Stress and Strength Analysis of Curved Glulam Beams With Box CrossSection
(2008)Civil Engineering
Structural Mechanics
 Abstract
 Glulam arches can be used when designing structures with large spans such as halls or arenas. Wood has low density compared to steel and concrete which keeps down the dead weight of the structure. The cross section of glulam arches is often built up as a boxsection for efficiency reasons. However, wood shows strongly orthotropic behavior where maximum allowed stress perpendicular to grain is only 12% of maximum stress along grain. Bending moment creates stress perpendicular to grain for a curved beam element. By altering the slope of the arch, moment forces can be minimized for a specific load distribution and the structure can be designed using a minimum of material.
Wood is a heterogeneous material which means that different parts... (More)  Glulam arches can be used when designing structures with large spans such as halls or arenas. Wood has low density compared to steel and concrete which keeps down the dead weight of the structure. The cross section of glulam arches is often built up as a boxsection for efficiency reasons. However, wood shows strongly orthotropic behavior where maximum allowed stress perpendicular to grain is only 12% of maximum stress along grain. Bending moment creates stress perpendicular to grain for a curved beam element. By altering the slope of the arch, moment forces can be minimized for a specific load distribution and the structure can be designed using a minimum of material.
Wood is a heterogeneous material which means that different parts of the
material have different properties. The volume of wood needed for designing an arch big enough for a structure as a hall or an arena is substantial. As the volume of wood under stress is increased the probability that a small part of the volume has a low ultimate stress value also increases. This effect can be handled using Weibull statistics theory.
In this thesis expressions for calculation of normal stress, shear stress and stress perpendicular to grain are derived for a curved beam with box cross section using beam theory. By using equilibrium conditions and an
approximation method, the force vector corresponding to a distributed load
of a curved beam element is described without the need of shape functions.
With use of the finite element method, reaction forces can be calculated for an arbitrary system of curved beams. If the reaction forces are known, it’s possible to calculate the section forces using the equilibrium conditions. Finally, Weibull theory is used to calculate the strength of such a structural system.
The theory is implemented using MATLAB/CALFEM to create a toolbox which can be used for strength design of structures made of curved glulam beams.
Calculations carried out using the toolkit developed show that the Weibull
theory size effect has a large impact on the strength of large arches. Analysis of an arch with a span of about 90 meters shows that the strength may be heavily overestimated if the size effect is disregarded. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/3566885
 author
 Persson, Erik
 supervisor

 PerJohan Gustafsson ^{LU}
 Arne Emilson
 Roberto Crocetti ^{LU}
 organization
 year
 2008
 type
 H3  Professional qualifications (4 Years  )
 subject
 report number
 TVSM5154
 ISSN
 02816679
 language
 English
 id
 3566885
 date added to LUP
 20130805 11:13:35
 date last changed
 20130916 17:41:29
@misc{3566885, abstract = {Glulam arches can be used when designing structures with large spans such as halls or arenas. Wood has low density compared to steel and concrete which keeps down the dead weight of the structure. The cross section of glulam arches is often built up as a boxsection for efficiency reasons. However, wood shows strongly orthotropic behavior where maximum allowed stress perpendicular to grain is only 12% of maximum stress along grain. Bending moment creates stress perpendicular to grain for a curved beam element. By altering the slope of the arch, moment forces can be minimized for a specific load distribution and the structure can be designed using a minimum of material. Wood is a heterogeneous material which means that different parts of the material have different properties. The volume of wood needed for designing an arch big enough for a structure as a hall or an arena is substantial. As the volume of wood under stress is increased the probability that a small part of the volume has a low ultimate stress value also increases. This effect can be handled using Weibull statistics theory. In this thesis expressions for calculation of normal stress, shear stress and stress perpendicular to grain are derived for a curved beam with box cross section using beam theory. By using equilibrium conditions and an approximation method, the force vector corresponding to a distributed load of a curved beam element is described without the need of shape functions. With use of the finite element method, reaction forces can be calculated for an arbitrary system of curved beams. If the reaction forces are known, it’s possible to calculate the section forces using the equilibrium conditions. Finally, Weibull theory is used to calculate the strength of such a structural system. The theory is implemented using MATLAB/CALFEM to create a toolbox which can be used for strength design of structures made of curved glulam beams. Calculations carried out using the toolkit developed show that the Weibull theory size effect has a large impact on the strength of large arches. Analysis of an arch with a span of about 90 meters shows that the strength may be heavily overestimated if the size effect is disregarded.}, author = {Persson, Erik}, issn = {02816679}, language = {eng}, note = {Student Paper}, title = {Stress and Strength Analysis of Curved Glulam Beams With Box CrossSection}, year = {2008}, }