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Timber (Wood) Design

4% of exam

NDS allowable-stress design of sawn-lumber and glulam beams and columns, adjustment factors, bending and horizontal shear, bearing, stability, and combined bending and axial loads.

3 concepts

D. Timber

NDS Timber Design: Adjustment Factors

How the NDS reference design values become adjusted (allowable) values F' through the chain of adjustment factors — CD, CM, Ct, CF, CL, CP, Cr and the rest.

Timber design on the PE Civil exam is, at heart, one disciplined piece of bookkeeping: you start with a tabulated reference design value —

F_b

,

F_v

,

F_c

,

F_{c\perp}

,

F_t

,

E

,

E_{min}

— and you walk it through a chain of multiplicative adjustment factors to reach the adjusted (allowable) value

F'

that you actually compare against the applied stress. Almost every point lost in this area is lost not in the trigonometry or the section properties but in the factor chain: an examinee forgets the load-duration factor

C_D

, applies the wet-service factor

C_M

to a dry member, or multiplies in a size factor that does not apply to the species and size at hand. Because NCEES has you work wood in Allowable Stress Design (ASD), this whole concept lives in the National Design Specification for Wood Construction (NDS 2018) and its Supplement of design values — there is no timber design content in the NCEES PE Civil Reference Handbook, so cite the NDS, not a handbook page.

Reference design values and the master equation

The NDS Supplement tabulates reference design values for each species, grade, and product (visually graded sawn lumber, MSR lumber, glued-laminated timber, etc.). These are baseline stresses valid for one reference condition: normal load duration, dry service, normal temperature, and a benchmark size. Every adjusted value is that reference value multiplied by the applicable factors. The general form is identical for each property; you simply pick the factors that apply to that property. The adjusted modulus of elasticity for stability,

E'_{min}

, is what later feeds the beam- and column-stability calculations.

F'_b = F_b \, C_D\,C_M\,C_t\,C_L\,C_F\,C_{fu}\,C_i\,C_r

Load duration C_D — wood gets stronger for short loads

Wood carries a higher stress for a load applied briefly than for one applied for years; the load-duration factor

C_D

captures this. The reference values are normalized to ten years (the 'normal' duration that floor live load is taken to represent), so

C_D = 1.0

there. Common values are

C_D = 0.9

for permanent (dead-only) loading,

1.0

for occupancy live load,

1.15

for snow,

1.25

for construction or a seven-day load,

1.6

for wind or seismic, and

2.0

for impact. The governing rule: in any one load combination, use the

C_D

of the shortest-duration load in that combination, and check every combination separately.

C_D

applies to all strength properties but never to

E

,

E_{min}

, or

F_{c\perp}

.

C_D:\quad 0.9\ (\text{permanent}),\ 1.0\ (10\text{-yr}),\ 1.15\ (\text{snow}),\ 1.6\ (\text{wind/seismic})

Service-condition factors C_M, Ct, Ci

Three factors correct for the environment. The wet-service factor

C_M

reduces values when the in-service moisture content exceeds the reference threshold (above

19\%

for sawn lumber,

16\%

for glulam); for fully dry interior members

C_M = 1.0

and is simply omitted. The temperature factor

C_t

reduces values for sustained service above

100^\circ\text{F}

; ordinary buildings sit below that, so

C_t = 1.0

. The incising factor

C_i

applies only when sawn lumber has been incised to improve preservative penetration. The exam usually states the service conditions explicitly — read for 'wet', 'exposed', 'sustained high temperature', or 'incised'; absent those words, these factors are unity, and a frequent error is dragging a

C_M < 1

into an obviously dry, heated building.

Geometry factors C_F, C_fu, C_r

The size factor

C_F

corrects

F_b

,

F_t

, and

F_c

of visually graded sawn lumber for members deeper or wider than the reference size, because larger members have more flaws and a lower characteristic strength — deep bending members get

C_F < 1

. For glulam, the analogous bending correction is the volume factor

C_V

, which competes with the beam-stability factor

C_L

(you use the smaller of the two, never both). The flat-use factor

C_{fu}

raises

F_b

when a member is loaded on its wide face. The repetitive-member factor

C_r = 1.15

rewards

F_b

when three or more parallel members (joists, studs, rafters) spaced no more than

24

in. are tied by a load-sharing deck. These geometry factors apply only to the properties named for each — applying

C_F

to shear or to

E

is a classic slip.

\text{Glulam bending: use } \min(C_L,\ C_V),\ \text{never both}

Stability factors C_L and C_P

Two factors are not table look-ups but computed quantities tied to slenderness. The beam-stability factor

C_L

reduces

F_b

for a laterally unsupported compression edge (lateral-torsional buckling); it is

1.0

when the compression edge is continuously braced or the depth-to-breadth ratio is small. The column-stability factor

C_P

reduces

F_c

for a slender column (flexural buckling); it falls toward zero as

\ell_e/d

grows. Both are evaluated from the same Euler-type term

F_{cE}

or

F_{bE}

built on

E'_{min}

, and both have their own dedicated concepts. The key discipline here is sequencing: you compute

F_b^{*}

(every factor except

C_L

) and

F_c^{*}

(every factor except

C_P

) first, because the stability factor itself depends on that starred value through the ratio

F_{cE}/F_c^{*}

.

F^{*}_c = F_c\,C_D\,C_M\,C_t\,C_F\,C_i,\qquad F'_c = F^{*}_c\,C_P

Reading the NDS adjustment-factor applicability table

The NDS gives a single applicability table (NDS 2018 Table 4.3.1 for sawn lumber, 5.3.1 for glulam) with a checkmark grid: rows are design properties, columns are factors. The professional move is to reproduce the relevant row mentally for the property you need.

E

and

E_{min}

take essentially none of the stress factors — no

C_D

, no

C_F

— because elastic behavior is duration-independent.

F_{c\perp}

(bearing) takes

C_M

,

C_t

,

C_i

, and the bearing-area factor

C_b

, but not

C_D

and not

C_F

. Compression parallel

F_c

takes the column factor

C_P

; bending

F_b

takes the beam factor

C_L

; the two are never swapped. Build the chain property-by-property, not as one universal list.

Exam strategy

Make the factor chain a checklist you write down before computing anything: list

C_D

,

C_M

,

C_t

,

C_F

(or

C_V

),

C_L

/

C_P

,

C_r

,

C_{fu}

,

C_i

,

C_b

and strike out the ones the problem makes unity. Decide

C_D

per load combination and use the shortest-duration load's value — and never apply

C_D

to

E

,

E_{min}

, or

F_{c\perp}

. Compute the starred values

F_b^{*}

and

F_c^{*}

first so the stability factors

C_L

and

C_P

have something to reference. Default everything environmental to

1.0

unless the words 'wet', 'exposed', 'high temperature', or 'incised' appear. Finally, cite NDS 2018 (ASD) — the editions NCEES supplies are fixed, so write 'NDS 2018', not a later year.

Key equations

Adjusted bending value

F'_b = F_b\,C_D\,C_M\,C_t\,C_L\,C_F\,C_{fu}\,C_i\,C_r

Reference $F_b$ (psi) times every applicable factor; $C_L$ is the beam-stability factor, $C_F$

Adjusted compression (parallel)

F'_c = F_c\,C_D\,C_M\,C_t\,C_F\,C_i\,C_P = F^{*}_c\,C_P

Adjusted shear value

F'_v = F_v\,C_D\,C_M\,C_t\,C_i

Adjusted bearing (perp. to grain)

F'_{c\perp} = F_{c\perp}\,C_M\,C_t\,C_i\,C_b

Adjusted modulus (stability)

E'_{min} = E_{min}\,C_M\,C_t\,C_i

Starred reference (pre-stability)

F^{*}_b = F_b\,C_D\,C_M\,C_t\,C_F\,C_{fu}\,C_i\,C_r

Load-duration factor values

C_D = 0.9,\ 1.0,\ 1.15,\ 1.25,\ 1.6,\ 2.0

Permanent, 10-yr (normal), snow, 7-day/construction, wind/seismic, impact. Use the shortest-duration load in each combination.

Repetitive-member factor

C_r = 1.15

Applies to $F_b$ only when 3+ parallel members spaced $\le 24$

ASD demand-to-capacity

f \le F' \quad\Longleftrightarrow\quad \dfrac{f}{F'} \le 1.0

Worked examples

Adjusted bending value of a roof rafter

Problem. A No. 2 Douglas Fir-Larch 2x10 rafter ( $F_b = 900\ \text{psi}$ ) carries snow load and is part of a system of rafters spaced $16\ \text{in.}$ on center sheathed with plywood. The attic is dry and unheated. The size factor for a 2x10 in bending is $C_F = 1.1$ . Find the adjusted bending value $F'_b$ .

Solution. Build the chain for

F_b

: - Load duration: snow governs, so

C_D = 1.15

. - Wet service: dry interior,

C_M = 1.0

F'_b = 900\,(1.15)(1.1)(1.15) = 1{,}309\ \text{psi}

Choosing C_D across two load combinations

Problem. A No. 1 DF-L 6x6 post ( $F_c = 1{,}000\ \text{psi}$ , dry, heated interior, not slender so take $C_P = 0.70$

Common pitfalls

•Citing the NCEES PE Civil Reference Handbook for timber. The handbook has NO wood-design content; the governing source is NDS 2018 (ASD). Attributing the factor chain to a handbook section is a sourcing error.
•Applying $C_D$ to the wrong properties. Load duration adjusts strength values ( $F_b$ , $F_v$ , $F_c$ , $F_t$ ) but NEVER $E$ , $E_{min}$ , or bearing $F_{c\perp}$ .
•Using a single $C_D$ for all combinations. $C_D$ is the shortest-duration load IN THAT combination; check dead-only ( $0.9$ ), live ( $1.0$
•Multiplying $C_L$ and $C_V$ together for a glulam beam. Use only the SMALLER of the two — using both double-counts the strength reduction.
•Forgetting that the stability factors are computed last. $C_P$ depends on $F^{*}_c$ (all factors except $C_P$
•Dragging $C_M < 1.0$ into a dry, heated building. The wet-service factor applies only above the moisture threshold ( $19\%$ sawn, $16\%$ glulam); absent 'wet/exposed', it is $1.0$ .
•Citing a later edition (NDS 2015 or a future year). NCEES supplies NDS 2018 for the PE Civil structural exam — cite that edition, in ASD, exactly.

References

AWC National Design Specification (NDS) for Wood Construction, 2018 edition (ASD method) — Ch. 2 general adjustment factors + Ch. 4/5 applicability tables
NDS Supplement, 2018 — Design Values for Wood Construction (reference $F_b$, $F_v$, $F_c$, $F_{c\perp}$, $E$, $E_{min}$ and size factors $C_F$)
AWC NDS 2018 Table 4.3.1 (sawn lumber) and Table 5.3.1 (glulam) — adjustment-factor applicability grids

Timber Beam: Bending, Shear & Bearing

The four ASD checks for a wood beam — bending f_b = M/S ≤ F'_b, horizontal shear f_v = 1.5V/A ≤ F'_v, bearing perpendicular to grain, and deflection.

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Timber Column & Combined Bending + Axial

The column stability factor C_P from slenderness l_e/d and F_cE, the adjusted F'_c, and the NDS interaction equation for combined axial compression plus bending.

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the size factor (sawn) or

C_V

the volume factor (glulam — use only the smaller of

C_L

,

C_V

).

$F^{*}_c$ is every factor except $C_P$ ; the column-stability factor $C_P$ is computed last from $F_{cE}/F^{*}_c$ .

Horizontal shear; takes duration and service factors but NOT $C_F$ , $C_L$ , or $C_r$ .

Bearing perpendicular to grain; $C_b$ is the bearing-area factor. Note: NO load-duration factor $C_D$ and NO size factor.

Feeds $F_{cE}$ and $F_{bE}$ . Elasticity is duration-independent, so no $C_D$ and no $C_F$ ever apply to $E$ or $E_{min}$ .

All factors except $C_L$ ; the ratio $F_{bE}/F^{*}_b$ then yields $C_L$ . Same idea for $F^{*}_c$ and $C_P$ .

in. share load through a deck (joists, studs, rafters).

The ASD check: actual stress $f$ (e.g., $f_b = M/S$ ) must not exceed the adjusted allowable $F'$ . Never mix in LRFD $\phi$ -factors.

. - Temperature: unheated but below

100^\circ\text{F}

,

C_t = 1.0

. - Size:

C_F = 1.1

(given for 2x10). - Repetitive: rafters spaced

\le 24

in.,

\ge 3

members, sheathed, so

C_r = 1.15

. - Beam stability: rafters braced by sheathing on the compression edge,

C_L = 1.0

.

F'_b = 900(1.15)(1.0)(1.0)(1.0)(1.1)(1.15) = 1{,}309\ \text{psi}

. **Answer:

F'_b \approx 1{,}310\ \text{psi}

.** Sanity check: the reference

900\ \text{psi}

is boosted by snow duration and load sharing to a little over

1{,}300\ \text{psi}

— a

45\%

increase, reasonable given

1.15\times1.1\times1.15 = 1.45

and every other factor unity.

) must be checked for two combinations: (a) dead + floor live load, and (b) dead + wind. Which combination governs the allowable compression value, and what is

F'_c

for each?

Solution. Only

C_D

differs between the combinations;

C_M = C_t = C_F = C_i = 1.0

for a dry, heated, square post, and

C_P = 0.70

is given. (a) Dead + floor live: shortest-duration load is the 10-yr live load,

C_D = 1.0

.

F'_c = 1{,}000(1.0)(0.70) = 700\ \text{psi}

. (b) Dead + wind: shortest-duration load is wind,

C_D = 1.6

.

F'_c = 1{,}000(1.6)(0.70) = 1{,}120\ \text{psi}

. **Answer: each combination is checked separately; the allowable is

700\ \text{psi}

for the live-load case and

1{,}120\ \text{psi}

for the wind case.** Sanity check: the wind case allows

60\%

more stress (exactly the

C_D

ratio

1.6/1.0

), but it also carries a different factored demand, so 'governs' is decided by demand-to-capacity, not by

F'_c

alone — never apply

C_D = 1.6

to the gravity-only check.

F'_{c,\text{live}} = 1000(1.0)(0.70) = 700,\quad F'_{c,\text{wind}} = 1000(1.6)(0.70) = 1{,}120\ \text{psi}

), snow (

1.15

), and wind/seismic (

1.6

) separately.

); compute the starred value first, then

C_P

.