Civil's Guide
Design Manual and Codes
Timber Design Codes and Capacities
Structural timber such as glulam can be used for beams and column, and just as we would check the bending and shear capacities for steel and concrete members, we do the same for timber as well as other checks depending on how we are using the structural element.
For exmaple, if we were looking a timber beam under a Uniformly distributed load pinned at each support, we would analyse the beam an element where the bottom of the beam would be in tension and top part in compression (i.e, typical bending moment for a simply supported beam), we would then look at the bending capacity of the timber beam and makes sure that it passes (i.e, bending capacity is greater than the design moment). This would be done for other similar checks.
Below are the definitions of symbols used frequently in Euroocode 5:
- \(\chi\) = characteristic value of strength property
- \(\phi\) = multiple of relavant member and system modification factors
- \(\alpha_{M}\) = material safety factor
- \(f_{m,y,k}\) = characteristic bending strength about y-y axis
- \(k_{mod}\) = is a factor to allow for service class (moisture condition) and load duration
- \(k_{h}\) = relates to depth of section
- \(k_{m,\alpha}\) = relates to bending for tapered beams
- \(k_{sys}\) = relates to load sharing systems
Load duration classes
Duration classes are is linked to the time a structural element is under loads and this affects the timber capacities in subsequent equations.
| Load-duration class | Order of accumulated duration of characteristic load |
|---|---|
| Permanent | more than 10 years |
| Long-term | 6 months – 10 years |
| Medium-term | 1 week – 6 months |
| Short-term | less than one week |
| Instantaneous |
Examples of Load duration
| Load-duration class | Examples of loadings |
|---|---|
| Permanent | Self-weight |
| Long-term | Storage |
| Medium-term | imposed floor load, snow |
| Short-term | Snow, wind |
| Instantaneous | Wind, accidental load |
Material Partial factors of Saftey
This table can be found in BS EN 1995-1-1 (Table 2.3)
| Solid Timber | 1.3 |
| Glued Laminated timber | 1.25 |
| LVL,plywood and OSB | 1.2 |
| Particleboards | 1.3 |
| Connections | 1.3 |
| Punched metal plate fasteners | 1.25 |
| Accidental combinations | 1.0 |
Service Classes
Service Class 1: \(20^{\circ}\) and \(65%\) relative humidity in air, timber average moisture content \(\leq12%\)
Service Class 2: \(20^{\circ}\) and relative humidity> 85% for only a few weeks/year, timber average moisture content \(leq 20%\)
Service Class 3: timber average moisture content > Service Class 2
Values for \(k_{mod}\)
| Material | Standard | Service Class | Load duration class | ||||
|---|---|---|---|---|---|---|---|
| Permanent action | Long term action | Medium term action | Short term action | Instantaneous action | |||
| Solid Timber, Plywood Parts 1,2 and 3 | EN 14081-1 | 1,2 | 0.6 | 0.7 | 0.8 | 0.9 | 1.10 |
| Glulam | BS EN 14080 | 1,2 | 0.6 | 0.7 | 0.8 | 0.9 | 1.10 |
| Solid timber, glulam, plywood part 3 and LVL | 3 | 0.5 | 0.55 | 0.65 | 0.7 | 0.9 | |
| OSB | BS EN 300 | ||||||
| OSB/2 | 1 | 0.30 | 0.45 | 0.65 | 0.85 | 1.1 | |
| OSB/3, OSB/4 | 1 | 0.40 | 0.50 | 0.70 | 0.90 | 1.10 | |
| OSB/3, OSB/4 | 2 | 0.30 | 0.40 | 0.55 | 0.70 | 0.90 | |
Depth factors \(k_h\)
Bending and tension strength for soild timber, \(k_h = min. (\frac{150}{h})^{0.2} or 1.3\) for \(h < 150 mm\)
h = depth in bending or maximum cross section
Bending and tension strength for glulam timber, \(k_h = min. (\frac{600}{h})^{0.1} or 1.1\)
h = depth in bending or maximum cross section
Bending for LVL, \(k_h = min. (\frac{300}{h})^{s} or 1.2\)
h = depth in bending in mm and s = size effect parameter declared by manufacturer
| Example of Use | Limit State | Instantaneous/Final | Recommended limits for beams spanning between 2 supports |
|---|---|---|---|
| Cracking of plasterboard, glass,ceramics etc. in roofs, ceilings or floorss | Irreversible | Final | \(w_{fin}\leq\frac{L}{250}\) where \(w_{fin} = deflection due to permanent + imposed loads + creep. |
| Apperance of roofs and ceilings with no attatched brittle finishes | Reversible | Final | \(w_{fin}\leq\frac{L}{150}\), where \(w_{fin}\) = deflection due to permanent + imposed loads + creep |
| In fire, at end of required period of fire resistance, where protecttion depends on attatched plasterboard, unless proved by test | Accidental | Instantaneous | \(w_{inst}\leq\frac{L}{150}\) where \(w_{inst}\) = instantaneous deflection due to permanent + imposed loads |
Load-sharing system factor, \(k_{sys}\)
When several equally spaced similar members, components, or assemblies are laterally connected by a continuous load distribution system, the members strength properties may be multiplied by a system strength factor \(k_{sys}\).
Provided the continous load-distribution system is capable of transferring the loads from one member to the neighbouring members, \(k_{sys} = 1.1\)
Shear modification factor, \(k_{CR}\)
A reduction in shear capacity of timber is taken to allow for drying splits and glue-line failure. This can be found in the National Annex (Table NA.4) to BS EN 1995-1-1.
| Material | Modification factor \(K_{CR}\) |
|---|---|
| Solid Timber | 0.67 |
| Glulam | 0.67 |
| LVL | 1.0 |
| Wood based panels | 1.0 |
Compression strength perpendicular to the grain for solid timber and glulam, \(k_{c,90}\)
\(k_{c,90}\) is usually taken as 1.0 but can be increased for the following:
For members on discrete continuous supports which undertakes distributed loads/ or concentrated loads further away from supports than \(l_1 = 2h\),
where \(l\) is the contract length and \(h\) is the depth of the member.
\(k_c,90\) = 1.5 for solid softwwood Timber
\(k_c,90\) = 1.75 for glued laminated softwood timber provided that \(l \leq 400\)mm
This can be found in BS EN 1995-1-1, section 6.1.5.
Bi-axial Bending Check
There are two expressions below that need to be to be satisfied.
\(\frac{\sigma_{m,y,d}}{f_{m,y,d}}+k_m\frac{\sigma_{m,z,d}}{f_{m,z,d}} \leq 1.0\) (6.11)
\(k_m\frac{\sigma_{m,y,d}}{f_{m,y,d}}+\frac{\sigma_{m,z,d}}{f_{m,z,d}} \leq 1.0\) (6.12)
\(\sigma_{m,y,d}\) and \(\sigma_{m,z,d}\) are the design bending stresses about the principle axes as shown in Figure 6.1;
\(f_{m,y,d}\) and \(f_{m,z,d}\) are the corresponding design bending strengths.
- For rectangular sections: \(k_m = 0.7\)
- For other cross-sections: \(k_m = 1.0\)
- For other wood-based structural products, for all cross-sections: \(k_m = 1.0\)
This can be found in BS EN 1995-1-1, section 6.1.6.
Modification factor for notched beams
At support locations, notches can be made into the timber, which will affect the stress concentrations in those areas.
\(k_v\) is the reduction factor and can be taken as 1.0.
This can be found in BS EN 1995-1-1, section 6.5.2
Elastic analysis of a beam - bending analysis - lateral stability
- Find \(L_{eff}\)
- Find \(\sigma_{m,eff}\)
- Find \(\lambda_{rel,m}\)
- Find \(k_{crit}\)
- Check \(\sigma_{m,d} \leq k_{crit} \times f_{md}\)
\(l_eff\) can be found in table 6.1 from BS EN 1995-1-1 which has been tabulated below:
| Beam Type | Loading type | \(l_{ef}/l^a\) |
|---|---|---|
| Simply supported | Constant moment | 1.0 |
| Uniformly distributed load | 0.9 | |
| Concentrated force at the middle of the span | 0.8 | |
| Cantilever | Uniformly distributed load | 0.5 |
| Concentrated force at the free end | 0.8 |
\(^a\)The ratio between the effetice length \(l_{ef}\) and the span \(l\) is valid for a beam with torsionally restrained supports and loaded at the centre of gravity. If the load is applied at the compression edge of the beam, \(l_{ef}\) should be increased by 2h and may be decreased by 0.5h for a load at the tension edge of the beam.
For exmaple, in a 2m simply supported beam with a height of 300mm with a uniformly distributed load would have an effective length of 0.9 x 2.0 + 2 x 0.3 = 2.4m
\(\sigma_{m,crit} = \frac{0.78b^2}{hl_{ef}}E_{0,05}\)
\(\lambda_{rel,m} = \sqrt{\frac{f_{m,k}}{\sigma_{m,crit}}}\)
\(k_{crit}\) can be determined from expression 6.34
| \(k_{crit}\) | |
| For \(\lambda_{rel,m} \leq 0.75\) | 1 |
| For \(0.75 < \lambda_{rel,m} \leq 1.4\) | \(1.56-0.75\lambda_{rel,m}\) |
| For \(1.4 < \lambda_{rel,m}\) | \(\frac{1}{\lambda^2_{rel,m}}\) |
Deflection Design
When calculating the deflection of a timber member, it undergoes instantaneous deflection due to permanent and variable loads but also due to creep. The deflection due to creep is calculated using the deformation factor \(k_{def}\) which is taken from BS EN 1995-1-1, tabel 3.2.
| Material | Standard | Service Class | ||
|---|---|---|---|---|
| 1 | 2 | 3 | ||
| Solid timber | EN 14081-1 | 0.6 | 0.8 | 2.0 |
| Glued Laminated timber | EN 14081 | 0.6 | 0.8 | 2.0 |
| LVL | EN 14374, EN 14279 | 0.6 | 0.8 | 2.0 |
| Plywood | EN 636 | 0.8 | 1.0 | 2.5 |
| OSB/2 | EN 300 | 2.25 | ||
| OSB/3, OSB/4 | EN 300 | 1.50 | 2.25 | |
Deformation is defined in BS EN 1995-1-1, clause 2.2.3, equation 2.2
Total deformation = instantaneous deflection + creep deflection
Where \(U_{fin} = U_{inst} + U_{creep}\) which is shown in the codes as \(u_{fin} = u_{fin,G} + u_{fin,Q1} + \Sigma u_{fin,Q1}\)
\(u_{fin,G} = u_{inst,G}(1+k_{def})\) for permanent action, G
\(u_{fin,Q,1} = u_{inst,Q,1}(1+\psi_{2,1} k_{def})\) for the leading variable action, Q1
\(u_{fin,Q,i} = u_{inst,Q,i}(\psi_{0,i}+\psi_{2,i} k_{def})\) for accompanying variable action, Qi (i>1)
\(\psi_0 and \psi_2 can be found in table NA.A1.1\)
| Action | \(\psi_0\) | \(\psi_1\) | \(\psi_2\) |
|---|---|---|---|
| Category A: domestic, residental areas | 0.7 | 0.5 | 0.3 |
| Category B: Office areas | 0.7 | 0.5 | 0.3 |
| Category C: Congregation areas | 0.7 | 0.7 | 0.6 |
| Category D: shopping areas | 0.7 | 0.7 | 0.6 |
| Category E: storage areas | 1.0 | 0.9 | 0.8 |
| Category F: traffic areas, vehicle weight \(\leq 30 kN\) | 0.7 | 0.7 | 0.6 |
| Category H: traffic areas \(30 kN < vehicle weight \leq 160 kN\) | 0.7 | 0.5 | 0.3 |
| Snow loads on buildings (see EN 1991-3) | |||
| for sites located at altitude H>1000 m a.s.l. | 0.7 | 0.5 | 0.2 |
| for sites located at altitude \(H\leq1000\) m a.s.l. | 0.5 | 0.2 | |
| Wind loads on buildings (See BS EN 1991-1-4) | 0.5 | 0.2 | |
| Temperature (non-fire) in buildings (see EN 1991-1-5) | 0.6 | 0.5 |