Module 2: Timber Tension and Compression Members

Learning Objectives

  • Design timber tension members using gross and net-section concepts appropriate to wood.
  • Avoid importing the steel staggered-hole net-area equation into timber design.
  • Evaluate timber compression members using effective length, column slenderness, Euler stress, and the NSCP column-stability factor.
  • Check compression perpendicular to grain and local bearing where forces enter or leave a member.
  • Recognize splitting, row tear-out, group tear-out, and connection geometry as potential controlling conditions.
  • Relate column proportions and connection details to architectural space, exposure, and constructability.

NSCP Code Basis

Use NSCP 2015 Section 616 — Design Provisions and Equations together with Section 617 — Sawn Lumber or the appropriate engineered-wood section. Connection-related net-section and tear-out behavior must also be coordinated with Section 619 — Timber Connectors and Fasteners.

Net section

The remaining effective wood section at a critical cross-section after deducting material removed by holes, notches, cuts, or other discontinuities as required by the governing timber provisions.

Timber Tension Members

Tension parallel to grain can be efficient in clear, straight-grained wood, but knots, slope of grain, holes, and connection zones are highly influential because timber is relatively brittle in tension parallel to grain. Evaluate the member away from connections and then review the connection region separately.

A complete tension-member review includes the applicable adjusted tension design value, gross/net section, local stress concentration introduced by connection geometry, and timber-connection failure modes.

Tension Stress Check

Basic axial stress comparison for a timber tension member using the critical code-defined area.

ft=PAcrit≤Ft′f_t=\frac{P}{A_{\text{crit}}}\le F_t'

Variables

SymbolDescriptionUnit
PPAxial tensile force for the applicable design combination.-
AcritA_{\text{crit}}Critical area after code-required deductions at the section being checked.-
ftf_tActual tensile stress parallel to grain.-
Ft′F_t'Adjusted tension design value parallel to grain.-

Do Not Use the Steel Stagger Correction for Timber

The familiar steel net-area term involving s2/(4g)s^2/(4g) is not the general NSCP timber net-section rule. For timber, deduct the projected removed material and apply the timber-specific provisions for staggered fasteners and connection tear-out. Adjacent rows may have to be treated as acting at the same critical section when the code spacing condition is met.

Critical-Section Geometry

Increase the hole diameter and watch the removed strips grow in the projected section. The member is 140 mm wide with two deductions at that section; changing thickness changes both the section drawing and net area. Compare the resulting parallel-to-grain tension resistance without applying a steel stagger correction. Splitting, tear-out, fastener resistance, and minimum distances remain independent checks.

Timber Tension Connection — Critical Section Geometry

The critical timber section deducts the projected removed material and must be reviewed together with splitting, row tear-out, group tear-out, fastener resistance, and end/edge geometry. The steel stagger correction is not applied to this timber section.

Controls

26 mm
50 mm
8.0 MPa
critical projected sectionend distancegrain direction →PPhole deduction
Projected timber net section140 × 50 mm · shaded strips removed
Net area: (140 − 2dh)t4400 mm²
Modeled tension resistance35.20 kN

Conceptual geometry only; actual hole size, spacing, end/edge distances, stagger treatment, and tear-out checks must follow NSCP Sections 616–619 for the selected timber connection.

Connection-Region Failure Modes in Tension

The member can be adequate in simple axial stress yet fail at the connection. Review net-section tension, local crushing/bearing, row tear-out, group tear-out, splitting perpendicular to grain, fastener strength, and any eccentricity introduced by one-sided connection geometry.

Architecturally exposed knife plates or side plates should be detailed to avoid placing large tension perpendicular to grain near a member end.

Effective column length

The idealized buckling length Le=KLL_e=KL used to represent the member length and end-restraint condition in the stability calculation.

Selecting the Effective-Length Factor K

For mechanics and preliminary design checks, the following idealized end conditions provide useful reference values. They describe perfect boundary conditions, not automatically the restraint of a real timber frame.

Idealized column end conditionTheoretical KeK_eNDS recommended design KeK_e when the ideal condition is only approximated
Fixed–fixed, sidesway inhibited0.500.500.650.65
Fixed–pinned, sidesway inhibitedabout 0.700.700.800.80
Pinned–pinned1.001.001.001.00
Fixed–free cantilever2.002.002.102.10

How to use the table: the theoretical values explain Euler buckling behavior. For design, use the effective-length procedure permitted by the adopted NSCP/NDS basis; where Appendix G's ideal-condition approximation is used, prefer the recommended design values rather than automatically taking the lower theoretical values. Partial rotational restraint, frame sidesway, weak surrounding members, or uncertain bracing can require a larger KeK_e.

K Is a Structural-System Assumption

The same physical column can have different effective lengths about its two axes because the surrounding walls, beams, diaphragms, braces, and connections may restrain the directions differently. State the assumed end condition and KK for each axis in the calculation.

Timber Compression Members

A short stocky member may be governed primarily by crushing parallel to grain; a slender member is increasingly governed by instability. NSCP timber design represents this transition through the column-stability procedure rather than by using unrelated short/intermediate/long-column equations as competing design methods.

What short, intermediate, and long mean

These are behavioral classifications, not three separate NSCP design equations:

Behavioral regimeDominant responsePractical interpretation
Short / stockyCrushing or material strengthFcEF_{cE} is high relative to Fc∗F_c^*, so stability causes little reduction
IntermediateCombined material yielding/crushing and bucklingFcEF_{cE} and Fc∗F_c^* are of comparable importance; CPC_P provides the transition
Long / slenderBuckling dominatesFcEF_{cE} becomes small relative to Fc∗F_c^* and strongly reduces Fc′F_c'

There is no single universal Le/dL_e/d number that separates all three behavioral labels for every wood product. The code procedure uses the unified CPC_P equation across the permitted range.

Build the Adjusted Axial Values Before Checking the Member

The axial formulas in this module require property-specific adjusted values, not an unexplained Ft′F_t' or Fc′F_c' copied from a previous example.

For sawn lumber in ASD:

Ft′=FtCDCMCtCFCiF_t' = F_t C_D C_M C_t C_F C_i

For compression parallel to grain, first form the pre-stability value

Fc∗=FcCDCMCtCFCiF_c^* = F_c C_D C_M C_t C_F C_i

and the stability modulus

Emin′=EminCMCtCiCT.E_{min}' = E_{min} C_M C_t C_i C_T.

Only after the effective-length and slenderness checks are complete should the column-stability factor be applied:

Fc′=Fc∗CP.F_c' = F_c^* C_P.

For local bearing,

Fc⊥′=Fc⊥CMCtCiCb,F_{c\perp}' = F_{c\perp} C_M C_t C_i C_b,

with CbC_b included only when the bearing geometry satisfies the provision that permits the bearing-area adjustment. Do not use CDC_D for compression perpendicular to grain merely because the surrounding load combination contains a short-duration load.

Axial Design Values Must Match the Governing Load Combination

When several ASD load combinations are checked, CDC_D can change between combinations. Re-form Ft′F_t' or Fc∗F_c^* for the combination being evaluated rather than carrying one adjusted value through every load case. Moisture, temperature, incising, and size conditions may remain constant, but load duration is tied to the governing combination.

Timber Axial-Member Design Workflow

The workflow separates tension, compression stability, and local bearing so the correct adjusted property is formed before each member or connection-region check.

Timber Axial-Member Design Workflow

Complete tension, compression, bearing, stability, and connection sequence for timber axial members.

Timber Axial-Member Design WorkflowComplete tension, compression, bearing, stability, and connection sequence for timber axial members.. Determine axial demand, load path, and governing load combination → Primary action?; Primary action? — Bearing → Bearing: form Fc⊥′ and apply Cb only when permitted; Primary action? — Tension → Tension: form Ft′ using applicable factor chain; Primary action? — Compression → Compression: form Fc* before CP and form Emin′ for stability; Bearing: form Fc⊥′ and apply Cb only when permitted → Check connection, splitting, and hardware; Tension: form Ft′ using applicable factor chain → Determine gross/net section and connection paths; Determine gross/net section and connection paths → Check connection, splitting, and hardware; Compression: form Fc* before CP and form Emin′ for stability → Establish K, effective length, and Le/d; Establish K, effective length, and Le/d → Within column-slenderness limit?; Within column-slenderness limit? — No → Revise section or bracing restraint; Within column-slenderness limit? — Yes → Compute FcE, CP, and Fc′; Revise section or bracing restraint → Compression: form Fc* before CP and form Emin′ for stability; Compute FcE, CP, and Fc′ → Check connection, splitting, and hardware; Check connection, splitting, and hardware → Member, stability, bearing, and connection pass?; Member, stability, bearing, and connection pass? — Yes → Document governing utilization; Member, stability, bearing, and connection pass? — No → Revise section, restraint, bearing, or detail; Revise section, restraint, bearing, or detail → Primary action?

Determine axial demand, load path, and governing load combination → Primary action?; Primary action? — Bearing → Bearing: form Fc⊥′ and apply Cb only when permitted; Primary action? — Tension → Tension: form Ft′ using applicable factor chain; Primary action? — Compression → Compression: form Fc* before CP and form Emin′ for stability; Bearing: form Fc⊥′ and apply Cb only when permitted → Check connection, splitting, and hardware; Tension: form Ft′ using applicable factor chain → Determine gross/net section and connection paths; Determine gross/net section and connection paths → Check connection, splitting, and hardware; Compression: form Fc* before CP and form Emin′ for stability → Establish K, effective length, and Le/d; Establish K, effective length, and Le/d → Within column-slenderness limit?; Within column-slenderness limit? — No → Revise section or bracing restraint; Within column-slenderness limit? — Yes → Compute FcE, CP, and Fc′; Revise section or bracing restraint → Compression: form Fc* before CP and form Emin′ for stability; Compute FcE, CP, and Fc′ → Check connection, splitting, and hardware; Check connection, splitting, and hardware → Member, stability, bearing, and connection pass?; Member, stability, bearing, and connection pass? — Yes → Document governing utilization; Member, stability, bearing, and connection pass? — No → Revise section, restraint, bearing, or detail; Revise section, restraint, bearing, or detail → Primary action?

  • Determine axial demand, load path, and governing load combination: terminator
  • Primary action?: decision
  • Bearing: form Fc⊥′ and apply Cb only when permitted: process
  • Tension: form Ft′ using applicable factor chain: process
  • Determine gross/net section and connection paths: subprocess
  • Compression: form Fc* before CP and form Emin′ for stability: process
  • Establish K, effective length, and Le/d: subprocess
  • Within column-slenderness limit?: decision
  • Compute FcE, CP, and Fc′: process
  • Revise section or bracing restraint: process
  • Check connection, splitting, and hardware: subprocess
  • Member, stability, bearing, and connection pass?: decision
  • Revise section, restraint, bearing, or detail: process
  • Document governing utilization: terminator

Solid-Column Slenderness Limit

For the solid rectangular-column procedure used here, the governing slenderness ratio must satisfy

Led≤50\frac{L_e}{d}\le 50

Check this limit about both principal directions before calculating the final column resistance. A geometry outside the permitted range is not made acceptable merely because the algebra returns a positive FcEF_{cE} or CPC_P.

Column Slenderness Ratio

Slenderness measure for a rectangular timber column about the axis being evaluated.

Led=KLd\frac{L_e}{d}=\frac{KL}{d}

Variables

SymbolDescriptionUnit
KKEffective-length factor representing end restraint.-
LLUnsupported member length.-
ddCross-sectional dimension associated with buckling about the axis checked.-
LeL_eEffective column length.-

Timber Euler Buckling Stress

Euler-type reference stress used by the NSCP/NDS column-stability procedure.

FcE=0.822Emin⁡′(Le/d)2F_{cE}=\frac{0.822E_{\min}'}{(L_e/d)^2}

Variables

SymbolDescriptionUnit
Emin⁡′E_{\min}'Adjusted minimum modulus of elasticity applicable to column stability.-
Le/dL_e/dColumn slenderness ratio for the axis being checked.-
FcEF_{cE}Reference elastic buckling stress used in the column-stability equation.-

Column Constant c by Product Family

The stability equation includes the product constant cc. The commonly used NDS-family values associated with the NSCP wood framework are:

Wood productcc
Sawn lumber0.800.80
Round timber poles and piles0.850.85
Structural glued-laminated timber0.900.90
Structural composite lumber / CLT where the adopted provision permits the same column model0.900.90

Use the value corresponding to the actual product and adopted code provision. Do not leave c=0.80c=0.80 simply because the first worked example used sawn lumber.

Column Stability Factor

Unified stability-factor form used to reduce the compression design value as slenderness increases.

CP=1+FcE/Fc∗2c−(1+FcE/Fc∗2c)2−FcE/Fc∗cC_P= \frac{1+F_{cE}/F_c^*}{2c} - \sqrt{ \left(\frac{1+F_{cE}/F_c^*}{2c}\right)^2 - \frac{F_{cE}/F_c^*}{c} }

Variables

SymbolDescriptionUnit
CPC_PColumn stability factor.-
Fc∗F_c^*Compression design value with the factors that precede the column-stability adjustment.-
FcEF_{cE}Euler buckling reference stress.-
ccMaterial/product constant specified by the governing timber provisions.-

Adjusted Compression Design Value

Final compression value after column stability is applied.

Fc′=Fc∗CPF_c'=F_c^*C_P

Variables

SymbolDescriptionUnit
Fc′F_c'Adjusted compression design value parallel to grain.-
Fc∗F_c^*Compression value before the column-stability factor.-
CPC_PColumn stability factor.-

Interactive Exploration

Increase effective length while holding the section fixed: the Euler design stress falls with the square of effective length, reducing the column-stability factor and modeled axial resistance. Swap width and depth to see the governing direction change. The resistance is withheld outside the modeled slenderness limit; a positive computed stress alone does not make that geometry acceptable. Reset restores the initial sawn-lumber case.

Timber Column Stability

Concept and model scope

NSCP Section 616 stability workflow using effective length, adjusted minimum modulus, Euler stress, and the unified CP reduction.

Width and depth: actual cross-section dimensions. Both buckling directions are checked.

L and K: physical unsupported length and effective-length factor; together they define the modeled effective buckling length.

Fc* and Emin′: pre-stability compression value and adjusted minimum modulus used by the NSCP column-stability calculation.

c: product constant: 0.80 sawn lumber, 0.85 round timber poles/piles, and 0.90 glulam/SCL/CLT in the NDS-family framework used by this lesson.

Limit: the modeled solid-column procedure is withheld when governing Le/d exceeds 50.

Controls

150 mm
200 mm
3000 mm
1.00
12.0 MPa
4000 MPa

Idealized K presets

These presets are the NDS Appendix G recommended design values for commonly approximated ideal conditions. The corresponding theoretical Euler values are 0.50, 0.70, 1.00, and 2.00.

Column constant c

Use the product family permitted by the adopted timber provision.

Cross-section · physical scale

150 × 200 mm

Elevation · physical scale

Le = 3000 mmL = 3000 mm
KL/b20.00
KL/d15.00
Governing slenderness20.00
FcE8.22 MPa
CP0.550
Fc′6.60 MPa
Modeled axial resistance198.11 kN
Within modeled Le/d ≤ 50 scope

Product constant c

The geometry panels use uniform physical scale within each view. The simulator isolates column stability; bearing, connection, durability, fire, and verified NSCP reference-value adjustments remain separate checks.

Check Both Buckling Axes

For a rectangular or built-up column, compute stability about both principal directions. The smaller cross-sectional dimension often produces the larger slenderness ratio, but bracing conditions can change the governing effective length. Do not assume the weak geometric axis automatically governs without checking KL/dKL/d for both directions.

Compression Perpendicular to Grain and Bearing

Timber is much more deformable perpendicular to grain than parallel to grain. Beam seats, column caps, sill plates, and concentrated reactions therefore require a local bearing check using the applicable adjusted compression-perpendicular design value and bearing-area provisions.

Bearing deformation can also be an architectural/serviceability issue where exposed framing must remain aligned with partitions, glazing, or finish tolerances.

Bearing-Area Factor Cb

For sawn-lumber compression perpendicular to grain, the NDS-family bearing-area increase is limited to small interior bearing areas. For a bearing length b<6 in.b<6\text{ in.} located at least 3 in.3\text{ in.} from the member end, the permitted factor is

Cb=b+0.375bC_b=\frac{b+0.375}{b}

with bb in inches. The direct metric equivalent uses 9.525 mm9.525\text{ mm} in place of 0.375 in.0.375\text{ in.}.

Do not apply CbC_b to a bearing at the member end, to a bearing 6 in.6\text{ in.} or longer, or outside the provision's scope. In those cases, use Cb=1.0C_b=1.0 unless another governing product provision explicitly states otherwise.

Bearing Stress

Average compression-perpendicular stress over the effective bearing area.

fc⊥=RAb≤Fc⊥′f_{c\perp}=\frac{R}{A_b}\le F_{c\perp}'

Variables

SymbolDescriptionUnit
RRReaction or force transferred through the bearing interface.-
AbA_bCode-defined effective bearing area.-
fc⊥f_{c\perp}Actual compression stress perpendicular to grain.-
Fc⊥′F_{c\perp}'Adjusted compression-perpendicular design value.-

Architectural Column Decisions

Column size is not determined by area alone. Increasing the dimension about the weak buckling direction can be more efficient than simply adding the same amount of material elsewhere. In exposed timber, this affects visual proportion, bay planning, wall integration, connection concealment, fire-exposed sacrificial section, and the space needed for steel plates or fasteners.

Key Takeaways
  • Timber tension design uses timber-specific net-section and connection provisions; the steel s2/(4g)s^2/(4g) stagger correction is not a general timber rule.
  • Compression-member design should use the NSCP column-stability procedure consistently, with FcEF_{cE}, CPC_P, and Fc′F_c'.
  • Check column stability about every relevant axis and respect the code slenderness applicability limits.
  • Local bearing and compression perpendicular to grain can govern beam seats, column caps, sill plates, and connection regions.
  • Member strength and connection-zone failure modes must be checked together for a review-ready timber design.

References