Module 3: Timber Beams - Examples & Applications

A simply supported rectangular timber beam (width $b = 100 \text{ mm}$, depth $d = 200 \text{ mm}$) spans $3 \text{ meters}$ and carries a uniform load.

Structural analysis reveals the following maximum internal forces:

• Maximum bending moment ($M$) = $5 \text{kN}\cdot\text{m}$
• Maximum shear force ($V$) = $10 \text{kN}$

Given Adjusted Design Values:

• Bending ($F_b'$): $12 \text{MPa}$
• Shear ($F_v'$): $1.0 \text{MPa}$

Evaluate the isolated bending and horizontal-shear checks using the supplied adjusted design values. Bearing, stability, serviceability, and detailing are outside this first example.

Calculate the Beam Stability Factor ($C_L$) for an unbraced roof beam spanning $5.0 \text{ m}$. The dimensions are $100 \text{ mm} \times 300 \text{ mm}$.

Given Parameters:

• Reference bending design value ($F_b^*$): $14.0 \text{ MPa}$
• Minimum Modulus of Elasticity ($E_{min}'$): $6,000 \text{ MPa}$
• Effective unbraced length ($l_e$): $5,000 \text{ mm}$

A $150 \text{ mm} \times 300 \text{ mm}$ timber beam has a main span of $4.0 \text{ m}$ and a $1.5 \text{ m}$ overhang. It carries a uniform service load of $5 \text{ kN/m}$ over the full $5.5 \text{ m}$ length. For this ASD bending check, use $F_b'=10 \text{ MPa}$.

A uniformly loaded simply supported timber floor joist spans $4.0 \text{ m}$. The immediate (instantaneous) deflections due to the applied loads have been calculated as follows:

• Immediate Dead Load Deflection ($\Delta_{DL}$): $8 \text{ mm}$
• Immediate Live Load Deflection ($\Delta_{LL}$): $10 \text{ mm}$

For this stated problem, use the NDS long-term deformation factor $K_{cr}=2.0$ for the sustained dead-load component, while the live load is treated as transient. The project serviceability criterion limits the resulting total deflection to $L/240$. Actual $K_{cr}$ and deflection criteria must come from the applicable NSCP/NDS/product provisions and project requirements.

Evaluate the stated serviceability criterion for the joist.

A $100 \text{ mm} \times 200 \text{ mm}$ timber joist spans $3.0\text{ m}$. A service live load of $2\text{ kN/m}$ acts only over the left half of the span ($a=1.5\text{ m}$). Use $E=10{,}000\text{ MPa}$ and determine the maximum immediate elastic deflection.

A long-span timber beam ($6.0 \text{ m}$) is expected to deflect $15 \text{ mm}$ under dead load and $10 \text{ mm}$ under live load. The architect wants the floor to be perfectly flat under dead load. Determine the required initial camber.

A $150 \text{ mm} \times 300 \text{ mm}$ timber beam is simply supported on a concrete wall. For this ASD/service-load bearing check, the support reaction is $R=45\text{ kN}$ and the adjusted compression-perpendicular-to-grain design value is $F_{c\perp}'=2.5\text{ MPa}$.

A $100 \text{ mm} \times 250 \text{ mm}$ timber joist has an allowable shear stress of $F_v' = 1.2 \text{ MPa}$. However, it is notched at the support on its tension (bottom) face to fit over a ledger board. The notch depth is $50 \text{ mm}$, leaving a reduced net depth ($d_n$) of $200 \text{ mm}$ at the support.

Calculate the maximum allowable shear force ($V$) the notched end can support.

A $20 \text{ kN}$ point load is applied to the top edge of a timber beam via a steel bearing plate. The beam is $100 \text{ mm}$ wide. $F_{c\perp}' = 3.0 \text{ MPa}$. Find the minimum required length of the steel plate along the beam axis.