Module 4: Combined Stresses in Timber & Connections - Examples & Applications

Module 4: Combined Stresses in Timber & Connections - Examples & Applications

Combined Axial and Bending Loads

Basic: Checking a Truss Bottom Chord (Tension + Bending)

The bottom chord of a heavily loaded timber roof truss is subjected to an axial tensile stress of

f_t = 3.0 \text{ MPa}

due to the truss action. Simultaneously, it experiences a bending stress from its own self-weight and an attached ceiling, calculated as

f_b = 5.0 \text{ MPa}

Given Adjusted Allowable Stresses:

Tensile ( $F_t'$ ): $6.0 \text{ MPa}$
Bending ( $F_b'$ ): $10.0 \text{ MPa}$

Determine if the chord member is safe under this combined loading.

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Intermediate: Designing a Top Chord (Compression + Bending)

The top chord of a roof truss acts as a beam supporting roof loads while simultaneously being compressed axially by the overall truss action. The maximum calculated compressive stress is

f_c = 2.5 \text{ MPa}

and the maximum bending stress is

f_b = 6.0 \text{ MPa}

. The adjusted allowable compressive stress is

F_c' = 8.0 \text{ MPa}

and the adjusted allowable bending stress is

F_b' = 12.0 \text{ MPa}

. Assume P-Delta amplification effects are negligible for this specific case (magnification factor

\approx 1.0

Verify if the top chord is adequate.

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Conceptual: Understanding P-Delta Effects

A tall, slender timber column supports a heavy gravity load (

P

) while also resisting a strong lateral wind force (

w

). Explain conceptually why simply adding the direct compressive stress (

P/A

) to the direct bending stress (

M/S

) from the wind is insufficient for a safe design.

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Timber Fasteners and Connections

Basic: Bearing Capacity at an Angle (Hankinson's Formula)

A steel tie rod transfers a compressive force to a wooden timber via a steel bearing plate. The load is applied at an angle of

45^\circ

to the grain of the wood.

Given Parameters for the wood species:

Adjusted allowable bearing stress parallel to grain ( $P$ ): $12.5 \text{ MPa}$
Adjusted allowable bearing stress perpendicular to grain ( $Q$ ): $3.8 \text{ MPa}$

Determine the allowable bearing stress ( $N$ ) for the timber at the contact surface.

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Intermediate: Group Action Factor in a Bolted Joint

A heavy timber connection uses a single row of 6 bolts parallel to the grain to transfer a tensile load between two members. The allowable capacity of a single bolt (

Z

) is calculated as

15 \text{ kN}

. Based on the number of bolts in the row, the NSCP dictates a Group Action Factor (

C_g

) of

0.85

Calculate the total allowable capacity of the bolted joint.

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Conceptual: Fastener Selection based on Failure Modes

A carpenter needs to attach heavy roof sheathing to rafters in an area prone to severe hurricanes (high uplift wind forces). They are considering using either standard smooth-shank nails or lag screws. Recommend the appropriate fastener and justify the choice based on anticipated failure modes.

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Advanced: Geometry Factor ($C_\Delta$) for Bolted Joints

A tension splice between two

50 \text{ mm} \times 150 \text{ mm}

timber members uses two

16 \text{ mm}

bolts. The required end distance for full capacity is

112 \text{ mm}

. However, due to an error, the actual end distance is only

80 \text{ mm}

. The minimum absolute allowed end distance is

56 \text{ mm}

. Calculate the Geometry Factor (

C_\Delta

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