Mechanical Properties of Wood - Comprehensive Notes

Mechanical Properties of Wood

Introduction

• Wood is idealized as orthotropic, meaning it has three distinct directions:
  • Longitudinal (fiber direction)
  • Radial
  • Tangential

Direction of Loading

• The direction of loading significantly affects strength.
• Strength differs when the load is parallel versus perpendicular to the grain.

Types of Loading

• Compression
• Tension
• Shear
  • Transverse shear
  • Longitudinal shear
• Bending

Important Considerations

• Nature of the material and its variability.
• Loading direction and potential failure modes.

Compression Strength and Grain Angle

• Hankinson's formula is used to predict compression strength at different grain angles.
• Experimental values are compared with Hankinson's formula.

Hankinson Formula

• $F_{0}$ = strength parallel-to-grain
• $F_{90}$ = strength perpendicular-to-grain
• $\Theta$ = angle between load and direction of fibers
• The formula is: $f = \frac{f<em>{0} f</em>{90}}{f<em>{0} \sin^2 \theta + f</em>{90} \cos^2 \theta}$

Structural Designs and 5th Percentile Strengths

• Structural designs use 5th percentile strengths.
• This means there's a 95% probability that the material's strength will exceed the design value.

Characteristic Strength

• The design strength is often called the “characteristic strength.”
• It is provided in design standards for various product grades.
• Assignment methods:
  • Visual grading
  • Machine-stress grading

Characteristic Strength Assignment

• $f$ = characteristic strength
• Assigned using real size members.

Machine Stress Grading

• Involves a system of rollers (support, fixed, and load rollers) to apply force and measure deformation.
• Coloured lines may indicate stress grading of each part.

Machine-Stress Grading Details

• Evaluates either strength or stiffness.
• The strength of the piece is assigned based on the relationship between deformation and strength or force and strength, which are determined previously.

Acoustic Grading

• A sonic stress wave is sent through the piece to determine the modulus of elasticity, $E$.
• Strength is then assigned based on the relationship between $E$ and strength.

Visual Grading

• Strength of visually graded timber is assigned based on knot sizes.
• Grade marking is done using paint.

Grades for Sawn Timber

• Factors include: species, grade, and moisture condition.
• Moisture condition is either dry (m/c = 16%) or green (m/c = 25%).
• Properties listed include bending strength, compression strength, tension strength, modulus of elasticity, and lower bound modulus of elasticity.
• Example species: Radiata pine & Douglas fir.
• Visual grades listed: VSG10, VSG8, G8.
• No.1 Framing grade isn't verified for strength/stiffness and follows NZS 3631.
• Green condition values used when moisture may be 25%+. Durability must meet NZS 3602:2003.
• Shear and compression strengths provided for dry and green Radiata pine and Douglas fir.
• Modulus of rigidity is taken as $G = E/15$.

Strength Grades for Sawn Timber - Machine Graded

• Includes grades like MSG15, MSG12, MSG10, MSG8, MSG6.
• Shear strength for dry Radiata pine is $f<em>s = 3.8$ MPa and Douglas fir is $f</em>s = 3.0$ MPa.
• Compression perpendicular to grain for dry Radiata pine and Douglas fir is $f_p = 8.9$ MPa.
• Grades are verified as per NZS 3622.

Strength Modifiers

• Factors affecting strength:
  • Load duration
  • Service conditions (wet or dry)
  • Treatment

Load Duration Effect

• Load duration ↑ means Strength ↓

Load Duration Effect Details

• The Madison Curve (USA) illustrates the relationship between load duration and strength ratio, obtained from small clear specimens.
• Strength of wood pieces must be adjusted depending on the load's duration.
• This is a fundamental difference from steel and concrete design.

Design Modification

• $f<em>{design} = f(k</em>1 …..)$
• $k_1$ is the load duration factor.

Load Duration Factor Examples

• Permanent loads (stores, library stacks, fixed plant, soil pressures): $k_1 = 0.60$
• Medium loads (snow, live loads, crowd loadings, concrete formwork, vehicle, pedestrian and cattle loadings): $k_1 = 0.80$
• Brief loads (wind, earthquake, impact, erection and maintenance loadings, pile driving): $k_1 = 1.00$

Service Conditions

• Dry timber has moisture content (MC) below 16%.
• Wet timber has MC above 16%.

Moisture Effect

• $f<em>{design} = f (k</em>1 k_2 …..)$
• $k_2$ accounts for moisture condition and deflection during load duration.
• Some standards provide $f<em>{dry}$ and $f</em>{wet}$ as separate values.

Design of Members in Sawn Timber (NZS 3603)

• Basis of design: $S* ≤ φ R_n$
  • $S*$ - Imposed design action
  • \φ - Strength reduction factor
  • $R_n$ - Nominal resistance

Available Sizes and Properties of Sawn Timbers

• Nominal and actual dimensions (breadth, depth) are given in mm.
• Properties include area, weight, section modulus, and second moment of area.

Strength Reduction Factors - φ

• For timber, poles, and glulam: $\phi = 0.8$
• For nails in lateral loading: $\phi = 0.8$
• For toothed metal plate connectors: $\phi = 0.8$
• For other types of fasteners: $\phi = 0.7$
• For plywood: $\phi = 0.9$
• For actions derived from the strength of ductile elements under large displacements: $\phi = 1.0$
• Design for fire resistance: $\phi = 1.0$