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Journal of Wood Science

, Volume 64, Issue 5, pp 578–590 | Cite as

Static analysis of lattice columns

  • Krzysztof ŚliwkaEmail author
Original Article
First Online:
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Abstract

The paper focuses on timber structures. Static analysis was performed in the paper of timber lattice columns with N and V lattice configuration made in variants of timber, plywood, fibreboard and particleboard. As a part of the study, formulae determining critical force in the column and the column slenderness ratio were derived basing on the theory by Timoshenko and Gere. In addition, the paper includes formulae applicable to shearing forces occurring in the column as well as maximum shearing forces that a column can carry, also based on the theory by Timoshenko and Gere. Basing on the formulae described above and the formulae given in the literature (EN-1995 Eurocode 5 Standard), a comparative analysis was carried out of the load-bearing capacity of columns and calculations for the truss. The calculations demonstrate that there are discrepancies between the static values being compared and both calculation methods lead to partially divergent results.

Keywords

Lattice columns Truss Shear strain Critical load-bearing capacity Shearing in columns 

Symbols

Latin letters

a

Initial maximum column curvature

A

Cross-sectional area

Af

Cross-sectional area of a flange

As

Cross-sectional area of a vertical

Ak

Cross-sectional area of a diagonal

e

Eccentric of the joints, eccentric of the force application P

E

Modulus of elasticity

Emean

Mean value of modulus of elasticity

Ek

Modulus of elasticity of a diagonal

Es

Modulus of elasticity of a vertical

E0.05

Fifth percentile of the modulus of elasticity of column shafts

\(E_{{0.05}}^{k}\)

Fifth percentile of the modulus of elasticity of diagonals,

\(E_{{0.05}}^{s}\)

Fifth percentile of the modulus of elasticity of verticals

fc,0,k

Characteristic compressive strength of timber along the grain

fc,0,d

Design compressive strength of timber along the grain

fr,k

Characteristic planar (rolling) shear strength

fv,k

Characteristic shear strength

g

Truss elements thickness

G

Shear modulus

h

Distance of the flanges

i

Radius of gyration of a column considered as solid

I

Second moment of area of a section

If

Second moment of area of a flange

kc

Instability factor

l

Span (height of a latticed column)

lc

Buckling span of a column

l1

Distance between adjacent nodes

M(x)

Bending moment

n

Load-bearing capacity of a column

P

Compressive force

q(x)

Transverse load

\(V_{p}^{{}}\)

Shear force

\(V_{p}^{a}\)

Maximum shear force, caused by compressive force P, for a column with its initial curvature described with a sinusoid

\(V_{p}^{e}\)

Maximum shear force, caused by compressive force P, for a column, where force P acts on eccentric e

\(V_{p,{\text{max}}}^{a}\)

Maximum shear force a column can carry, for a column with its initial curvature described with a sinusoid

\(V_{p,{\text{max} }}^{e}\)

Maximum shear force a column can carry, for a column, where force P acts on eccentric e

y(x)

Deflection line function

zmax

Distance from the neutral axis to the extreme grain

Greek letters

α

Angle between a diagonal and a vertical

λef

Slenderness ratio for a column

µ

Energetic shear coefficient

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Copyright information

© The Japan Wood Research Society 2018

Authors and Affiliations

  1. 1.Faculty of Civil Engineering and ArchitectureWest Pomeranian University of TechnologySzczecinPoland

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