D5.C.2 Analysis Methodology
Symbol | Description |
---|---|
St0d | Design tensile stress parallel (at zero degree) to grain alignment. |
St90d | Design tensile stress perpendicular (at 90 degrees) to grain alignment. |
Sc0d | Design compressive stress parallel to grain alignment. |
Sc90d | Design compressive stress perpendicular to grain alignment. |
Smzd | Design bending stress about zz axis. |
Smyd | Design bending stress about yy axis. |
Svd | Design shear stress. |
Stor_d | Design torsional stress. |
Ft0d | Design tensile strength - parallel to the grain alignment. |
Ft90d | Design tensile strength - perpendicular to the grain alignment. |
Fc0d | Design compressive strength - parallel to the grain alignment. |
Fc90d | Design compressive strength - perpendicular to the grain alignment. |
Fmzd | Design bending strength - about zz-axis. |
Fmyd | Design bending strength - about yy-axis. |
Fvd | Design shear strength about yy axis. |
RATIO |
Permissible ratio of stresses as input using the The default value is 1. |
lz ,lrel,z | Slenderness ratios corresponding to bending about zz axis. |
ly,lrel,y | Slenderness ratios corresponding to bending about yy axis. |
E0,05 | Fifth percentile value of modulus of elasticity parallel to grain. |
G0,05 | Fifth percentile value of shear modulus parallel to grain. |
Iz | Second moment of area about the strong z-axis. |
Iy | Second moment of area about the weak y-axis. |
Itor | Torsional moment of inertia. |
fmk | Characteristic bending strength. |
b, h | Width and depth of beam. |
Equations for Characteristic Values of Timber Species as per Annex-A of EN 338:2003
The following equations were used to determine the characteristic values:
For a particular Timber Strength Class (TSC), the following characteristic strength values are required to compute the other related characteristic values.
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Bending Strength – fm,k
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Mean Modulus of Elasticity in bending – E0, mean
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Density - ρk
SI No. | Property | Symbol | Wood Type | |
---|---|---|---|---|
Softwood (C) | Hardwood (D) | |||
1. | Tensile Strength parallel to grain | ft,0,k | 0.6 × fm,k | |
2. | Tensile Strength perpendicular to grain | ft,90,k | Minimum of {0.6 and (0.0015×rk)} | |
3. | Compressive Strength parallel to grain | fc,0,k | 5 × (fm,k ) 0.45 | |
4. | Compressive Strength perpendicular to grain | fc,90,k | 0.007×rk | 0.0015×rk |
5. | Shear Strength | fv,k | Minimum of {3.8 and (0.2×fm,k 0.8)} | |
6. | Modulus of Elasticity parallel to grain | E0,05 | 0.67× E0,mean | 0.84× E0,mean |
7. | Mean Modulus of Elasticity perpendicular to grain | E90,mean | E0,mean /30 | E0,mean /15 |
8. | Mean Shear Modulus | Gmean | E0,mean /16 | |
9. | Shear Modulus | G0,05 | E0,05 /16 |
The values of the characteristic strengths computed using the above equations, may differ with the tabulated values in Table-1 of EN 338:2003. However, in all such cases, the values obtained from the provided equations are treated as actual and is used by the program, as the values of Table-1 are based on these equations.
D5.C.2.1 Design Values of CharacteristicStrength
As per clause 2.4.1, Design values of a strength property shall be calculated as:
The member resistance in timber structure is calculated in STAAD.Pro according to the procedures outlined in EC5. This depends on several factors such as cross sectional properties, different load and material factors, timber strength class, load duration class, service class and so on. The methodology adopted in STAAD.Pro for calculating the member resistance is explained here.
D5.C.2.2 Check for Tension Stresses
If the direction of applied axial tension is parallel to the direction of timber grain alignment, the following formula should be checked per Equation 6.1 of EC-5 2004:
RATIO
If the direction of applied axial tension is perpendicular to the direction of timber grain alignment, the following formula should be checked:
RATIO
D5.C.2.3 Check for Compression Stresses
If the direction of applied axial compression is parallel to the direction of timber grain alignment, the following formula should be checked per Equation 6.2 of EC-5 2004:
RATIO
If the direction of applied axial compression is perpendicular to the direction of timber grain alignment, the following formula should be checked per Equation 6.3 of EC-5 2004:
RATIO
D5.C.2.4 Check for Bending stresses
If members are under bending stresses, the following conditions should be satisfied per Equations 6.11 and 6.12 of EC-5 2004.
D5.C.2.5 Check for Shear Stresses
Horizontal stresses are calculated and checked against allowable values per Equation 6.13 of EC-5 2004:
RATIO
D5.C.2.6 Check for Torsional Stresses
Members subjected to torsional stress should satisfy Equation 6.14 of EC-5 2004:
RATIO
D5.C.2.7 Check for Combined Bending and AxialTension
Members subjected to combined action of bending and axial tension stress should satisfy Equations 6.17 and 6.18 of EC-5 2004:
While evaluating the lateral-torsional stability of a member against the strong axis moment as per Cl.6.3.3.(3) [EN 1995-1-1 (2004)], the applicable bending stress is reduced for the case of axial tension combined with bending. Equation 6.33 [EN 1995-1-1 (2004)] is modified as:
This approach is adopted from Cl.5.4.2 of Manual for the design of timber building structures to Eurocode 5. The Institution of Structural Engineers / TRADA. 2007. London, UK.
D5.C.2.8 Check for Combined Bending and AxialCompression
If members are subjected to bending and axial compression stress, Equations 6.19 and 6.20 of EC-5 2004 should be satisfied:
D5.C.2.9 Stability check
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Column Stability check
The relative slenderness ratios should be calculated per Equations 6.21 and 6.22 of EC-5 2004.
Note: In STAAD.Pro z-z axis is the strong axis.If both λrel,z and λrel,y are less than or equal to 0.3 the following conditions should be satisfied:
In other cases, the conditions in Equations 6.23 and 6.24 of EC-5 2004 should be satisfied.
Note: In STAAD.Pro z-z axis is the strong axis.Where (Equations 6.25 through 6.28 of EC-5 2004):
The value of βc incorporated in the software is the one for solid timber (i.e., 0.2).
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Beam Stability check
If members are subjected to only a moment about the strong axis z, the stresses should satisfy Equation 6.33 of EC-5 2004:
Smzd/(Kcrit×Fmzd) ≤RATIO
Where a combination of moment about the strong z-axis and compressive force exists, the stresses should satisfy Equation 6.35 of EC-5 2004 (ref. to Equations 6.32 and 6.34 of the same):
[Smzd/(Kcrit×Fmzd)]2 + Sc0d/(Kcz×Fc0d) ≤RATIO
Where:
- Kcrit = 1.0 when λrel,m ≤ 0.75
- Kcrit = 1.56 - 0.75×λrel,m when 0.75 < λrel,m ≤ 1.4
- Kcrit = 1/( λrel,m)2 when 1.4 < λrel,m
- λrel,m = (fmk/Sm,crit)1/2
For hardwood, use Equation 6.30 of EC-5 2004:
Sm,crit = π×(E0,05×Iy×G0,05×Itor)1/2/(lef×Wz)For softwood, use Equation 6.31 of EC-5 2004:
Sm,crit = 0.78×b2×E0,05/(h×lef)