CELE Steel & Timber Design — Timber DesignStudy Notes

Timber design departs fundamentally from steel LRFD (AISC 360) and concrete LRFD (ACI 318) by employing Allowable Stress Design. The method follows: **Core principle:** Allowable stress = Reference design value × (product of adjustment factors) Mathematically: $$F' = F \times C_D \times C_M \times C_t \times C_F \times C_L \times C_r \text{ (and others as applicable)}$$ where: - $F$ = reference value for the species and grade (e.g., No. 2 Douglas Fir, Southern Pine Grade 1) - $F'$ = adjusted allowable stress - $C$ factors = dimensionless multipliers accounting for load duration, moisture, temperature, size, stability, etc. **Design check:** Actual stress must not exceed allowable stress: $$f \le F'$$ For bending: $f_b = \frac{M}{S} \le F'_b$ For shear (parallel to grain): $f_v = \frac{3V}{2A} \le F'_v$ For compression (parallel to grain): $f_c = \frac{P}{A} \le F'_c$ **Why ASD for timber?** Wood exhibits high capacity under short-duration loads (wind, seismic, impact) because wood fibers have time-dependent creep resistance. The $C_D$ (load duration) factor, ranging from 0.9 to 2.0, quantifies this behavior—a unique feature that makes timber ASD mechanistically different from strength-based design. This distinction is frequently tested on the CELE. **NSCP 2015 Chapter 6 Framework:** The standard provides reference values from the National Forest Products Association (NFPA) for common Philippine timber species (Yakal, Tanguile, Lawaan). Designers consult grade-specific tables, then systematically apply adjustment factors to reach the allowable stress.

NSCP 2015 Chapter 6 defines seven principal adjustment factors. Understanding each is essential for board exams. **C_D — Load Duration Factor** Wood sustains higher stresses for brief loads because creep is time-dependent. - Permanent load: C_D = 0.9 (e.g., self-weight, floor live load) - 10-year load: C_D = 1.0 (long-term storage, typical live load) - 2-month load: C_D = 1.15 (construction, seasonal) - 7-day load: C_D = 1.25 (short-term construction) - Wind or seismic: C_D = 1.6 (brief duration, dynamic) - Impact: C_D = 2.0 (sudden loads like dropped objects) **Strategy for CELE:** Identify the governing load. If a timber beam carries permanent self-weight plus a 2-month construction surcharge, use C_D = 1.15 (the higher factor does not apply to both—use the **most critical** combination). On combo-load problems, the **controlling load duration** defines C_D. **C_M — Service Condition (Moisture Content)** Wood exposed to moisture swells and loses strength. - Dry service (≤12% equilibrium MC): C_M = 1.0 (interior building, protected) - Wet service (>12% equilibrium MC): C_M = 0.7–0.9 (outdoor, wet environments) **Note:** Philippine tropical climate makes wet-service timbers common in coastal areas and exterior formwork. Expect CELE questions pairing wet service with reduced allowables. **C_t — Temperature Factor** Extreme heat degrades wood strength. - Normal temperature (up to ~38°C): C_t = 1.0 - Elevated temperature (>38°C): C_t reduces (e.g., 0.8 at 50°C) - Cryogenic: rarely tested, but C_t increases slightly **C_F — Size Factor (Sawn Lumber)** Larger members have lower strength because defects are statistically more likely. - Small sections (e.g., 2×4): C_F ≈ 1.3–1.4 - Large sections (e.g., 12×12): C_F ≈ 1.0 For design, use the reference value's size class and interpolate per NSCP tables. **C_L — Beam Stability Factor (Lateral-Torsional)** Wide, shallow beams lacking lateral bracing tend to buckle sideways. $$C_L = \frac{1 + (\lambda_B/\lambda_c)}{2c} - \sqrt{\left[\frac{1 + (\lambda_B/\lambda_c)}{2c}\right]^2 - \frac{\lambda_B/\lambda_c}{c}}$$ where $\lambda_B$ is the lateral-unsupported span factor and $\lambda_c$ is a material property. For typical floor joists with continuous or closely-spaced lateral bracing, C_L ≈ 1.0 (or near it). Expect CELE questions asking students to identify when C_L drops below 1.0 (slender, unsupported beams). **C_P — Column Stability Factor** The wood analog of Euler buckling. Computed from effective slenderness ratio $\ell_e/d$: $$F_{cE} = \frac{0.822 \, E'_{\min}}{(\ell_e/d)^2}, \quad C_P = \frac{1 + \beta}{2c} - \sqrt{\left[\frac{1 + \beta}{2c}\right]^2 - \frac{\beta}{c}}$$ where $\beta = F_{cE}/F_c^*$ (the ratio of elastic buckling stress to adjusted compression stress, excluding C_P), and $c = 0.8$ for sawn lumber, 0.90 for glulam. As $\ell_e/d$ increases, $C_P$ falls toward zero—short stocky columns near 1.0, long slender ones near 0.3–0.5. **C_r — Repetitive Member Factor** Multiple members (joists, rafters, studs) that share load enjoy a 15% increase if they are spaced ≤0.6 m on center and tied together: - Single member: C_r = 1.0 - Repetitive members: C_r = 1.15 (typical floor/roof systems) **CELE trap:** Forgetting to apply C_r to multiple floor joists or roof rafters can lead to undersizing—a classic board-exam error. **Combining factors:** The product is taken sequentially. However, **C_F and C_L should not both be at their maximum**; use the more conservative (smaller) result or apply per-NSCP guidance on interaction.

Bending is the primary stress state for beams, joists, and rafters. **Bending stress formula:** $$f_b = \frac{M}{S}$$ where $M$ is the maximum bending moment and $S$ is the section modulus. For a rectangular section (breadth $b$, depth $h$): $$S = \frac{bh^2}{6}$$ **Design check:** $$f_b \le F'_b = F_b \times C_D \times C_M \times C_t \times C_F \times C_L \times C_r$$ **Design approach (two common scenarios):** 1. **Verification:** Given a section, calculate $f_b = M/S$ and verify $f_b \le F'_b$. Adequate if the inequality holds. 2. **Sizing:** Given $M$ and $F'_b$, solve for required section modulus: $$S_{\text{req}} = \frac{M}{F'_b}$$ then select the smallest standard section with $S \ge S_{\text{req}}$. **Lateral-torsional buckling (C_L factor):** For deep, slender beams without lateral support (e.g., a tall unsupported façade beam), the top flange can rotate out of plane. NSCP tables give C_L as a function of the lateral unsupported length and depth; typical building joists with flooring or roof diaphragm bracing have $C_L \approx 1.0$. Expect CELE questions on identifying when C_L < 1.0 applies. **Deflection (serviceability):** Timber design codes often require deflection checks—typical limits are $\Delta \le L/240$ (live load) or $\Delta \le L/180$ (total load). Although not the primary focus of ASD stress checks, deflection limits appear on board exams and must not be overlooked when sizing timber members. **Common CELE pitfalls:** - Forgetting to apply adjustment factors (especially C_D and C_r) - Confusing nominal vs. dressed (actual) dimensions—NSCP tables use dressed dimensions - Neglecting C_L on unsupported wide beams - Using reference $F_b$ directly without adjustment

Shear parallel to grain often governs short, deep timber beams—a key stress state frequently underestimated on the CELE. **Shear stress formula (rectangular section):** $$f_v = \frac{3V}{2A}$$ where $V$ is the maximum shear force and $A = b \times h$ is the gross cross-sectional area. The factor 1.5 arises from the parabolic shear distribution in a rectangular section (analogous to ACI 318 and AISC 360 formulas). **Design check:** $$f_v \le F'_v = F_v \times C_D \times C_M \times C_t \times C_r$$ Note that $C_F$ and $C_L$ typically do **not** apply to shear. **Wood is weak in shear:** Reference values for shear parallel to grain ($F_v$) are typically 1–2 MPa, much lower than bending values. A short, deep beam can easily exceed shear capacity. **CRITICAL: Notched beams (common support detail):** When a beam is notched at the support (e.g., a rafter notched to sit on a plate), the net depth at the notch is $d_n < d$ (full depth). Shear stress amplifies: $$f_v = \frac{3V}{2 \times b \times d_n} \times \frac{d}{d_n}$$ The amplification factor $(d/d_n)$ can double or triple shear stress. **Board exams frequently test notched beam shear**—it is a classic failure mode. NSCP 2015 places limits on notch depth (typically ≤ 1/4 of depth, sometimes 1/3) to avoid this amplification. **Design approach:** 1. Calculate maximum shear $V$ (often at support, $V = w \times L/2$ for uniform load). 2. Check nominal (no notch): $f_v = 3V/(2A) \le F'_v$. 3. If notched, amplify shear by $(d/d_n)$ and verify $(f_v \times d/d_n) \le F'_v$. 4. If shear fails, increase section depth, reduce span, or increase reference $F_v$ by species/grade selection. **Common CELE mistakes:** - Forgetting the 1.5 factor in the shear formula - Neglecting notch amplification (a frequent board-exam trap) - Confusing shear **parallel** (along grain) with shear **perpendicular** (across grain) - Using $F_v$ directly without adjustment factors

Compression parallel to grain governs studs, posts, and timber columns. Unlike bending, compressive stresses must account for **slenderness** via the column stability factor $C_P$—wood's analog of Euler buckling. **Compression stress formula:** $$f_c = \frac{P}{A}$$ where $P$ is the axial load and $A$ is the gross cross-sectional area. **Design check:** $$f_c \le F'_c = F_c^* \times C_P$$ where $F_c^*$ is the compression stress adjusted for all factors **except** $C_P$: $$F_c^* = F_c \times C_D \times C_M \times C_t \times C_F$$ Note: $C_r$ does not apply to compression; $C_L$ is column-specific and merged into $C_P$. **Column Stability Factor $C_P$ (the key step):** The effective slenderness ratio governs stability: $$\ell_e / d$$ where $\ell_e$ is the effective length (= $K \times L$, with $K$ from boundary conditions: 1.0 pin-pin, 0.8 fixed-free, 0.65 fixed-fixed) and $d$ is the minimum dimension (smaller of width or depth for rectangular sections). The elastic buckling stress is: $$F_{cE} = \frac{0.822 \, E'_{\min}}{(\ell_e / d)^2}$$ where $E'_{\min}$ is the modulus of elasticity (minimum value, adjusted for service conditions and other factors). Note the constant 0.822 (which replaces $\pi^2 / 12$ in wood theory). Then: $$\beta = \frac{F_{cE}}{F_c^*}, \quad C_P = \frac{1 + \beta}{2c} - \sqrt{\left[ \frac{1 + \beta}{2c} \right]^2 - \frac{\beta}{c}}$$ where $c = 0.8$ for sawn lumber, $c = 0.90$ for glulam. **Behavior of $C_P$:** - For short stocky columns ($\ell_e / d$ small): $F_{cE}$ large, $\beta$ large, $C_P \approx 1.0$. - For long slender columns ($\ell_e / d$ large): $F_{cE}$ small, $\beta$ small, $C_P$ falls (can drop to 0.3–0.5 or below). - At the **limiting slenderness**, $F_{cE} = F_c^*$ (i.e., $\beta = 1$), $C_P \approx 0.58$ (for $c = 0.8$). **Allowable axial capacity:** $$P_{\text{allow}} = F'_c \times A = F_c^* \times C_P \times A$$ **Design approach:** 1. Compute effective slenderness: $\ell_e / d$. 2. Find $F_{cE}$. 3. Compute $F_c^*$ (with all factors except $C_P$). 4. Calculate $\beta$ and then $C_P$. 5. Find $F'_c = F_c^* \times C_P$. 6. Verify $f_c = P / A \le F'_c$. **Common CELE pitfalls:** - Forgetting to apply $C_P$ (or applying it incorrectly)—results in overestimated capacity - Confusing effective length factors (K) or using $L$ instead of $\ell_e$ - Using adjusted values (with $C_P$) in the $F_{cE}$ calculation—must use unadjusted $E'_{\min}$ - Misunderstanding that short columns can carry high stress (near $F_c^*$), while long columns drop significantly

Real members may experience combined bending and compression, or bending and shear. NSCP 2015 Chapter 6 provides interaction checks to verify that combined stresses do not exceed allowables. **Bending plus Compression:** When a column experiences both axial load and bending moment (e.g., a braced frame column with transverse load), the combined effect is checked via: $$\frac{f_c}{F'_c} + \frac{f_b}{F'_b} \le 1.0$$ In some formulations, lateral-torsional instability under combined loading may require adjustment to $C_L$ or additional bending-compression factors. Consult NSCP 2015 for specifics. **Bending plus Shear:** When a beam carries both bending and shear, the checks are typically independent (no explicit interaction formula), but both must be satisfied: $$f_b \le F'_b \quad \text{and} \quad f_v \le F'_v$$ In regions of high shear (near supports of short, deep beams), shear often dominates. In mid-span regions of long beams, bending dominates. A proper design checks both zones. **NSCP 2015 approach:** The standard may provide detailed interaction guidance in Chapter 6 or reference supplementary tables. For the CELE, focus on: 1. Computing each stress ($f_c$, $f_b$, $f_v$) accurately. 2. Obtaining the correct allowable ($F'_c$, $F'_b$, $F'_v$). 3. Applying the interaction formula where specified (typically $f_c/F'_c + f_b/F'_b \le 1.0$). **Common pitfalls:** - Applying one allowable factor (e.g., $C_D$) to both compression and bending when they have different governing load durations - Forgetting that combined stresses are more restrictive than single-stress checks - Misunderstanding independence of shear vs. bending checks (they are independent; no single interaction formula needed)

The National Structural Code of the Philippines (NSCP) 2015, Chapter 6, governs timber design in the country. Key aspects relevant to the CELE: **Scope and Species:** NSCP 2015 references Philippine timber species (Yakal, Tanguile, Lawaan, Tangile, Kamagong, and others) with grade classifications (Select Structural, No. 1, No. 2, Grade 3). Reference design values are tabulated for each species/grade combination. Foreign wood (e.g., Southern Pine, Douglas Fir) may be used if verified by equivalent grading standards. **Load Duration Category:** The Code aligns load duration with typical Philippine construction practice: - Permanent loads (self-weight): $C_D = 0.9$ - 10-year loads (typical floor live load): $C_D = 1.0$ - 2-month construction loads: $C_D = 1.15$ - 7-day formwork/falsework: $C_D = 1.25$ - Wind and seismic: $C_D = 1.6$ - Impact (rare): $C_D = 2.0$ The tropical Philippine climate often mandates wet-service conditions ($C_M < 1.0$) for outdoor or partially exposed members, particularly in coastal zones. **Formwork and Falsework:** Many CELE questions involve timber formwork for concrete (scaffold systems, beam formwork). NSCP Chapter 6 provides guidance on design of props, shores, and struts. The 7-day load duration ($C_D = 1.25$) typically applies to formwork supporting fresh concrete. **Connection Design:** While NSCP Chapter 6 covers timber member stress design, connection design (nails, bolts, rivets) is addressed in Chapter 7. Board exams may ask about connection verification or member capacity in the context of bolted or nailed joints, requiring reference to both chapters. **Interaction with ACI 318 and AISC 360:** Timber is often combined with concrete (beams on concrete walls) or steel (brackets, connections). Ensure consistent load factors and design methodologies when mixing materials. Typically, timber ASD (allowable stress) is used independently; concrete and steel use LRFD, so design teams must be careful not to mix methodologies incorrectly. **Reference Values and NFPA Standards:** NSCP references the National Forest Products Association (NFPA) standard, which provides reference values. Some reference values may appear in NSCP tables directly; others require consultation of the NFPA database or supplementary design aids. On the CELE, assume that reference values are either given or standard (e.g., typical Yakal Grade 1 F_b ≈ 18–20 MPa). **Board-Exam Context:** Expect 2–5 questions on timber design on the CELE, typically covering: 1. Bending and shear checks (verification). 2. Column design with $C_P$ (stability). 3. Adjustment factors and allowable stress calculation. 4. Notched beam shear (classic trap). 5. Combined stress interaction.

The following problems are representative of the CELE and strategic for exam preparation. **Problem Type A: Bending Stress Check and Sizing** **Problem A1 (Verification):** A simply supported timber joist (150 × 300 mm) spans 6.0 m and carries distributed dead load 0.6 kN/m and live load 3.0 kN/m. Material is No. 2 Yakal with F_b = 14.5 MPa. Joists are spaced 0.4 m o.c. and tied by flooring (repetitive members). Dry service, 10-year load duration. Lateral bracing is continuous (C_L = 1.0). Assume C_F = 1.1 for the size. Check bending adequacy. **Solution:** Total load: w = 0.6 + 3.0 = 3.6 kN/m. Maximum moment (uniform load, simple span): M = wL²/8 = (3.6 × 6.0²) / 8 = 16.2 kN·m = 16.2 × 10⁶ N·mm. Section modulus: S = (bh²)/6 = (150 × 300²) / 6 = 2.25 × 10⁶ mm³. Bending stress: f_b = M/S = (16.2 × 10⁶) / (2.25 × 10⁶) = 7.2 MPa. Adjustment factors: - C_D = 1.0 (10-year load) - C_M = 1.0 (dry) - C_t = 1.0 (normal temp) - C_F = 1.1 (size, sawn) - C_L = 1.0 (braced) - C_r = 1.15 (repetitive members, ≤0.6 m o.c.) Allowable: F'_b = 14.5 × 1.0 × 1.0 × 1.0 × 1.1 × 1.0 × 1.15 = 18.3 MPa. Check: f_b = 7.2 MPa < F'_b = 18.3 MPa. **Adequate; ratio f_b / F'_b = 0.39 (39% utilization).** **Problem Type B: Shear Verification** **Problem B1 (Notched Beam):** A 100 × 250 mm timber rafter is notched at a support. Full depth d = 250 mm; notch depth = 80 mm, leaving d_n = 170 mm. Maximum shear V = 5.5 kN. Reference F_v = 1.1 MPa. Dry service, wind load (C_D = 1.6). Check shear adequacy. **Solution:** Area at notch: A_n = 100 × 170 = 17,000 mm². Nominal shear stress at notch: f_v,nom = (3V) / (2A_n) = (3 × 5,500) / (2 × 17,000) = 16,500 / 34,000 = 0.485 MPa. Amplification factor: d / d_n = 250 / 170 = 1.47. Amplified shear: f_v = 0.485 × 1.47 = 0.714 MPa. Allowable: F'_v = 1.1 × 1.6 × 1.0 × 1.0 × 1.0 = 1.76 MPa. Check: f_v = 0.714 MPa < F'_v = 1.76 MPa. **Adequate.** **Problem Type C: Column with Slenderness** **Problem C1 (Design):** Design a square sawn timber column to support P = 40 kN, effective length ℓ_e = 3.0 m, pin-pin ends. Material properties: F_c = 10.5 MPa, E_min = 6800 MPa, c = 0.8. Dry service, permanent load (C_D = 0.9). **Solution:** Assuming compact section with no size penalty: C_F = 1.0; also C_D = 0.9, C_M = 1.0, C_t = 1.0. F_c* = 10.5 × 0.9 = 9.45 MPa. Try a 150 × 150 mm section: d = 150 mm. ℓ_e / d = 3000 / 150 = 20. F_cE = (0.822 × 6800) / 20² = 5589.6 / 400 = 13.97 MPa. β = 13.97 / 9.45 = 1.48. C_P = [(1 + 1.48) / (2 × 0.8)] - √{[(1 + 1.48) / (2 × 0.8)]² - 1.48/0.8} = [2.48 / 1.6] - √[1.55² - 1.85] = 1.55 - √[2.40 - 1.85] = 1.55 - √0.55 = 1.55 - 0.742 = 0.808. F'_c = 9.45 × 0.808 = 7.64 MPa. Allowable capacity: P_allow = F'_c × A = 7.64 × (150 × 150) = 7.64 × 22,500 = 172 kN >> 40 kN. **Over-sized.** Try 100 × 100 mm: d = 100 mm. ℓ_e / d = 3000 / 100 = 30. F_cE = 5589.6 / 900 = 6.21 MPa. β = 6.21 / 9.45 = 0.657. C_P = [1.657 / 1.6] - √[(1.657 / 1.6)² - 0.657/0.8] = 1.036 - √[1.075 - 0.821] = 1.036 - √0.254 = 1.036 - 0.504 = 0.532. F'_c = 9.45 × 0.532 = 5.03 MPa. P_allow = 5.03 × 10,000 = 50.3 kN > 40 kN. **Adequate.** **Select 100 × 100 mm.** (Or try 125 × 125 for a margin.) **Problem Type D: Adjustment Factor Application** **Problem D1 (Multi-factor Calculation):** A timber beam's reference bending value is F_b = 16.0 MPa. Calculate the adjusted allowable F'_b for the following conditions: - Load duration: 2-month construction (C_D = 1.15) - Moisture: exposed to weather, wet service (C_M = 0.8) - Temperature: normal (C_t = 1.0) - Lumber size: 200 × 400 mm (C_F = 1.05) - Lateral support: beam is unsupported in the mid-region over 8.0 m span, width b = 200 mm, depth h = 400 mm (assess C_L) - Repetitive member: single beam, no repetition (C_r = 1.0) **Assessment of C_L:** The beam is 8.0 m unsupported, wide (b = 200 mm), and relatively shallow (h = 400 mm), giving a wide/deep ratio of 200/400 = 0.5. The lateral unsupported length is 8.0 m. Per NSCP tables or NFPA, this would likely result in C_L < 1.0; assume C_L ≈ 0.85 (partial lateral instability). **Calculation:** F'_b = F_b × C_D × C_M × C_t × C_F × C_L × C_r = 16.0 × 1.15 × 0.8 × 1.0 × 1.05 × 0.85 × 1.0 = 16.0 × 1.15 × 0.8 × 1.05 × 0.85 = 16.0 × 0.806 = 12.9 MPa. **Result:** F'_b = 12.9 MPa. Compared to dry, braced, short-duration allowables (~18–20 MPa), the wet, long unsupported condition significantly reduces capacity—a realistic design scenario for outdoor or temporary structures in the Philippines.

**Stress Formulas:** $$f_b = \frac{M}{S}, \quad S = \frac{bh^2}{6} \text{ (rectangular)}$$ $$f_v = \frac{3V}{2A} \text{ (parallel to grain, rectangular)}$$ $$f_c = \frac{P}{A}$$ **Adjusted Allowable Stresses:** $$F'_b = F_b \times C_D \times C_M \times C_t \times C_F \times C_L \times C_r$$ $$F'_v = F_v \times C_D \times C_M \times C_t \times C_r$$ $$F'_c = F_c^* \times C_P, \quad F_c^* = F_c \times C_D \times C_M \times C_t \times C_F$$ **Column Stability:** $$\ell_e / d = \text{effective slenderness}$$ $$F_{cE} = \frac{0.822 \, E'_{\min}}{(\ell_e/d)^2}$$ $$\beta = \frac{F_{cE}}{F_c^*}, \quad C_P = \frac{1+\beta}{2c} - \sqrt{\left(\frac{1+\beta}{2c}\right)^2 - \frac{\beta}{c}}, \quad c = 0.8 \text{ (sawn)}, 0.90 \text{ (glulam)}$$ **Load Duration Factor C_D:** | Load Type | Duration | C_D | |-----------|----------|-----| | Permanent | - | 0.9 | | 10-year | typical live | 1.0 | | 2-month | construction | 1.15 | | 7-day | formwork | 1.25 | | Wind/Seismic | brief | 1.6 | | Impact | momentary | 2.0 | **Adjustment Factor Ranges:** - $C_M$: 0.7–1.0 (wet service reduces) - $C_t$: ≈1.0 (normal temp); <1.0 if elevated - $C_F$: 1.0–1.4 (sawn lumber only; glulam ≈1.0) - $C_L$: <1.0–1.0 (lateral-torsional; well-braced → 1.0) - $C_P$: <1.0–1.0 (column buckling; stocky → 1.0, slender → <0.6) - $C_r$: 1.0 or 1.15 (repetitive members spaced ≤0.6 m) **Deflection Limits:** - Live load: Δ ≤ L/240 (typical) - Total load: Δ ≤ L/180 (typical) **Design Checks (must all be satisfied):** $$f_b \le F'_b, \quad f_v \le F'_v, \quad f_c \le F'_c, \quad \Delta \le \text{limit}$$ For combined bending + compression: $$\frac{f_c}{F'_c} + \frac{f_b}{F'_b} \le 1.0$$