7.3 Timber and Masonry Design

Timber and Masonry Design per NDS and TMS

Timber and masonry design represent specialized material sections on the PE Civil exam. Wood design is governed by the National Design Specification (NDS) for Wood Construction, while masonry design is governed by the The Masonry Society (TMS) 402/602 standard.

1. Design of Wood Members

Unlike isotropic materials like steel, wood is an orthotropic, organic material whose strength depends on grain direction, duration of load, moisture, and size. Design in timber uses reference design values (such as $F_b$ for bending, $F_v$ for shear, $F_t$ for tension, $F_c$ for compression parallel to grain) that are modified by multiple adjustment factors to obtain the adjusted design values ($F'$).

Key NDS Adjustment Factors

The adjusted design value ($F'$) is calculated as the reference value multiplied by the product of all applicable factors: $F'_b = F_b \times C_D \times C_M \times C_t \times C_L \times C_F \times C_{fu} \times C_r$

Here are the most critical factors tested on the PE exam:

• Load duration factor ($C_D$): Accounts for the ability of wood to carry higher loads for short periods. Since wood creeps under sustained loads, reference values are adjusted based on the shortest duration load in a combination:
  • Dead Load: $C_D = 0.90$
  • Occupancy Live Load: $C_D = 1.00$
  • Snow Load: $C_D = 1.15$
  • Construction / Wind / Seismic Load: $C_D = 1.60$
  • Impact Load: $C_D = 2.00$
• Wet service factor ($C_M$): Applies when the moisture content of the wood in service exceeds 19% for sawn lumber. Reference design values are reduced (typically $C_M < 1.0$) under wet conditions.
• Size factor ($C_F$): Applies to visually graded sawn lumber to account for the statistical likelihood of larger members containing larger natural defects.
• Repetitive member factor ($C_r$): A 15% increase ($C_r = 1.15$) applied to bending stress $F_b$ for joists, rafters, or studs that are spaced no more than 24 inches on center, are at least three in number, and are joined by a transverse load-distributing element (like sheathing).
• Beam stability factor ($C_L$): Adjusts $F_b$ to account for lateral-torsional buckling when the compression edge of a beam is not continuously braced.
• Column stability factor ($C_P$): Adjusts $F_c$ (compression parallel to grain) to account for buckling.
• Flat use factor ($C_{fu}$): Increases bending capacity when lumber is bent about its minor axis.

NDS groups wood species (such as Southern Pine, Douglas Fir-Larch, Hem-Fir, Spruce-Pine-Fir) into categories. Note that Southern Pine is unique because its size factor $C_F$ is already built into its reference design values for some sizes, unlike other species.

Flexural design

The bending stress ($f_b = M/S$) must not exceed the adjusted bending design value ($F'_b$): $f_b \le F'_b$

Compression Parallel to Grain and Column Design

The compressive stress parallel to grain ($f_c = P/A$) must not exceed the adjusted compressive design value ($F'_c$): $f_c \le F'_c = F_c \times C_D \times C_M \times C_t \times C_F \times C_P$

The column stability factor ($C_P$) is computed as: $C_P = \frac{1 + (F_{cE} / F_{c}^*)}{2 c} - \sqrt{ \left[ \frac{1 + (F_{cE} / F_{c}^*)}{2 c} \right]^2 - \frac{F_{cE} / F_{c}^*}{c} }$ Where:

• $F_{c}^*$ is the reference compressive value adjusted by all factors except $C_P$.
• $F_{cE} = \frac{0.822 E_{min}'}{(l_e / d)^2}$ is the critical buckling stress.
• $c = 0.8$ for sawn lumber, $0.85$ for round timber poles, and $0.9$ for glulam.
• $l_e / d$ is the column slenderness ratio, which must not exceed 50.

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2. Timber Connections

Timber connections are critical because wood has low shear strength parallel to the grain and virtually no tensile strength perpendicular to the grain. Connections typically use dowel-type fasteners (bolts, lag screws, wood screws, nails).

Connection Load Capacities

Fastener connections must be checked for two primary modes of load transfer:

1. Withdrawal capacity ($W$): The force required to pull a fastener straight out of the member perpendicular to the wood surface. Nails, wood screws, and lag screws have allowable withdrawal capacities expressed in pounds per inch of penetration.
2. Lateral capacity ($Z$): The shear capacity of the fastener acting perpendicular to the fastener axis. Calculated using the NDS yield limit equations, which account for wood crushing and fastener yielding.

Connection Adjustment Factors

Similar to members, connections have reference design values ($W, Z$) modified by factors: $Z' = Z \times C_D \times C_M \times C_t \times C_g \times C_{\Delta}$ Where:

• $C_g$ is the group action factor (reduces capacity when multiple bolts are aligned in a row because the load is not shared equally).
• $C_{\Delta}$ is the geometry factor (reduces capacity if minimum end distances, edge distances, or spacing requirements are not met).

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3. Design of Masonry Walls per TMS 402/602

Masonry design on the PE Civil exam is based on the TMS 402/602 standard (Building Code Requirements and Specification for Masonry Structures).

Masonry Material Components

Masonry is a composite material consisting of:

• Concrete masonry units (CMU) or clay brick units. Clay masonry is designed using nominal dimensions that are 3/8 inch larger than actual dimensions to account for mortar joints.
• Mortar: Places units together and binds them. Mortar is categorized into types from highest to lowest compressive strength: M, S, N, O (often remembered using the mnemonic "MaSoN wOrK"). Type M is typically used for below-grade foundation walls, Type S for high lateral loads, Type N for general above-grade walls, and Type O for non-load bearing interior partitions.
• Grout: A fluid concrete mixture poured into the cells of CMUs to increase strength and embed reinforcement.

Design Methods

TMS 402 allows two design methods: allowable stress design (ASD) and strength design (SD). In ASD, actual stresses under service loads are compared to allowable limits (e.g., $f_b \le F_b$, $f_a \le F_a$). In strength design, factored nominal capacities are used with strength reduction factors ($\phi$).

Axial Capacity of Masonry Walls

The axial compressive capacity of masonry walls is reduced by slenderness. The allowable axial compressive force ($P_a$) in ASD is based on the slenderness ratio ($h/r$):

• For $h/r \le 99$: $P_a = (0.25 f'_m A_n + 0.65 A_{st} F_{sc}) \left[ 1 - \left(\frac{h}{140r}\right)^2 \right]$
• For $h/r > 99$: $P_a = (0.25 f'_m A_n + 0.65 A_{st} F_{sc}) \left[ \frac{70r}{h} \right]^2$

Where:

• $f'_m$ is the specified compressive strength of masonry.
• $A_n$ is the net cross-sectional area of the masonry.
• $h$ is the effective height of the wall.
• $r$ is the radius of gyration.
• $A_{st}$ is the area of longitudinal steel, and $F_{sc}$ is the allowable compressive stress in the steel.

Flexural Design of Masonry Walls

Out-of-plane bending loads (such as wind or lateral earth pressures) create flexural stresses. In strength design, the nominal flexural strength ($M_n$) of a reinforced masonry wall is computed similarly to concrete beams under flexure: $M_n = A_s f_y \left(d - \frac{a}{2}\right)$ Where the compression block depth $a$ is: $a = \frac{A_s f_y}{0.80 f'_m b}$ And the strength reduction factor ($\phi$) for flexure in masonry is 0.90.