Report - Internal Stud Wall Calculator to BS 5268-2:2002

Timber stud details

Timber strength class	C16
Width	b = 47 mm
Depth	d = 72 mm
Stud spacing	s = 600 mm
Stud wall comprises of 4 or more studs

Diagrams not to scale

Timber stud wall height details

Stud wall height	L_wall = 1,000 mm
Stud height	L = L_wall - (2 × b) = 906 mm
Stud effective height	L_eff = L × 0.85 = 770 mm
BS 5268-6.1 Clause 4.6.2 recommends L x 0.85 for stud walls restrained by sheathing or plasterboard lining.

Loading details

Total load	F_total = 4.7 kN/m
Total load per stud	F = F_total × s = 2.82 kN

Modification factors

Load duration factor	K₃ = 1.00
Bearing modification factor	K₄ = 1.00
Load sharing modification factor	K₈ = 1.10
Compression member factor (calculated using equation in BS5268-2 Annex B)	K₁₂ = 0.81

Section properties

Minimum modulus of elasticity	E_min = 5,800 N/mm²
Cross sectional area	A = b × d = 3,380 mm²
Second moment of area	I = b × d³ / 12 = 1,460,000 mm⁴
Radius of gyration	i = √ ( I / A ) = 20.8 mm
Slenderness ratio	λ = L_eff / i = 37.05
	37.05 < 180 therefore OK

Check compression stress parallel to grain on stud

Compression stress parallel to grain	σ_c,par = 6.8 N/mm²
Permissible compression stress	σ_c,adm = σ_c,par × K₃ × K₈ × K₁₂ = 6.08 N/mm²
Applied compression stress	σ_c,a = F × 10³ / A = 0.833 N/mm²
	σ_c,a <= σ_c,adm (0.833 N/mm² <= 6.075 N/mm² ) therefore OK

Check bearing stress perpendicular to grain on rail

Compression stress perpendicular to grain	σ_t,c,g,perp = 1.7 N/mm²
Permissible compression stress perpendicular to grain	σ_t,c,adm = σ_t,c,g,perp × K₃ × K₄ = 1.7 N/mm²
Applied compression stress	σ_c,a = F × 10³ / A = 0.833 N/mm²
	σ_c,a <= σ_t,c,adm (0.833 N/mm² <= 1.7 N/mm² ) therefore OK

Design summary

	Permissible	Applied/Actual	Utilisation	Result
Slenderness ratio	180	37	20.6 %	OK
Compression stress parallel to grain on stud (N/mm²)	6.08	0.83	13.7 %	OK
Bearing stress perpendicular to grain on rail (N/mm²)	1.7	0.83	49 %	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.

Timber to be covered, this calculation is not to be used for timber which is fully exposed to the elements.

The studs are restrained in the plane of panel by sheathing or plasterboard provided and constructed in accordance with recommendations given in BS 5268-6.1.

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.

These calculations are only applicable for stud walls consisting of four or more studs.

DEMO

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