Timber Design - Cheat Sheet
Your 30-minute exam reference for timber design under NSCP 2015 Chapter 6 Allowable Stress Design (ASD). Master the adjustment factor system, bending, shear, and compression checks. Every formula, every trap, every value you need.
Allowable Stress Design (ASD) Foundation
Formulas
F′ = F × C_D × C_M × C_t × C_F × C_L × C_P × C_r (and others as applicable)
Meaning
F = reference design value (species/grade); C_* = adjustment factors; F′ = adjusted allowable stress
Watch out
Do NOT apply all factors blindly. Some factors interact (e.g., C_F and C_L for bending interact; use the controlling one, not the product). Read NSCP carefully for which factors apply to each stress type.
When to use
Always — this is the backbone of every timber check; multiply reference value by the relevant adjustment factors for the loading and member type.
f ≤ F′
Meaning
f = actual stress (from loads); F′ = adjusted allowable; design is OK if actual ≤ allowable
Watch out
Forgetting to compute f correctly (e.g., using gross area instead of net area for tension; using the wrong section modulus formula for bending).
When to use
Final check for every bending, shear, and compression member
Common values
Value
0.9
Symbol
C_D,perm
Quantity
Load duration factor C_D (permanent load)
Value
1.0
Symbol
C_D,standard
Quantity
Load duration factor C_D (standard 10-year load)
Value
1.15
Symbol
C_D,const
Quantity
Load duration factor C_D (2-month construction load)
Value
1.25
Symbol
C_D,7day
Quantity
Load duration factor C_D (7-day load)
Value
1.6
Symbol
C_D,wind
Quantity
Load duration factor C_D (wind or seismic load)
Value
2.0
Symbol
C_D,impact
Quantity
Load duration factor C_D (impact load)
Important facts
- ASD is the mandated method for timber under NSCP 2015 Chapter 6 (not LRFD).
- Wood is unique: C_D varies from 0.9 (permanent) to 2.0 (impact), rewarding short-duration loads.
- Reference values F are tabled in NSCP Appendix 6.A or equivalent species/grade tables.
- Adjustment factors depend on moisture content (≥20% moisture is 'wet service'), temperature, and member geometry.
- C_P (column stability) and C_L (beam stability) are the wood analogs of buckling — essential for slender members.
Key definitions
Reference Design Value (F)
Example
F_b = 16.5 MPa for a specific grade of Mahogany or Pine — before any adjustments.
Tabulated stress for a timber species and grade under standard conditions; reduced by adjustment factors for real design.
Adjustment Factor (C)
Example
C_D = 1.6 for wind/seismic (short duration); C_D = 0.9 for permanent loads — same timber, different load.
Multiplier reflecting load duration, moisture, temperature, member size, stability, and other conditions.
Allowable Stress Design (ASD)
Example
Unlike LRFD steel (load factor on loads), timber ASD divides the safe load by a safety factor into the allowable.
Working-stress method: design stress (actual) must not exceed allowable (reference × factors); safety is in the allowable, not in load factors.
Diagrams to know
- Adjustment factor flow diagram: which factors apply to bending, shear, compression.
- C_D vs. load duration curve (or table): 0.9–2.0 over permanent to impact.
Bending (Flexural Members)
Formulas
f_b = M / S ≤ F′_b
Meaning
f_b = actual bending stress (MPa); M = bending moment (N⋅mm); S = section modulus (mm³); F′_b = adjusted allowable bending stress
Watch out
Using gross section modulus when the section is notched or perforated; use net S. Also, many students forget to apply C_L (beam stability factor) for lateral-torsional buckling of slender beams.
When to use
Every timber beam under bending load; M is max moment and S is for the governing orientation.
S = b × h² / 6 (rectangular cross-section)
Meaning
b = width (smaller dimension); h = depth (larger dimension); S in units of width × depth².
Watch out
Some codes define b and h differently; always use the formula S = I/c where I = moment of inertia and c = distance to extreme fiber. For rectangles, S = bh²/6 is correct.
When to use
Standard rectangular timber sections (sawn lumber, rough lumber).
F′_b = F_b × C_D × C_M × C_t × C_F × C_L × C_r (and others as applicable)
Meaning
F_b = reference bending stress; each C is an adjustment; for bending, C_r (repetitive member) may apply if three or more members spaced ≤600 mm.
Watch out
C_F (size factor) and C_L (beam stability) often compete for the same failure mode in sawn lumber. NSCP may require using the more conservative (lower) value or a specific interaction formula, not the product.
When to use
Compute allowable bending stress before comparing to f_b.
C_L = (1 + λ_b) / 1.9 − √[(1 + λ_b)² / 3.61 − λ_b / 0.95] (for sawn lumber, slenderness formula)
Meaning
λ_b = slenderness ratio for lateral-torsional buckling; reduces C_L for deep, unsupported beams.
Watch out
This formula is approximate and varies by code edition; NSCP may use a simplified lookup or a different formula. Verify in the applicable code edition. If the beam is well-braced (e.g., joists on a deck), C_L ≈ 1.0.
When to use
When a beam is slender in the lateral direction and may buckle sideways.
I = b × h³ / 12 (moment of inertia for rectangular section)
Meaning
b = width; h = depth; I governs deflection and lateral buckling.
Watch out
Ensure you use the correct h (the dimension perpendicular to the bending axis).
When to use
Computing deflection or designing for lateral stability.
Common values
Value
1.15 (for three or more spaced ≤600 mm); 1.0 otherwise
Symbol
C_r
Quantity
Repetitive member factor C_r
Value
1.0 (no lateral-torsional buckling concern)
Symbol
C_L,braced
Quantity
Fully braced beam stability factor C_L
Important facts
- Bending is the primary design driver for most timber beams.
- Maximum moment M occurs at the center of a simply supported uniform beam: M = w L² / 8.
- Section modulus scales with depth: S ∝ h². A deeper beam is much stronger in bending.
- Lateral-torsional buckling is a failure mode unique to beams; shear and compression are more straightforward.
- For sawn lumber, size factors C_F and beam stability C_L interact; use the controlling value (check your NSCP edition for the specific rule).
- Repetitive members (three or more, ≤600 mm spacing) get a 15% bonus (C_r = 1.15) because load sharing increases the effective strength.
Key definitions
Section Modulus (S)
Example
A 150 × 300 mm sawn beam has S = (150 × 300²) / 6 = 2.25 × 10⁶ mm³.
Geometric property S = I / c (moment of inertia divided by distance to extreme fiber); larger S = stronger beam in bending.
Lateral-Torsional Buckling
Example
A long, deep timber beam with no lateral bracing along its span may buckle to the side under a bending moment.
Sideway buckling of a beam's compression flange when not braced perpendicular to bending; C_L accounts for this.
Repetitive Member Factor (C_r)
Example
A deck with joists on 400 mm centers gets C_r = 1.15, increasing allowable bending stress.
Upward adjustment (often 1.15) when three or more identical members are spaced ≤600 mm and act together (e.g., floor joists).
Diagrams to know
- Bending moment diagram (BMD) for simple beams (parabolic for uniform load, triangular for point load).
- Shear force diagram (SFD) to identify max shear location.
- Lateral bracing effect on C_L: fully braced → C_L = 1.0; unbraced → C_L < 1.0 as slenderness increases.
Reactions or equations
f_b = M / S
Note
Do not confuse this with shear stress or compression; f_b is purely bending-induced normal stress on fibers.
Conditions
M in N⋅mm, S in mm³; both computed at the section of maximum moment.
Horizontal Shear (Parallel to Grain)
Formulas
f_v = (3 V) / (2 A) ≤ F′_v (rectangular cross-section)
Meaning
f_v = actual shear stress (MPa); V = shear force (N); A = gross cross-sectional area (mm²); F′_v = adjusted allowable shear stress; factor 1.5 accounts for parabolic shear distribution.
Watch out
Forgetting the 1.5 factor. Also, at notched supports, shear stress is amplified significantly — use the reduced net depth and an amplification formula from NSCP (often the d / d_n ratio is large, making shear critical).
When to use
Short, deep beams where shear governs (high V, low M). Always check; wood is weak in parallel shear.
F′_v = F_v × C_D × C_M × C_t × C_H (and others per NSCP)
Meaning
F_v = reference shear stress; C_D, C_M, C_t are standard adjustments; C_H may account for notches or reduced section.
Watch out
Shear adjustment factors differ slightly from bending factors; C_L does not apply to shear (shear is a different failure mode). Some factors like C_H (notch factor) are specific to shear and compression.
When to use
Compute allowable shear before comparing to f_v.
f_v,notch = f_v × (d / d_n) (amplified shear at notched supports)
Meaning
d = full beam depth; d_n = net depth at the notch; amplification can be 1.5 to 3× for deep notches.
Watch out
Notched beams are a classic CELE trap. Do NOT forget this check. Many students ignore the notch entirely and fail shear. Always examine supports for notches or other reductions.
When to use
When a beam is notched at a support to rest on a ledger or pocket; shear capacity drops sharply.
Common values
Value
0.8–1.5 MPa (species and grade dependent)
Symbol
F_v
Quantity
Typical reference shear stress F_v (timber)
Important facts
- Shear stress f_v = (3V) / (2A) for rectangular sections; the 1.5 factor reflects the actual shear distribution.
- Wood is inherently weak in shear parallel to grain; shear often governs for short, deep beams.
- Shear check must be done at distances d (or c for round logs) from the support to account for stress concentration at the bearing.
- Notched beams lose significant shear capacity; a notch at a support can increase shear stress by 50–200% depending on notch depth.
- F_v is typically 0.5–1.5 MPa, much lower than F_b (bending), making shear a frequent design driver.
- At mid-span (low V), shear is rarely the control; it matters near supports and over interior posts.
Key definitions
Horizontal Shear (Parallel to Grain)
Example
In a timber beam spanning 2 m under 10 kN point load, shear is high near the supports and may govern design.
Shear stress acting along grain direction within a beam; timber is weak here (low F_v).
Notched Beam
Example
A beam notched 50 mm deep on a 200 mm beam (d_n = 150 mm) at a support sees 1.33× shear amplification.
Beam with a rectangular cut (notch) at a support to reduce bearing area or fit on a ledger; drastically reduces shear and bearing capacity.
Diagrams to know
- Shear force diagram (SFD): linear for uniform load, showing V = w L / 2 at supports.
- Notch amplification diagram: showing how net depth reduction and V increase shear stress.
Reactions or equations
V = w L / 2 (for uniform load on simply supported beam)
Note
Shear is zero at mid-span for symmetric loading, maximum at reactions.
Conditions
w = load per unit length; L = span; max shear occurs at supports.
Compression Parallel to Grain
Formulas
f_c = P / A ≤ F′_c
Meaning
f_c = actual axial compression stress (MPa); P = axial load (N); A = cross-sectional area (mm²); F′_c = adjusted allowable compression stress.
Watch out
Forgetting to account for slenderness (C_P factor). A column is not just A × F_c; buckling reduction via C_P is essential for slender members.
When to use
For timber columns or axially loaded posts; also used for bearing on supports (perpendicular to grain uses different formula).
F′_c = F_c* × C_P, where F_c* = F_c × C_D × C_M × C_t × C_F
Meaning
F_c* = adjusted reference compression stress (all factors except C_P); C_P = column stability factor (wood buckling reduction); product gives allowable.
Watch out
Do NOT apply C_P directly to the reference F_c; it applies to F_c* (which includes D, M, t, F factors). Mistaking the order is a common error.
When to use
Always compute F_c* first, then apply C_P based on slenderness.
F_{cE} = (0.822 × E′_{min}) / (ℓ_e / d)²
Meaning
F_{cE} = critical Euler buckling stress for the column; E′_{min} = adjusted minimum modulus (adjusted for wet, temp, etc.); ℓ_e = effective length; d = least dimension.
Watch out
Use the MINIMUM modulus, not the average; E′_{min} is typically E × 0.66 or given in tables. Also, ℓ_e (effective length) is K × L, where K depends on end conditions (fixed, pinned, etc.).
When to use
Used within the C_P formula to compute the buckling reduction factor.
C_P = [(1 + β) / (2c)] − √{[(1 + β) / (2c)]² − (β / c)}, where β = F_{cE} / F_c*, c = 0.8 (sawn), 0.90 (glulam)
Meaning
C_P computes the wood analog of the buckling reduction (ϕ_b for steel or χ in ACI); β is the Euler-to-yield ratio; c is a material constant.
Watch out
This formula is algebraically messy; a calculator error is easy. Also, c = 0.8 for sawn lumber (typical), 0.90 for glulam — using the wrong c gives wrong C_P. If β > ~1, C_P ≈ 1 (short column); if β << 1, C_P drops (slender column).
When to use
Once F_{cE} and F_c* are found, use this to get C_P.
ℓ_e / d = K L / d (slenderness ratio for wood columns)
Meaning
K = effective length factor (0.5 fixed, 1.0 pinned, 2.0 cantilever); L = actual unsupported length; d = least width/depth of section.
Watch out
For timber, end conditions matter: pinned = K = 1.0 is the baseline. Fixed ends reduce K. Do not use the same K table as steel without checking timber code.
When to use
Computing the slenderness ratio to find F_{cE}.
Common values
Value
0.8
Symbol
c
Quantity
Material constant c (sawn lumber)
Value
0.90
Symbol
c
Quantity
Material constant c (glulam)
Value
1.0
Symbol
K_pinned
Quantity
Effective length factor K (both ends pinned)
Value
0.5
Symbol
K_fixed
Quantity
Effective length factor K (both ends fixed)
Value
2.0
Symbol
K_cantilever
Quantity
Effective length factor K (one end fixed, one free)
Important facts
- Compression parallel to grain is similar to simple bearing; the C_P factor makes it wood's version of column buckling.
- Slenderness ratio ℓ_e / d is the key: short stocky columns have C_P ≈ 1.0 (little reduction); slender columns have C_P << 1.0 (major reduction).
- Wood columns use NSCP formulas; they are not the same as AISC steel columns (different material constants, c = 0.8 vs. other values).
- F_{cE} uses Euler formula with the minimum modulus E′_{min}; this is conservative but accounts for material variability.
- C_P depends on both ℓ_e / d and the ratio F_{cE} / F_c*; long, slender columns are heavily reduced.
- The formula for C_P can yield a result between 0 and 1; C_P = 1 means no buckling reduction (short column).
Key definitions
Column Stability Factor (C_P)
Example
A 150 × 150 mm sawn timber column with ℓ_e / d = 20 and F_c* = 10 MPa has C_P ≈ 0.78, reducing allowable to 7.8 MPa.
Reduction factor for buckling; similar to ϕ_b in steel or χ in concrete; accounts for slenderness (ℓ_e / d) and material behavior.
Effective Length (ℓ_e)
Example
A 3 m column with pinned ends: ℓ_e = 1.0 × 3000 = 3000 mm. If fixed at both ends: ℓ_e = 0.5 × 3000 = 1500 mm.
ℓ_e = K × L; accounts for end conditions (fixed, pinned, free) and determines buckling behavior.
Least Dimension (d)
Example
A 100 × 300 mm beam used as a column has d = 100 mm (least), so ℓ_e / d is based on 100, not 300.
Smaller of width or depth of a rectangular cross-section; used in slenderness ratio because buckling occurs about the weaker axis.
Diagrams to know
- C_P vs. slenderness ratio (ℓ_e / d) curve: C_P = 1 for short columns; C_P → 0 as ℓ_e / d increases (classic buckling curve shape).
- Effective length diagram: showing K values for different end conditions (fixed, pinned, cantilever).
Reactions or equations
P_{allow} = F′_c × A = (F_c* × C_P) × A
Note
This is the fundamental timber column design equation; if P > P_{allow}, the column fails in buckling.
Conditions
P_{allow} is the maximum axial load the column can support; must not exceed actual load P.
Compression Perpendicular to Grain (Bearing)
Formulas
f_c⊥ = P / (A bearing) ≤ F′_c⊥
Meaning
f_c⊥ = actual bearing stress perpendicular to grain (MPa); P = concentrated load (N); A_bearing = actual contact area perpendicular to grain (mm²); F′_c⊥ = adjusted allowable.
Watch out
Ensure you use the actual bearing area (not the full cross-section). If a beam rests on a 100 mm wide ledge, use only that 100 mm length in calculating A_bearing. Also, F_c⊥ is much weaker than F_c (parallel), typically 1/3 to 1/2 the value.
When to use
Checking timber members resting on ledges, bearing plates, or other supports where load is perpendicular to grain.
F′_c⊥ = F_c⊥ × C_D × C_M × C_t (typically; no C_F, C_P, or C_L for perpendicular compression)
Meaning
F_c⊥ = reference value perpendicular to grain; adjusted by D, M, t only (no size or stability factors).
Watch out
Some codes include a bearing area factor C_b (length of bearing divided by depth of member); NSCP may or may not include this — check the edition.
When to use
Compute the allowable perpendicular compression stress; usually fewer adjustments than parallel.
Common values
Value
2–4 MPa (varies by species)
Symbol
F_c⊥
Quantity
Typical reference bearing stress F_c⊥ (perpendicular to grain)
Important facts
- F_c⊥ is typically 2–4 MPa, much lower than F_c (parallel, often 8–12 MPa).
- Bearing area A is the contact length times the member width; use only the actual contact zone.
- If a joist bears on a sill, the bearing length is often only the width of the supporting wall or beam (often 50–100 mm).
- Bearing perpendicular can fail by crushing and indentation; it is a localized failure near supports.
Key definitions
Bearing Perpendicular to Grain
Example
A 150 × 300 mm beam (300 mm depth) resting on a 100 mm ledge has bearing area = 150 × 100 = 15,000 mm².
Load applied normal to the wood grain direction (e.g., a beam pressing down on a ledger); wood is much weaker here than parallel.
Diagrams to know
- Bearing area diagram: showing the contact zone (ledge width × member width).
Tension Parallel to Grain
Formulas
f_t = P / A_net ≤ F′_t
Meaning
f_t = actual tensile stress (MPa); P = axial tensile load (N); A_net = net cross-sectional area accounting for holes/knots (mm²); F′_t = adjusted allowable tension stress.
Watch out
USE THE NET AREA, not gross. Any bolt holes, knots, or defects reduce A. Also, ensure the net section is at the critical plane (where a hole or defect is largest or where the grain runs out).
When to use
For tied members, tension chords of trusses, or strut members in tension.
F′_t = F_t × C_D × C_M × C_t × C_g
Meaning
F_t = reference tension stress; C_g = grain angle factor (reduces strength if grain is not parallel to load direction).
Watch out
Timber members in tension must have a relatively straight grain (C_g = 1 for 0° angle). If grain is at an angle, C_g < 1 and tension capacity drops. This is less commonly tested than bending and compression but can appear on exams.
When to use
Compute the adjusted tension allowable; C_g is unique to tension.
Common values
Value
5–10 MPa (varies by species and grade)
Symbol
F_t
Quantity
Typical reference tension stress F_t (parallel to grain)
Important facts
- Tension parallel to grain is less common in timber design than bending or compression.
- Grain angle significantly reduces tension capacity; straight grain is required.
- Knots and defects are critical in tension; the net area at the worst cross-section governs.
- Typical F_t is 5–10 MPa, moderate compared to bending and compression.
Key definitions
Net Section (Tension)
Example
A 100 × 300 mm beam with a 25 mm diameter bolt hole has A_net = 100 × 300 − 100 × 25 = 27,500 mm².
Cross-sectional area minus the area of holes, knots, or defects in the critical failure plane.
Adjustment Factors — Quick Reference
Common values
Value
1.0
Symbol
C_M,dry
Quantity
C_M (dry service < 12% moisture)
Value
0.80–0.97 (varies by stress type)
Symbol
C_M,wet
Quantity
C_M (wet service > 20% moisture)
Value
1.0
Symbol
C_t,normal
Quantity
C_t (normal temperature, < 100°C)
Value
1.0
Symbol
C_r,single
Quantity
C_r (single member or wide spacing)
Value
1.15
Symbol
C_r,repetitive
Quantity
C_r (three+ members, ≤600 mm spacing)
Important facts
- C_D is the most impact-heavy adjustment; 0.9 to 2.0 range is huge.
- C_M applies whenever moisture is elevated; outdoor timber and green lumber always get C_M < 1.0.
- C_F applies mainly to sawn lumber (2×4, 2×6, etc.); glulam and large timbers have C_F close to 1.0.
- C_L and C_P are buckling-type factors; their values depend on slenderness ratios and must be computed, not just looked up (though NSCP tables may provide shortcuts).
- C_r is a bonus for repetitive members; joists and similar elements spaced close together get this.
- No single formula applies all adjustments equally; each stress type (bending, shear, compression) uses a specific subset of factors.
Key definitions
C_D — Load Duration Factor
Example
Permanent load: C_D = 0.9 (10% reduction). Wind/seismic: C_D = 1.6 (60% increase). Impact: C_D = 2.0.
Multiplier reflecting how long the load acts; wood is stronger for brief loads, weaker for permanent loads.
C_M — Wet Service Factor
Example
C_M = 1.0 for dry service (< 12% MC). C_M = 0.85–0.97 for wet service (e.g., outdoor, always damp).
Reduction for moisture content > 20% (equilibrium moisture during service).
C_t — Temperature Factor
Example
C_t = 1.0 for normal temperature. C_t = 0.8 at 150°C (not common in structural design).
Reduction for service temperatures > 100°C.
C_F — Size Factor (Sawn Lumber)
Example
C_F = 1.5 for shallow beams. C_F = 1.0 for large glulam beams. Decreases as member size increases.
Upward adjustment for small cross-sections (smaller members often stronger per unit area).
C_L — Beam Lateral Stability Factor
Example
C_L = 1.0 fully braced. C_L = 0.6–0.9 for longer unsupported spans (varies with slenderness).
Reduction for lateral-torsional buckling of unsupported compression flange.
C_P — Column Stability Factor
Example
C_P = 1.0 for short, stocky columns. C_P = 0.3–0.7 for slender columns with high ℓ_e/d.
Reduction for axial column buckling (Euler-type).
C_r — Repetitive Member Factor
Example
Floor joists 400 mm on center: C_r = 1.15. Single beam or joists > 600 mm apart: C_r = 1.0.
15% upward adjustment when three or more members are spaced ≤ 600 mm and act together (load sharing).
C_b — Bearing Area Factor
Example
C_b = 1.25 + (0.375 × L_b / d) where L_b = bearing length, d = member depth (if NSCP includes it).
May apply to compression perpendicular to grain based on bearing length vs. member depth (NSCP variation).
Diagrams to know
- Adjustment factor interaction table: showing which factors apply to which stress types (bending, shear, parallel compression, perpendicular compression, tension).
Modulus of Elasticity (E) — Deflection & Stability
Formulas
E′ = E × C_M × C_t (adjusted modulus for deflection and buckling)
Meaning
E = reference modulus (from tables); E′ = adjusted for wet service and temperature; no other modulus factors.
Watch out
For buckling (C_P formula), use E′_{min} (typically E × 0.66), not the average modulus. For deflection, use the standard adjusted E′. Do not apply C_D to modulus — only for stress.
When to use
Computing deflection (Δ = 5wL⁴ / 384 E′I) or Euler buckling stress (F_cE = 0.822 E′_min / (ℓ_e/d)²).
Common values
Value
9650 MPa
Symbol
E_SouthernPine
Quantity
Reference modulus E (Southern Pine, typical)
Value
7550 MPa
Symbol
E_SPF
Quantity
Reference modulus E (Spruce-Pine-Fir, typical)
Value
0.66 × mean E
Symbol
E_min
Quantity
Minimum modulus (rule of thumb)
Important facts
- E is used for deflection checks and buckling (Euler formula), not directly for stress checks (stress uses adjusted F).
- E is adjusted only by C_M and C_t (moisture and temperature); no C_D, C_F, C_L, or C_P for modulus.
- The distinction between mean E and E_min is critical: buckling formulas use E_min to be conservative.
- Deflection limits for timber are typically L/240 (live load) or L/180 (total load); E′ determines if a member will deflect excessively.
Key definitions
Modulus of Elasticity (E)
Example
Southern Pine: E ≈ 9650 MPa. Spruce-Pine-Fir: E ≈ 7550 MPa. Varies by species.
Stiffness measure; higher E means less deflection and less buckling for a given slenderness.
Minimum Modulus (E_min)
Example
For a species with mean E = 10,000 MPa, E_min ≈ 6,600 MPa is used in the F_cE formula.
Conservative estimate (often 0.66 × mean E) used in Euler buckling formula to be safe; accounts for material variability.
Diagrams to know
- Deflection curve for a simply supported beam: maximum at mid-span, governed by Δ = 5wL⁴ / 384 E′I.
Reactions or equations
F_cE = (0.822 × E′_min) / (ℓ_e / d)²
Note
This is the critical stress above which the column buckles elastically (wood analog of Euler buckling in steel).
Conditions
Euler buckling stress for timber columns; E′_min is adjusted minimum modulus; ℓ_e/d is slenderness ratio.
Design Workflow & Board-Style Problems
Important facts
- STEP 1: Identify loads (dead, live, wind, etc.) and determine load duration → C_D.
- STEP 2: Assume a trial section or use design formulas to find required section.
- STEP 3: Compute adjusted allowable stresses (F′) for bending, shear, compression from reference values and adjustment factors.
- STEP 4: Calculate actual stresses (f_b, f_v, f_c) from loads and section properties.
- STEP 5: Verify each stress: f ≤ F′. If not, iterate with a larger section.
- STEP 6: Check deflection (if applicable): Δ ≤ limit.
- STEP 7: Document all adjustments and assumptions (NSCP reference, species/grade, end conditions, moisture, etc.).
Key definitions
Design vs. Check
Example
Design: M = 20 kN·m, F′_b = 12 MPa → find S_req = M / F′_b = 1.67 × 10⁶ mm³ → choose beam. Check: given 150×300 beam, verify f_b ≤ F′_b.
Design: given load and limits, find required size/section. Check: given section and load, verify it is safe.
Diagrams to know
- Design decision tree: identify load case → select C_D → compute reference stresses → apply adjustment factors → calculate section properties → verify all stress checks.
Must remember
- ASD Baseline: F′ = F × (product of C factors); then verify f ≤ F′. Wood design is NOT LRFD — no load factors. Safety is in the allowable, not load amplification.
- C_D is unique to wood and ranges from 0.9 (permanent) to 2.0 (impact). This single factor can swing allowable stress by a factor of 2.2×. Always identify the load duration first.
- Bending formula: f_b = M / S ≤ F′_b. Section modulus S ∝ h² (depth squared). Doubling depth multiplies strength by 4. This is why deep beams are favored.
- Shear formula: f_v = (3V) / (2A) ≤ F′_v. The 1.5 factor is built-in (not 3V/A like some other materials). Wood is weak in shear parallel to grain (F_v typically 0.5–1.5 MPa).
- Notched beams are a CELE trap. Shear stress is amplified (d / d_n) and bearing area is reduced. Always check supports for notches; they can turn a safe beam into a failure.
- Column Stability: F′_c = F_c* × C_P, where F_c* has all adjustments except C_P. The C_P factor (buckling reduction) depends on ℓ_e / d and can drop allowable to 20–30% for slender columns. Forgetting C_P is a major error.
- Effective Length (ℓ_e = K × L): pinned ends K = 1.0 (baseline), fixed K = 0.5 (shorter), cantilever K = 2.0 (much longer). Even a small change in end condition alters slenderness and buckling behavior.
- C_P formula (messy algebra): β = F_cE / F_c*; use c = 0.8 for sawn lumber. If you mess up c or the algebra, C_P is wrong and the column design fails. Double-check or use code tables.
- Modulus E is NOT adjusted by C_D or C_F. Only C_M and C_t apply to E. For buckling, use E′_min (conservative); for deflection, use adjusted E′. Confusing these is common.
- Repetitive Members (C_r = 1.15): Three or more joists/rafters spaced ≤600 mm get a 15% bonus. This is for load sharing. Single beams or wide spacing: C_r = 1.0. Easy to forget but helps pass the design.
Last minute tips
- Before diving into calculations, identify the load duration (C_D) and moisture condition (C_M) — these two adjustments dominate the allowable stress and are easy to miss. A single wrong C_D or C_M can make your answer way off.
- Always check SHEAR at supports and NOTCHES at supports separately. Shear often governs short, deep timber beams and notches amplify it further. This is the #1 trap on the exam.
- For timber COLUMNS, compute C_P correctly: (1) find F_cE using E′_min and ℓ_e/d, (2) compute β = F_cE / F_c*, (3) plug into the C_P formula with the correct c value (0.8 sawn, 0.90 glulam). One wrong step and the column fails.
- NET AREA is critical for tension and for shear at notches. Do not use gross area for these checks. Knots, bolt holes, and notches reduce effective area and increase stress.
- If a problem says 'design' (find section) vs. 'check' (verify given section), use the right method: Design uses S_req = M / F′; Check uses f = M / S and verifies f ≤ F′. Mixing them up wastes time and causes errors.
Comparison tables
Stress Types, Formulas, and Governing Adjustment Factors
| Stress Type | Formula | Reference Value | Key Adjustments | Typical F′ Range (MPa) |
|---|---|---|---|---|
| Bending (Flexure) | f_b = M / S | F_b | C_D, C_M, C_t, C_F, C_L, C_r (interaction per NSCP) | 8–25 (varies by grade, species, adjustments) |
| Shear (Parallel to Grain) | f_v = 3V / 2A | F_v | C_D, C_M, C_t, C_H (notch reduction if applicable) | 0.5–2.0 |
| Compression Parallel | f_c = P / A | F_c | C_D, C_M, C_t, C_F (then × C_P for buckling) | 5–12 (before C_P); ↓ by C_P for slender columns |
| Compression Perpendicular | f_c⊥ = P / A_bearing | F_c⊥ | C_D, C_M, C_t (rarely C_F; may include C_b bearing length factor) | 1–4 |
| Tension Parallel | f_t = P / A_net | F_t | C_D, C_M, C_t, C_g (grain angle factor) | 5–10 |
Effective Length Factor K — End Conditions (Wood Columns)
| End Condition | K Value | Description | Example |
|---|---|---|---|
| Both ends pinned (standard) | 1.0 | Free to rotate at both ends; classic column case. | Two columns sitting on bases with pin connections. |
| Both ends fixed | 0.5 | Moments resist rotation; much stiffer, reduces effective length. | Columns rigidly embedded in concrete or welded to rigid frames. |
| One end fixed, one pinned | 0.7 | Intermediate case; one end is rigid, one free to rotate. | Column welded at base but pin-jointed at top. |
| One end fixed, one free (cantilever) | 2.0 | One end is rigid, the other is unsupported; worst case, large effective length. | Cantilever posts or flagpoles. |
Load Duration Categories and C_D Values (NSCP 2015, Wood)
| Load Type / Duration | C_D Factor | Load Duration | Typical Application |
|---|---|---|---|
| Permanent Load | 0.9 | > 10 years continuously | Dead load, long-term sustained load; reduces allowable because wood degrades under prolonged stress. |
| Standard (10-year) | 1.0 | Standard design load (baseline) | Normal floor live load, typical design case (baseline for reference values). |
| 2-month Load | 1.15 | ~ 2 months (construction phase, temporary loads) | Formwork load during construction; higher allowable due to short duration. |
| 7-day Load | 1.25 | ~ 1 week (short-term) | Emergency repairs, temporary barriers; higher allowable. |
| Wind or Seismic Load | 1.6 | Brief (seconds to minutes) | Wind gusts, earthquake; wood is temporarily stronger in short bursts. |
| Impact Load | 2.0 | Instantaneous (fraction of second) | Dropped object, sudden impact; maximum allowable boost; rarely used in structural design. |
C_F (Size Factor) Examples — Sawn Lumber (Approximate)
| Member Dimension / Category | C_F (Bending) | C_F (Compression) | Note |
|---|---|---|---|
| 2×4, 2×6 (small sawn) | 1.3–1.5 | 1.1–1.2 | Smaller sections get size bonus; higher strength per unit area. |
| 2×8 to 2×10 | 1.1–1.2 | 1.05–1.1 | Medium sections; intermediate C_F. |
| 2×12 and larger sawn | 1.0 | 1.0 | Large sawn lumber; no size bonus (or very small). |
| Glued-laminated (Glulam) | 1.0 (approx.) | 1.0 (approx.) | Engineered product; size factor typically 1.0 for most glulam beams. |
C_M (Wet Service Adjustment) — Typical Values
| Condition | Moisture Content | C_M (Bending, Compression Parallel) | C_M (Compression Perpendicular) | C_M (Tension, Shear) |
|---|---|---|---|---|
| Dry Service (typical indoor) | < 12% | 1.0 | 1.0 | 1.0 |
| Wet Service (outdoor, damp) | > 20% (equilibrium during service) | 0.8–0.85 | 0.67–0.8 | 0.80–0.97 (varies) |
Notched Beam Shear Amplification — Quick Check
| Notch Depth (mm) | Full Depth (mm) | Net Depth d_n (mm) | Amplification d / d_n | Interpretation | |
|---|---|---|---|---|---|
| 0 (no notch) | — | 200 | 200 | 1.0 | Standard shear; no amplification. |
| 25 | 25 | 200 | 175 | 1.14 | Minor notch; 14% increase in shear stress. |
| 50 | 50 | 200 | 150 | 1.33 | Moderate notch; 33% increase — significant. |
| 75 | 75 | 200 | 125 | 1.6 | Deep notch; 60% increase — critical risk of shear failure. |
Diagrams
Timber Design Adjustment Factors & Their Applications
Mind map showing the hierarchy of adjustment factors in timber ASD and their typical values. Use this to quickly identify which factors apply to your member and load case.
Timber Member Design Check Workflow
Step-by-step flowchart for checking a timber member. Start by identifying load duration and moisture, apply all relevant adjustment factors, calculate allowables, compute actual stresses, and verify each stress check. Iterate if any check fails.
Timber Column (Compression) Design — C_P Computation
Detailed flowchart for computing column stability factor C_P and allowable compression stress. This is critical for timber columns; missing or miscalculating C_P is a common exam error.
Beam Stress Check Decision Tree — Which Stress Controls?
State diagram showing the sequence of stress checks for a timber beam. Start with bending (primary), then shear (critical at supports), bearing (at supports), and deflection (serviceability). Each failure triggers iteration.
Typical Reasons for Timber Member Failure on PRC CELE Exams
Pie chart showing the breakdown of common exam errors in timber design. Load duration (CD) and notched shear are the biggest traps; column buckling (CP) and adjustment factors are frequent mistakes.