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Stress and Strength Analysis of Curved Glulam Beams With Box Cross-Section

Persson, Erik (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 box-section for efficiency reasons. However, wood shows strongly orthotropic behavior where maximum allowed stress perpendicular to grain is only 1-2% 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 box-section for efficiency reasons. However, wood shows strongly orthotropic behavior where maximum allowed stress perpendicular to grain is only 1-2% 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:
author
Persson, Erik
supervisor
organization
year
type
H3 - Professional qualifications (4 Years - )
subject
report number
TVSM-5154
ISSN
0281-6679
language
English
id
3566885
date added to LUP
2013-08-05 11:13:35
date last changed
2013-09-16 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 box-section for efficiency reasons. However, wood shows strongly orthotropic behavior where maximum allowed stress perpendicular to grain is only 1-2% 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         = {0281-6679},
  language     = {eng},
  note         = {Student Paper},
  title        = {Stress and Strength Analysis of Curved Glulam Beams With Box Cross-Section},
  year         = {2008},
}