After this chapter, you should be able to
- Calculate rectangular-section properties using consistent structural axes.
- Check axial tension and compression including net sections.
- Assess flexural buckling about both principal axes.
- Check bending, shear, bearing, notches and lateral-torsional stability.
- Calculate instantaneous and final deformation and identify vibration assessments.
- Check tension/compression with uniaxial or biaxial bending.
- Identify the governing check and an effective redesign route.
2.1 Purpose of this chapterSource §2.1
Chapter 1 material data are applied to straight members carrying axial force, bending, shear and combined actions. The design route brings strength, local details, member stability and serviceability into one auditable sequence.
2.2 Integrated member-design philosophySource §2.2
Identify the action system first, establish the governing section and restraints, then run every applicable resistance, stability and SLS check before selecting the governing utilisation.
2.3 Geometry, axes and section propertiesSource §2.3
Use target dimensions, explicitly label y/z axes and strong/weak directions, and distinguish gross from net section wherever holes, notches or machining remove material.
Keep the source y/z axes and member orientation consistent throughout every stress and stability check.
2.4 Axial tension parallel to grainSource §2.4
Tension design uses the net tensile area, the design strength parallel to grain and any permitted size factor. Connection zones, eccentricity and splitting-sensitive details remain separate checks.
Holes and connection details can reduce the gross section to the governing net area.
2.5 Axial compression and cross-section strengthSource §2.5
Direct compression verifies average stress against design compression strength, but it is only a cross-section check. Slender members must also pass flexural buckling about both axes.
2.6 Column stability, effective length and flexural bucklingSource §2.6
Effective length comes from the actual support and restraint system. Calculate slenderness, relative slenderness and instability factors independently about y and z; the weaker route governs.
Both principal axes require assessment using justified effective lengths and the stability modulus E0,05.
2.7 Beam behaviour and governing failure modesSource §2.7
A beam design coordinates bending, shear, notches, local bearing, lateral-torsional stability, deflection and vibration rather than treating flexural strength as the sole criterion.
2.8 Bending resistance and biaxial bendingSource §2.8
Calculate bending stress about each active axis using the matching section modulus. For biaxial bending, apply both interaction arrangements and retain the governing result.
Notches, support regions and product-specific effective dimensions may require additional reductions.
2.9 Shear, loads near supports and notched endsSource §2.9
Use the EC5 effective shear width concept where applicable and check support-region notches with their geometry reduction. Deep or poorly proportioned notches require redesign rather than an optimistic nominal-section check.
2.10 Compression perpendicular to grain at supports and load pointsSource §2.10
Bearing stress is based on the effective contact area and is checked against the perpendicular-to-grain design resistance with a justified kc,90 factor for the support arrangement.
2.11 Lateral-torsional buckling of beamsSource §2.11
Full bending strength is only available when the compression edge and torsional restraint are genuinely effective. Otherwise determine relative bending slenderness and the lateral stability reduction.
2.12 Deflection, shear deformation and creepSource §2.12
Separate instantaneous permanent and variable-load deflections, include shear deformation where relevant, and form final deformation with the source SLS combinations and kdef treatment.
The complete final deflection route separates permanent and variable components and applies the relevant creep terms and SLS combinations.
2.13 Residential floor vibrationSource §2.13
A strength and deflection pass does not automatically establish acceptable floor dynamics. Vibration screening needs floor-system mass, stiffness, span, spacing, continuity and connection behaviour.
2.14 Where combined actions occurSource §2.14
Studs, portal members, rafters, truss chords and eccentrically connected members commonly carry axial force and bending simultaneously, sometimes about both axes.
2.15 Eccentricity and design stressesSource §2.15
Model load eccentricity as the corresponding moment and calculate axial and bending stresses with consistent signs, axes and load cases before using an interaction equation.
2.16 Combined axial tension and bendingSource §2.16
Tension and bending interaction is checked in both biaxial arrangements. Net-section reduction and connection eccentricity must be reflected before evaluating the interaction.
Both interaction arrangements are checked and the larger utilisation governs.
2.17 Combined axial compression and bending — cross-section checkSource §2.17
The cross-section interaction verifies concurrent compression and bending resistance but does not replace column buckling or lateral-torsional stability.
2.18 Compression and bending with column bucklingSource §2.18
Apply the appropriate column instability factor about each axis within the interaction route. Very weak-axis slenderness can dominate even when direct stresses are modest.
2.19 Beam-columns with lateral-torsional bucklingSource §2.19
When bending compression zones are not fully restrained, combine axial buckling with the reduced lateral-torsional bending resistance and retain the least favourable interaction.
2.20 Practical application to joists, rafters, purlins, studs and chordsSource §2.20
The same equations are assembled differently for each member type. Presets are useful only when the actual actions, axes, support conditions, restraints and local details remain visible.
2.21 Interactive calculator specificationSource §2.21
The source calculator calls the Chapter 1 material card, exposes actions, section, axial, beam, stability, combined and SLS results, and never hides unresolved assumptions behind one score.
Integrated Timber Member Design Calculator
Transparent straight-member interaction calculator benchmarked to WE-02D, with the wider Chapter 2 design scope and unresolved checks explicitly reported.
- Inputs
- Section b × h · Axial tension · Major/minor moment · Design strengths · Interaction factor
- Outputs
- Section properties · Concurrent stresses · Two EC5 interaction utilisations · Governing result
- Status states
- PASS · FAIL · INVALID INPUT
- Validation
- Approved against the supplied worked-example results; project-specific verification remains required
Integrated Timber Member Design Calculator
Source-benchmarked tension and biaxial-bending interaction check using WE-02D; later project checks must also address net sections, compression stability, shear, bearing, LTB and SLS where applicable.
Interaction 6.17 governs at 0.973.
- Area A
- 9600 mm²
- Major section modulus Wy
- 256000 mm³
- Minor section modulus Wz
- 96000 mm³
- Axial stress σt,0,d
- 2.29 N/mm²
- Major bending stress σm,y,d
- 8.98 N/mm²
- Minor bending stress σm,z,d
- 2.08 N/mm²
- Interaction u1
- 0.973
- Interaction u2
- 0.833
- Governing utilisation
- 0.973
Show source calculation trail
A = b h = 9600 mm2; Wy = b h2 / 6 = 256000 mm3; Wz = h b2 / 6 = 96000 mm3u1 = σt/ft,0,d + σm,y/fm,d + km σm,z/fm,d = 0.973u2 = σt/ft,0,d + km σm,y/fm,d + σm,z/fm,d = 0.833
2.22 Worked examples — integrated member designSource §2.22
Five source examples demonstrate net tension, column buckling, a joist governed by deflection, tension–biaxial bending and a beam-column governed by weak-axis stability.
WE-02A · Bolted D50 collar tie in tension
Check a 100 × 50 mm D50 collar tie with a bolt hole, Service Class 3, under permanent and short-term design tension.
- Net section
Anet = [100 − (10 + 2)] 50
Anet = 4,400 mm2 - Permanent case
σt,0,d,P = 13.5 × 103 / 4,400
σt,0,d,P = 3.07 N/mm2 - Short-term case
σt,0,d,S = 21.0 × 103 / 4,400
σt,0,d,S = 4.77 N/mm2 - Design strengths
ft,0,d,P = 12.46; ft,0,d,S = 17.44 N/mm2
ηP = 0.25; ηS = 0.27
Result. PASS — short-term governs at 0.27. The connection itself remains a separate Chapter 3 design.
WE-02B · D60 truss diagonal in compression
Check a pin-ended 50 × 100 mm D60 diagonal, 1.5 m long, for the Service Class 3 permanent-action case.
- Design strength
fc,0,d = 0.50(33) / 1.30
fc,0,d = 12.69 N/mm2 - Weak-axis slenderness
iz = 50 / √12 = 14.43 mm; λz = 1,500 / 14.43
λz = 103.9 - Relative slenderness
λrel,z = (103.9 / π) √(33 / 14,300)
λrel,z = 1.59 - Buckling resistance
kc,z = 0.34; Nc,Rd = 0.34(5,000)(12.69)
Nc,Rd = 21.6 kN
Result. Weak-axis buckling governs; a direct compression check alone would substantially overestimate resistance.
WE-02C · D60 residential floor joist
Check a 75 × 150 mm D60 joist at 450 mm centres over 5.0 m for ULS, local support, stability and SLS.
- ULS load
qd = 1.35(0.151) + 1.50(0.900)
qd = 1.554 kN/m - Bending
Md = qd L2 / 8 = 4.856 kNm
ηm ≈ 0.47 PASS - Shear/notch/LTB
ηv ≈ 0.26; ηnotch ≈ 0.57; ηLT ≈ 0.52
ULS checks pass - Instantaneous deflection
uinst = 3.47 + 20.71
24.18 mm > L/300 = 16.67 mm - Final deflection
ufin = 6.25 + 25.68
31.93 mm > 20 mm
Result. OVERALL FAIL — serviceability governs. Increasing depth, reducing span/spacing or establishing composite action is more effective than strength alone.
WE-02D · C24 tie under tension and biaxial bending
Check a 60 × 160 mm C24 tie under Nt,Ed = 22 kN, My,Ed = 2.30 kNm and Mz,Ed = 0.20 kNm.
- Section
A = 9,600 mm2; Wy = 256,000 mm3; Wz = 96,000 mm3
Section defined - Stresses
σt = 2.29; σm,y = 8.98; σm,z = 2.08 N/mm2
Concurrent stresses calculated - Interaction 6.17
u1 = 0.266 + 0.608 + 0.099
u1 = 0.973 PASS - Interaction 6.18
u2 = 0.266 + 0.426 + 0.141
u2 = 0.833 PASS
Result. PASS — interaction 6.17 governs at 0.973 with limited reserve.
WE-02E · D60 beam under bending and compression
Determine the maximum compression for a 75 × 150 mm D60 beam over 5.0 m under qd = 1.0 kN/m with weak-axis column buckling and LTB.
- Bending
My,Ed = qd L2 / 8 = 3.125 kNm
σm,d = 11.11 N/mm2 - LT stability
λrel,m = 0.881; kcrit = 0.900
kcrit fm,d = 33.23 N/mm2 - Weak-axis factor
λrel,z = 3.531
kc,z = 0.0759 - Maximum compression
Nc,Ed,max = (1.369)(11,250)
Nc,Ed,max = 15.4 kN
Result. Weak-axis buckling controls; improving restraint is more effective than increasing timber strength alone.
2.23 Design decisions when a member failsSource §2.23
Respond to the governing mechanism: change depth for stiffness/bending, width for bearing/shear, span or spacing for action effects, restraint spacing for stability, or the local notch/connection detail where it controls.
2.24 Common mistakes and design decisionsSource §2.24
Frequent errors include swapping axes, using gross area at holes, ignoring weak-axis buckling, assuming restraint without a load path, omitting notches/bearing and treating characteristic strength as a design resistance.
2.25 Chapter summarySource §2.25
A complete timber member design is a coordinated ULS, local-detail, stability and SLS verification with the governing load case and assumption set recorded.
Key points
- Use target geometry and consistent axes.
- Check net tension and direct compression before member stability.
- Beams require bending, shear, bearing, notch, LTB and SLS checks.
- Both combined-action arrangements may govern.
- Redesign the governing mechanism rather than only increasing strength class.
Source references recorded by the supplied chapter
- University of Moratuwa Timber Parts 2–4.
- EN 1995-1-1:2004+A2:2014, Sections 5–7.
- IStructE/TRADA Manual, Sections 5 and 8.
- Porteous & Kermani, Chapters 4–5.
- Swedish Wood, Design of Timber Structures, Volumes 1–3.