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## Timber post details

 Timber strength class C16 Post width a a = 47 mm Post width b b = 72 mm Height L = 1000 mm Effective height Le = L × 1.0 = 1000 mm Timber pieces 1 Service class of timber 3

 Dead load Fd = 5.5 kN Imposed (live) load Fi = 2.1 kN Total load F = Fd + Fi = 7.6 kN

## Modification factors

 Timber service class modification factor K2 as table 16 Compression parallel to grain K2,par = 0.60 Min modulus of elasticity K2,mod = 0.80 Load duration factor K3 = 1.25 Modulus of elasticity modification factor (BS 5268-2 clause 2.9) K9 = 1.00 Compression member factor xx (calculated using equation in BS5268-2 Annex B) K12,xx = 0.747 Compression member factor yy (calculated using equation in BS5268-2 Annex B) K12,yy = 0.568

## Section properties

 Minimum modulus of elasticity Emin = 5,800 Cross sectional area A = a × b = 3,380 mm² Second moment of area about xx axis Ixx = a × b³ / 12 = 1,460,000 mm4 Radius of gyration about xx axis ixx = √ ( Ixx / A ) = 20.79 mm Slenderness ratio λ = Le / ixx = 48.11 Slenderness ratio = 48.11 < 180 therefore OK Second moment of area about yy axis Iyy = b × a³ / 12 = 623,000 mm4 Radius of gyration about yy axis iyy = √ ( Iyy / A ) = 13.57 mm Slenderness ratio λ = Le / iyy = 73.70 Slenderness ratio = 73.7 < 180 therefore OK

## Check compressive stress parallel to grain xx axis

 Compression stress parallel to grain σc,par = 6.8 N/mm² Permissible compression stress σc,adm = σc,par × K2,par × K3 × K12,xx = 3.81 N/mm² Applied compression stress σc,a = F × 10³ / A = 2.25 N/mm² σc,a <= σc,adm (2.246 N/mm² <= 3.811 N/mm² ) therefore OK

## Check compressive stress parallel to grain yy axis

 Compression stress parallel to grain σc,par = 6.8 N/mm² Permissible compression stress σc,adm = σc,par × K2,par × K3 × K12,yy = 2.9 N/mm² Applied compression stress σc,a = F × 10³ / A = 2.25 N/mm² σc,a <= σc,adm (2.246 N/mm² <= 2.897 N/mm² ) therefore OK

## Design summary

 Permissible Applied/Actual Utilisation Result Slenderness ratio, xx axis 180 48.1 26.7 % OK Slenderness ratio, yy axis 180 73.7 40.9 % OK Compressive stress parallel to grain xx axis (N/mm²) 3.81 2.25 58.9 % OK Compressive stress parallel to grain yy axis (N/mm²) 2.9 2.25 77.5 % OK

## Notes

This design is in accordance with BS 5268-2:2002 Structural use of timber – Part 2: Code of practice for permissible stress design, materials and workmanship.

The limitations on bow in most strength grading rules are inadequate for the selection of material for columns. Particular attention should therefore be paid to the straightness of column, for example, by limiting bow or spring to approximately 1/300 of the length.

The effect of holes need not to be calculated where circular holes with diameters not exceeding 25% of the width of the member are positioned on the neutral axis at between 25% and 40% of the actual length from the end.

DEMO