medför dock sällan ett problem trots att stora balkar används eftersom att överkanten i en rak balk nästan alltid är stabiliserad av åsar eller någon typ av beklädnad. I limträbågar medför dock såväl normalkrafter som moment ett tryck i... (More)
Limträbågar med lång spännvidd har ofta ett väldigt högt och slankt tvärsnitt. Detta medför risk för vippningsinstabilitet. En jämnsymmetrisk belastning av bågen ställer oftast inte till något problem, men då bågen belastas osymmetriskt uppkommer stora böjmoment som ökar risken för instabilitet markant.

Raka balkar som belastas med punktlaster eller utbredda laster får ett tryck i balkens överkant. Ett sådant tryck medför precis som för fallet då en pelare är tryckt en viss instabilitetsrisk. Detta medför dock sällan ett problem trots att stora balkar används eftersom att överkanten i en rak balk nästan alltid är stabiliserad av åsar eller någon typ av beklädnad. I limträbågar medför dock såväl normalkrafter som moment ett tryck i bågens ostagade underkant vilket medför en stor instabilitetsrisk.

Finita elementmetoden är en numerisk approximativ metod där man delar upp det fysikaliska problemet i element så att approximationer kan göras för vardera element och således kan hela problemet lösas. Denna metod används tillsammans med Finita elementprogrammet Abaqus för att dela upp balk eller båge i mindre element varpå instabilitetsanalyser kan utföras. Dessa instabilitetsanalyser sker genom egenvärdesanalys
eller en statisk olinjär analys och det är framför allt skal- eller balkelement som används.

För fritt upplagda raka balkar finns analytiska ekvationer för beräkning av instabilitet. Analyser med hjälp av Finita elementmetoden ger för raka balkar väldigt god överensstämmelse med de analytiska lösningarna. Speciellt studerades lastexcentricitetens inverkan på stabiliteten och denna inverkan visade sig vara ganska stor.

Vad gäller limträbågar är det inte lika lätt att hitta konkreta analytiska lösningar trots att många av de samband man hittar för en rak balk även är tillämpbara på en båge. En analytisk lösningsmetod är dock föreslagen men denna förutsätter att infästningsförhållandena mot sekundärbärverk är väldigt goda. Denna metod bygger på att man delar upp bågen i segment motsvarande raka balkar och kontrollerar
instabiliteten för värst belastad balk. Metoden verkar ge relativt goda resultat inte minst vid ojämn belastning av bågen. Hur anslutningar bör utformas eller hur styva dessa behöver vara behandlas utförligt i rapporten. (Less)
Abstract
Glulam arches with long span often have a very high and slender cross-section. This may cause lateral torsional buckling of the arch.
A symmetrical loading doesn’t usually become a problem, but if the arch is loaded asymmetrical there will be large bending moments that increases the risk of instability significantly.

Straight beams that are subjected to point loads or distributed loading will be subjected to compressive stresses in the upper edge of the beam. Such pressure will just like the case where a column is pressure-loaded have some instability risk. This is, however, rarely a problem even though large structures are used because the upper edge of a straight beam is almost exclusively stabilized by ridges or any type of... (More)
Glulam arches with long span often have a very high and slender cross-section. This may cause lateral torsional buckling of the arch.
A symmetrical loading doesn’t usually become a problem, but if the arch is loaded asymmetrical there will be large bending moments that increases the risk of instability significantly.

Straight beams that are subjected to point loads or distributed loading will be subjected to compressive stresses in the upper edge of the beam. Such pressure will just like the case where a column is pressure-loaded have some instability risk. This is, however, rarely a problem even though large structures are used because the upper edge of a straight beam is almost exclusively stabilized by ridges or any type of coverings. However, in glulam arches both the normal forces and torque leads to a pressure in the unstayed lower edge of the arch which means a high risk of instability.

The Finite Element Method is a numerical approximation method where a physical problem is divided into elements so that approximations can be made for each element and therefore the whole problem can be solved. This will be used with the FE-software Abaqus to divide beams and arches into elements whereupon instability analysis can be performed. The instability analysis is made by eigenvalue analysis or a static nonlinear analysis and particularly shell or beam elements are used.

For simply supported, straight beams there are analytical equations for calculation of instability available. Analysis using the Finite Element Method for straight beams gives very good conformity with the analytical solutions. The effect of loading eccentricity on the stability was specially studied and this effect proved to be quite
large.

For glulam arches, it is not as easy to find concrete analytical solutions, even though many of the conjunctions you find on a straight beam is also applicable to an arch. An analytical solution method is proposed but this presupposes that the connections to ridges or similar is very good. This method is based on dividing the arch into segments corresponding straight beams and controlling the instability on worst
loaded beam. The method seems to give relatively well results at least in asymmetrical loading of the arch. How connections should be designed or how stiff they need to be is addressed in the report. (Less)
Please use this url to cite or link to this publication:
author
Persson, David
supervisor
organization
course
VSM820
year
type
H3 - Professional qualifications (4 Years - )
subject
report number
TVSM-5168
ISSN
0281-6679
language
Swedish
id
3566957
date added to LUP
2013-08-01 14:34:53
date last changed
2013-10-07 13:08:07
@misc{3566957,
  abstract     = {Glulam arches with long span often have a very high and slender cross-section. This may cause lateral torsional buckling of the arch.
A symmetrical loading doesn’t usually become a problem, but if the arch is loaded asymmetrical there will be large bending moments that increases the risk of instability significantly.

Straight beams that are subjected to point loads or distributed loading will be subjected to compressive stresses in the upper edge of the beam. Such pressure will just like the case where a column is pressure-loaded have some instability risk. This is, however, rarely a problem even though large structures are used because the upper edge of a straight beam is almost exclusively stabilized by ridges or any type of coverings. However, in glulam arches both the normal forces and torque leads to a pressure in the unstayed lower edge of the arch which means a high risk of instability.

The Finite Element Method is a numerical approximation method where a physical problem is divided into elements so that approximations can be made for each element and therefore the whole problem can be solved. This will be used with the FE-software Abaqus to divide beams and arches into elements whereupon instability analysis can be performed. The instability analysis is made by eigenvalue analysis or a static nonlinear analysis and particularly shell or beam elements are used.

For simply supported, straight beams there are analytical equations for calculation of instability available. Analysis using the Finite Element Method for straight beams gives very good conformity with the analytical solutions. The effect of loading eccentricity on the stability was specially studied and this effect proved to be quite
large.

For glulam arches, it is not as easy to find concrete analytical solutions, even though many of the conjunctions you find on a straight beam is also applicable to an arch. An analytical solution method is proposed but this presupposes that the connections to ridges or similar is very good. This method is based on dividing the arch into segments corresponding straight beams and controlling the instability on worst
loaded beam. The method seems to give relatively well results at least in asymmetrical loading of the arch. How connections should be designed or how stiff they need to be is addressed in the report.},
  author       = {Persson, David},
  issn         = {0281-6679},
  language     = {swe},
  note         = {Student Paper},
  title        = {Sidostabiltet för limträbågar},
  year         = {2010},
}