# Static analysis of lattice columns

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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

*A*_{f}Cross-sectional area of a flange

*A*_{s}Cross-sectional area of a vertical

*A*_{k}Cross-sectional area of a diagonal

*e*Eccentric of the joints, eccentric of the force application

*P**E*Modulus of elasticity

*E*_{mean}Mean value of modulus of elasticity

*E*_{k}Modulus of elasticity of a diagonal

*E*_{s}Modulus of elasticity of a vertical

*E*_{0.05}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

*f*_{c,0,k}Characteristic compressive strength of timber along the grain

*f*_{c,0,d}Design compressive strength of timber along the grain

*f*_{r,k}Characteristic planar (rolling) shear strength

*f*_{v,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

*I*_{f}Second moment of area of a flange

*k*_{c}Instability factor

*l*Span (height of a latticed column)

*l*_{c}Buckling span of a column

*l*_{1}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

*z*_{max}Distance from the neutral axis to the extreme grain

## Greek letters

*α*Angle between a diagonal and a vertical

*λ*_{ef}Slenderness ratio for a column

*µ*Energetic shear coefficient

## References

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