# 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 1^{st} order or a 2^{nd} 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:

1^{st} order analysis, using the initial geometry of the structure or,

2^{nd} 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.

### 1^{st} order theory

For a 1^{st} 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 f_{y} / N_{cr}]^{1/2}

The critical normal force for flexural buckling **N _{cr}** 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:

λ_{LT} = [W f_{y} / M_{cr}]^{1/2}

The critical moment** M _{cr}** 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.

### 2^{nd} order theory

A 2^{nd} order calculation produces the critical normal force **N _{cr}** for flexural buck- ling and a corresponding stability check is not required. The critical moment

**M**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.

_{cr}**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.

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.

## Imperfections for global analysis of frames

The following imperfections should be taken into account:

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

### Conventional method

**Global initial sway imperfections**

This effect could be considered in two ways.

- By changing the frame geometry before analysis with the slope as shown below. The slope φ will be calculated according to the relevant code.
- 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 **e _{o}** 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.

# Load duration classes

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 **k _{mod}**, 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:

E_{mean,fin} = E_{mean} / (1 + k_{def})

G_{mean,fin} = G_{mean} / (1 + k_{def})

K_{ser,fin} = K_{ser} / (1 + k_{def})

**Ultimate Limit State**

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

E_{mean,fin} = E_{mean} / (1 + Ψ_{2} k_{def})

G_{mean,fin} = G_{mean} / (1 + Ψ_{2} k_{def})

K_{ser,fin} = K_{ser} / (1 + Ψ_{2} k_{def})

where:

**k _{def}** is a factor for the evaluation of creep deformation given in EN 1995-1-1 table 3.2.

**Ψ**is the factor for the quasi-permanent value of the action according to EN 1990 table A1.1. For permanent actions Ψ

_{2}_{2}= 1,0.

# Verification by the partial factor method

## Design value of material property

The design value of **X _{d}** of a strength property shall be calculated as:

X_{d} = k_{mod} X_{k} / γ_{M}

where:

**X _{d}** is the characteristic value of a strength property,

**k _{mod}** 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,

**γ _{M}** is the partial factor for a material property according to table below.

Recommended partial factors γ_{M} for material properties and resistance

**NA Norway**

LVL, plywood, OSB γ_{M} = 1,3

**NA Finland**

Solid timber < C35 γ_{M} = 1,4

Solid timber ≥ C35 γ_{M} = 1,25

Glued laminated timber γ_{M} = 1,2

Plywood, OSB, Particleboards, Fibreboards γ_{M} = 1,25

**NA Denmark**

Solid timber γ_{M} = 1,35 γ3

Glued laminated timber γ_{M} = 1,3 γ_{3}

LVL, Plywood, OSB, Particleboards, Fibreboards γ_{M} = 1,3 γ^{3}

The factor γ_{3} is chosen according to the following:

The design member stiffness properties shall be calculated as:

E_{d} = E_{mean} / γ_{M}

G_{d} = G_{mean} / γ_{M}

where:

E_{mean} is the mean value of modulus of elasticity,

G_{mean} 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 ρ_{k} ≤ 700 kg/m^{3} and depths in bending or widths in tension less than 150 mm the characteristic values for **f _{m,k}** and

**f**may be increased by the factor

_{t,0,k}**k**given by:

_{h}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 f_{m,k} and f_{t,0,k} may be increased by the factor k_{h} given by:

k_{h} = min [ (600 / h )^{0.1} , 1,1]

where:

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