# General

The following design considers EC5 (standard) and the National Annex (NA) for Denmark, Finland, Hungary, Norway and Sweden.

With the timber module arbitrary structures in space can be designed with regard to a 1st order or a 2nd order analysis.

In the Code Check all checks prescribed in the codes depending on acting section forces displayed.

# Global analysis

## General

The design can be performed using either:

1st order analysis, using the initial geometry of the structure or,
2nd order analysis, taking into account the influence of the deformation of the structure.

## Structural stability

The calculations with regard to instability will be performed in different ways depending on the type of analysis.

### 1st order theory

For a 1st order design the following apply:

Both the flexural and lateral torsional buckling are calculated depending on the slenderness with respect to reduction factors specified in the appropriate code. The reduced slenderness for flexural buckling may be computed as:
λ = [A fy / Ncr]1/2

The critical normal force for flexural buckling Ncr will in this case be calculated using appropriate buckling lengths defined by the user in both directions for all members.
The reduced slenderness for lateral torsional buckling may be computed as:

λLT = [W fy / Mcr]1/2

The critical moment Mcr will be calculated according to support conditions and load levels defined by the user for all members.

Imperfections
Initial bow imperfections may be neglected as these effects are included in the formulas for buckling resistance of the members.

For sway mode structures initial sway imperfections has to be considered. This could be done by changing the geometry before calculation or by defining systems of equivalent horizontal forces as described below.

### 2nd order theory

A 2nd order calculation produces the critical normal force Ncr for flexural buck- ling and a corresponding stability check is not required. The critical moment Mcr are not calculated since a basic finite element only contains the second order effects of the axial force. The effect of the lateral torsional buckling will then have to be calculated as for 1th order above.

Imperfections
For all structures initial deformations should be considered. See EN 1995-1-1 5.4.4.
As the flexural buckling design is based on the 2nd order effects of the bending moments it is vital that there is a moment distribution in all members. By considering initial deformations this is ensured also for hinged members without late- ral load.

Note! It is up to the user to ensure that all members have a 1st order moment distribution so the 2nd order effect and thereby also the buckling effect is considered.

For sway mode structures also initial sway imperfections has to be considered. This could be done in the conventional way by changing the geometry before calculation or by defining systems of equivalent horizontal forces as described in 2.4.2.3.1 below.

Note! When performing a 2nd order calculation a division of the members in more than one finite element could strongly influence the result. It is recommended to divide members in compression into an even member of elements e.g. four.

## Imperfections for global analysis of frames

The following imperfections should be taken into account:

1. Global imperfections for the structure as a whole.
2. Local imperfections for individual members.

### Conventional method

• Global initial sway imperfections This effect could be considered in two ways.

1. By changing the frame geometry before analysis with the slope as shown below. The slope φ will be calculated according to the relevant code.
2. By defining a system of equivalent horizontal forces as shown below: Where, in multi-storey beam and column building frames, equivalent forces are used they should be applied at each floor and roof level.
These initial sway imperfections should apply in all relevant horizontal directions, but need only be considered in one direction at a time.
The possible torsional effects on a structure caused by anti-symmetric sways at the two opposite faces, should also be considered. • Relative initial local bow imperfections of members for flexural buckling

Equivalent horizontal forces introduced for each member as shown below could consider this effect.
The value eo considering initial bow deformation is calculated according to EN 1995-1-1 5.4.4. # Ultimate limit state

For a second order linear elastic analysis of a structure, design values, not adjusted for duration of load, shall be used.

Actions shall be assigned to one of the load-duration classes given in EN 1995- 1-1 table 2.1.
Examples of load-duration assignment are given in EN 1995-1-1 table 2.2.

# Service classes

Structures shall be assigned to one of three service classes according to EN 1995-1-1 2.3.1.3.

# Materials and product properties

## Load-duration and moisture influences on strength

The influence of load-duration and moisture content on strength is considered by the modification factor kmod, see EN 1995-1-1 table 3.1.

## Load-duration and moisture influences on deformations

Serviceability Limit State

If the structure consists of members having different time-dependent properties, the final mean values of modulus of elasticity, shear modulus and slip modulus are calculated with the following expressions:

Emean,fin = Emean / (1 + kdef)

Gmean,fin = Gmean / (1 + kdef)

Kser,fin = Kser / (1 + kdef)

Ultimate Limit State

The final mean value of modulus of elasticity, shear modulus and slip modulus are calculated with the following expressions:

Emean,fin = Emean / (1 + &Psi;2 kdef)

Gmean,fin = Gmean / (1 + &Psi;2 kdef)

Kser,fin = Kser / (1 + &Psi;2 kdef)

where:

kdef is a factor for the evaluation of creep deformation given in EN 1995-1-1 table 3.2.
&Psi;2 is the factor for the quasi-permanent value of the action according to EN 1990 table A1.1. For permanent actions &Psi;2 = 1,0.

# Verification by the partial factor method

## Design value of material property

The design value of Xd of a strength property shall be calculated as:

Xd = kmod Xk / γM

where:

Xd is the characteristic value of a strength property,

kmod is a modification factor taking into account the effect of the duration of load and moisture content according to EN 1995-1-1 table 3.1,

γM is the partial factor for a material property according to table below.

Recommended partial factors γM for material properties and resistance NA Norway
LVL, plywood, OSB γM = 1,3

NA Finland
Solid timber < C35 γM = 1,4
Solid timber ≥ C35 γM = 1,25
Glued laminated timber γM = 1,2
Plywood, OSB, Particleboards, Fibreboards γM = 1,25

NA Denmark
Solid timber γM = 1,35 γ3
Glued laminated timber γM = 1,3 γ3
LVL, Plywood, OSB, Particleboards, Fibreboards γM = 1,3 γ3

The factor γ3 is chosen according to the following: The design member stiffness properties shall be calculated as:

Ed = Emean / γM
Gd = Gmean / γM

where:

Emean is the mean value of modulus of elasticity,
Gmean is the mean value of shear modulus

# Material properties

EN 1995-1-1 ch. 3

## Solid Timber

### Strength classes

EN 1995-1-1 3.2, EN 338 5

Strength classes - Characteristic values:  For rectangular solid timber with a characteristic density ρk ≤ 700 kg/m3 and depths in bending or widths in tension less than 150 mm the characteristic values for fm,k and ft,0,k may be increased by the factor kh given by:

kh = min [ (150 / h )0.2 , 1,3]

where:

h is the depth for bending members or width for tension members, in mm.

## Glued laminated timber

### Strength classes

Strength classes - Characteristic values: From these tables the following standard classes must be available:

Solid timber: C14, C16, C18, C20, C22, C24, C27, C30, C35, C40, C45, C50, D30, D35, D40, D50, D60, D70.

Glued laminated timber: GL 24, GL 28, GL 32, GL 36.

Any user defined material will also be possible to define.

As the modulus of elasticity and shear modulus are dependent of each other either one or the other could be defined by the user for user defied materials.

For rectangular glued laminated timber with depths in bending or widths in tension less than 600 mm the characteristic values for fm,k and ft,0,k may be increased by the factor kh given by:

kh = min [ (600 / h )0.1 , 1,1]

where:

h is the depth for bending members or width for tension members, in mm.

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