Report - Timber Post Calculator to BS 5268-2:2002

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	L_e = L × 1.0 = 1000 mm
Timber pieces	1
Service class of timber	3

Loading details

Dead load	F_d = 5.5 kN
Imposed (live) load	F_i = 2.1 kN
Total load	F = F_d + F_i = 7.6 kN

Modification factors

Timber service class modification factor K2 as table 16
Compression parallel to grain	K_2,par = 0.60
Min modulus of elasticity	K_2,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)	K_12,xx = 0.747
Compression member factor yy (calculated using equation in BS5268-2 Annex B)	K_12,yy = 0.568

Section properties

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

Check compressive stress parallel to grain xx axis

Compression stress parallel to grain	σ_c,par = 6.8 N/mm²
Permissible compression stress	σ_c,adm = σ_c,par × K_2,par × K₃ × K_12,xx = 3.81 N/mm²
Applied compression stress	σ_c,a = F × 10³ / A = 2.25 N/mm²
	σ_c,a <= σ_c,adm (2.246 N/mm² <= 3.811 N/mm² ) therefore OK

Check compressive stress parallel to grain yy axis

Compression stress parallel to grain	σ_c,par = 6.8 N/mm²
Permissible compression stress	σ_c,adm = σ_c,par × K_2,par × K₃ × K_12,yy = 2.9 N/mm²
Applied compression stress	σ_c,a = F × 10³ / A = 2.25 N/mm²
	σ_c,a <= σ_c,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

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