Module 2: Timber Tension and Compression Members

Module 2: Timber Tension and Compression Members

Axially Loaded Timber Members

Axial members carry loads parallel to their longitudinal axis. Because wood is orthotropic, its strength parallel to the grain (

F_t

F_c

) is significantly different from its strength perpendicular to the grain (

F_{c\perp}

). Tension members tend to fail by rupture, while compression members (columns) typically fail via buckling long before the material itself crushes.

Timber Tension Members

Timber tension members are relatively straightforward to design but require careful consideration of connections, as this is where failures most often occur due to reduced cross-sectional areas (holes) and the potential for shear block failure or splitting.

Checklist

Net Area ( $A_n$ ): The gross area minus any holes, notches, or daps used for fasteners (bolts, split rings).
Allowable Tensile Capacity ( $P_t$ ): The maximum load is calculated by multiplying the adjusted allowable tensile stress ( $F_t'$ ) by the net area.

$$
P_t = F_t' \\times A_n
$$

Staggered Fasteners

Net Area with Staggered Holes

When multiple rows of bolts are used, staggering them (rather than placing them side-by-side) can increase the net cross-sectional area and thus the member's tensile capacity. The calculation is similar to steel design, ensuring no diagonal failure path is weaker than a straight transverse path.

Evaluate all possible failure paths (straight across vs. zig-zag).
For any diagonal path, the net area is increased by a factor of $s^2 / 4g$ for each stagger, where $s$ is the longitudinal spacing (pitch) and $g$ is the transverse spacing (gauge).

Key Takeaways

Tension capacity is strictly governed by the net area ( $A_n$ ), which accounts for section loss due to fasteners.
Failures in tension members frequently occur at the connections due to the localized stresses and reduced area.

Slenderness Limit and Euler Buckling

Before classifying columns, timber design imposes a strict Slenderness Ratio limit to prevent catastrophic global buckling. The slenderness ratio is defined as

l_e / d

, where

l_e

is the effective length and

d

is the least dimension of the cross-section.

NSCP Slenderness Limit: For solid timber columns, the ratio

\frac{l_e}{d}

shall not exceed 50.

When a timber column becomes sufficiently slender, its failure is dictated not by the crushing strength of the wood fibers, but by elastic instability (buckling). The critical buckling stress for timber is derived from the theoretical Euler buckling formula, adjusted for the natural variability of wood (

K_{cE}

$$
F_{cE} = \frac{0.822 E_{min}'}{(l_e / d)^2}
$$

Column Classification

The compressive capacity of a wood column depends heavily on its slenderness ratio (

L_e / d

), where

L_e

is the effective unbraced length and

d

is the least dimension of the cross-section. The NSCP places a strict upper limit on slenderness for solid columns:

L_e/d \le 50

Checklist

Short Columns ( $L_e / d \le 11$ ): These stocky columns fail entirely by the wood fibers crushing. Buckling is not a concern. The allowable compressive stress ( $F_c'$ ) is equal to the adjusted reference compressive stress parallel to grain ( $F_c^*$ ).
Intermediate Columns ( $11 \lt L_e / d \le K$ ): These columns fail through a complex combination of wood fiber crushing and lateral inelastic buckling. The allowable stress must be reduced using an empirical formula dependent on the slenderness ratio and a slenderness factor $K$ .

$$
K = 0.671 \\sqrt{\\frac{E}{F_c}}
$$

Checklist

Long Columns ( $K \lt L_e / d \le 50$ ): These slender columns fail purely due to lateral elastic buckling (Euler buckling) before the wood fibers ever reach their crushing strength. The allowable compressive stress is determined solely by stiffness ( $E$ ) and slenderness.
The formula for $F_c'$ in long columns is directly derived from Euler's critical buckling stress ( $F_e = \pi^2 E / (L_e/d)^2$ ), modified by a safety factor for wood's natural variability.

$$
F_c' = \\frac{0.30 E}{(L_e / d)^2}
$$

Key Takeaways

Timber columns are classified as short, intermediate, or long based on their slenderness ratio ( $L_e/d$ ).
Short columns fail by crushing, intermediate columns fail by a combination of crushing and inelastic buckling, and long columns fail purely by elastic Euler buckling.
The NSCP strictly limits the slenderness ratio for solid timber columns to $L_e/d \le 50$ to prevent catastrophic buckling failures.

C_P

Modern timber design (NDS/NSCP) unifies the short, intermediate, and long column equations into a single, continuous curve using the Column Stability Factor (

C_P

). This factor (

C_P \le 1.0

) reduces the reference compressive stress (

F_c^*

) based on the possibility of buckling.

Calculating CP

The Column Stability Factor (

C_P

) modifies the adjusted reference compressive stress parallel to grain (

F_c^*

). It depends heavily on the critical buckling design value (

F_{cE}

$$
C_P = \\frac{1 + (F_{cE} / F_c^*)}{2c} - \\sqrt{ \\left[ \\frac{1 + (F_{cE} / F_c^*)}{2c} \\right]^2 - \\frac{F_{cE} / F_c^*}{c} }
$$

Key Takeaways

The Column Stability Factor ( $C_P$ ) accounts for the reduction in compressive capacity due to buckling.
$C_P$ relies on the interaction between the critical elastic buckling stress ( $F_{cE}$ ) and the reference compressive stress ( $F_c^*$ ).
The interaction parameter 'c' differs based on the material type: 0.8 for solid sawn lumber and 0.9 for glulam.

Spaced Columns

A spaced column consists of two or more individual members separated by spacer blocks at their ends and middle, and joined by shear plates or split ring connectors. Because the connectors force the individual members to act somewhat integrally, the entire assembly possesses greater buckling resistance (a higher effective stiffness) than the sum of its individual parts acting independently.

Checklist

Spaced columns effectively increase the allowable load by providing a "fixity" factor ( $K_x = 2.5$ or $3.0$ , depending on the end block connection) to the Euler buckling equation.
The slenderness limit for individual members within a spaced column assembly is relaxed to $L_e/d \le 80$ .
Condition: To qualify as a spaced column, the ratio of the thickness of the spacer block to the individual member thickness ( $t$ ) must be at least 1.0, and the clear space between members must be strictly maintained.

Built-up Solid Columns

A built-up solid column is constructed by nailing or bolting multiple laminations (layers of dimension lumber) together face-to-face to create a larger, stronger column.

Built-up Column Behavior and Slip

Unlike Glulam (which uses structural adhesive to create a truly solid member), mechanically fastened built-up columns exhibit slip between the laminations when subjected to bending or buckling. Because the nails or bolts bend slightly under load, the laminations cannot completely share horizontal shear forces.

Capacity Reduction: The allowable compressive capacity of a nailed or bolted built-up column is less than a solid timber column of the same dimensions.
Modification Factor ( $K_f$ ): The Column Stability Factor ( $C_P$ ) calculation is modified using a form factor ( $K_f$ ) to account for this reduced stiffness and interlayer slip.

Bearing Stress (Compression Perpendicular to Grain)

When a column rests on a sill plate or a beam transfers loads to its support, the bearing area is subject to compression perpendicular to the grain (

F_{c\perp}

Bearing Failure Mechanism

Unlike compression parallel to grain which can lead to catastrophic buckling, bearing failure (perpendicular to grain) is usually a serviceability issue. The wood fibers crush locally, leading to excessive deformation, but rarely causing total structural collapse. The allowable bearing stress (

F_{c\perp}'

) is adjusted primarily by the Bearing Area Factor (

C_b

) if the bearing length is short (less than 150mm).

K_e

Boundary Conditions

The unbraced length (

L

) of a column must be modified to an effective length (

L_e = K_e \\cdot L

) depending on its end restraints (boundary conditions). This reflects how freely the column ends can rotate or translate.

Pinned-Pinned ( $K_e = 1.0$ ): Ends can rotate but not translate. The standard theoretical baseline.
Fixed-Free ( $K_e = 2.10$ ): A flagpole or cantilever column, highly susceptible to buckling.
Fixed-Fixed ( $K_e = 0.65$ ): Theoretical value is 0.5, but the NSCP requires 0.65 for design due to the impossibility of achieving a perfectly rigid connection in timber.
Fixed-Pinned ( $K_e = 0.80$ ): Theoretical value is 0.7.

Key Takeaways

Spaced columns combine multiple members using spacer blocks and shear connectors to increase overall buckling resistance.
The structural assembly acts integrally, allowing a higher slenderness limit ( $L_e/d \le 80$ ) compared to solid columns.
Tension capacity is usually limited by the net section area at connections.
Compression capacity is heavily dictated by the slenderness ratio ( $L_e/d$ ), with buckling being the primary failure mode for intermediate and long columns.
The Column Stability Factor ( $C_P$ ) is a critical adjustment factor that unifies column design, accurately reducing allowable stress based on the geometric susceptibility to buckling.

PreviousModule 1: Introduction to Timber Engineering - Examples & Applications

NextModule 2: Timber Tension and Compression Members - Examples & Applications

Axially Loaded Timber Members

Timber Tension Members

Checklist

Staggered Fasteners

Net Area with Staggered Holes

Slenderness Limit and Euler Buckling

Column Classification

Checklist

Checklist

The Column Stability Factor (CPC_PCP​)

Calculating CP

Spaced Columns

Checklist

Built-up Solid Columns

Built-up Column Behavior and Slip

Bearing Stress (Compression Perpendicular to Grain)

Bearing Failure Mechanism

Effective Length Factor (KeK_eKe​)

Boundary Conditions

The Column Stability Factor ( $C_P$ )

Effective Length Factor ( $K_e$ )