Analysis and Design of Timber Floor Joists to Australian Standards

Designing a timber floor joist for a residential project in Australia involves following the relevant Australian standards to ensure the safety and structural integrity of the floor system.

We will compare the step-by-step process of analyzing timber floor joists using manual hand calculation versus using structural design software like ClearCalcs.

Jump straight to the contents:

• Analysing Timber Floor Joist by Hand Calculation
• Timber Floor Joist Design to Australian Standards Using ClearCalcs
• Timber Floor Joist Case Studies & Best Practices

In this example, we will design a timber floor joist for a residential room with the following specifications:

• Room Dimensions: 5 meters (length) x 4 meters (width).
• Live Load: 1.5 kPa (15 kg/m²)
  This includes the weight of furniture, occupants, etc. AS1170.1 Chapter 3 Table 3.1 details the imposed actions (live loads) that need to be considered for various building types. A uniformly distributed action of 1.5kPa should be considered for a self-contained dwelling.
• Dead Load: 0.5 kPa (5 kg/m²)
  This includes the weight of the floor finish, building services, subfloor, and other fixed loads.

TIP: Get a practical guide on things to consider when designing timber floor joists and different types of timber floor joists commonly used in residential construction.

Analysing Timber Floor Joist by Hand Calculation

Step 1: Select a trial timber species and grade:

If the project is subject to joist size requirements, then it is possible that you would select the size first and determine the species and grade based on that size using the supplementary notes provided in AS 1684, and from there, we can find the suitable timber species, grade, and span based on the size of the floor joist.

However, most projects have flexibility with joist sizes, and builders typically are only able to procure certain timber types due to location or price.

It is good practice for engineers to ask the builder what their timber preferences are in terms of supplier, species, and grade to ensure that the design provided is procurable and buildable.

So, for this example, we will assume the builder has a preference to use "Hardwood – F8" as the timber species and grade, which is a common type in the "Structural Grade" timber from the Australian Standard AS 1720.1-2010 - Timber Structures, which provides guidance on timber selection based on the intended use and loading conditions.

Step 2: Determine a trial joist spacing:

Table 5.3 from AS 1684.2-2010 - Residential Timber-Framed Construction specifies the maximum allowed joist spacing based on the floor loading, span, and timber grade, as shown below.

Figure 1: Guidance on maximum allowed joist spacing based on the floor loading, span, and timber grade in AS 1684.2-2010. (Reference)

Joists spaced more closely together provide a floor with a greater strength capacity but often can clash with building services, and more joists cost more money.

For our example, let's assume the builder has requested a joist spacing of 450 mm (0.45 meters), a common spacing in the industry.

Given the room length of 5 metres, we would have 12 joists.

$5000mm/450mm = 11.1$

This can be adjusted later if we cannot determine a suitable section size for our joists.

Step 3: Calculate the tributary area for each joist:

The tributary area is the portion of the floor that each joist supports. It is generally half of the spacing in each direction for uniform loads.

To calculate the tributary area, consider the following.

Tributary Width (TW) = Spacing = $0.45$

Tributary Area (TA) = Tributary Width (TW) x Joist Length (found from the room dimensions) = $0.45m x 4 m = 0.405 m²$

Step 4: Calculate the design moment action for each joist:

For simply supported timber members, moment will always be critical to the design (rather than shear).

AS 1170.0 Chapter 4 (excerpt shown below) provides guidance on the load factors and combinations that should be considered for the design load.

Figure 2: Load factors and combination to be considered for the design load in AS 1170.0 (Reference)

We always take the most significant load combination factors and design timber floor joists (and all structures) in accordance with the worst-case scenario.

For a floor joist, we will consider the permanent and imposed action loading combination (as wind and earthquake are not relevant) and assign a load factor of 1.2 to the dead load and 1.5 to the live load.

Uniformly Distributed Design Load, $UDL_{joist}$ = $(1.2 x Dead Load (DL_{dead}) + 1.5 x Live Load (DL_{live})) * Tributary Width (TW)$

Design Load, $UDL_{joist}$ = $(1.2 x 0.5 kPa + 1.5 x 1.5 kPa) * 0.45 m = 1.2825 kN/m$

Moment Action ($M^{*}$) =

$wL^2/8 = 1.2825 N/mm * 4000^2 / 8 = 2,565,000 Nmm$

Step 5: Calculate the minimum section modulus for each joist:

As per Section 3.2 of AS 1720.1 Timber Beam Design, we can solve for the minimum section modulus to achieve limit state design.

$M_d = φ*k_1*k_4*k_6*k_9*k_{12}*f_b^{'}*Z$

Using Limit State Design: $M_d$ = design capacity in bending≥ $M^*$v ≥ 2,565,000 Nmm $φ$ = capacity reduction factor (Clause 2.3 AS 1720.1) = 0.9 (refer table) $k_1$ = duration of load modification factor (Table 2.3 AS 1720.1) = 0.57 (50+years) $k_4$ = partial seasoning factor (Table 2.5 AS 1720.1) = 0.7 (seasoned timber) $k_6$ = temperature modification factor (Clause 2.4.3 AS 1720.1) = 1.0 (ambient conditions) $k_9$ = modification factor for strength sharing (Clause 2.4.5.3 AS 1720.1) = $g_31+(g_32-g_31 )*(1-2s/L)=1+(1.33-1)*(1-(2*0.45)/4)=1.25575$ $k_12$ = stability factor (Clause 3.2.4 AS 1720.1) = 1.0 (most conservative value) $f_b^{'}$ = characteristic value in bending = 8 MPa (stress grade F8) $Z$ = section modulus of beam about the axis of bending

We can solve for the minimum section modulus to achieve limit state design.

$Z≥M_d/(φ*k_1*k_4*k_6*k_9*k_12*f_b^{'} )≥(2,565,000 )/(0.9*0.57*0.7*1.0*1.25575*1.0*8)≥711,000mm^3$

Step 6: Trial Section Sizes:

By trialing different section sizes, we can find a suitable section that has a section modulus greater than the required above.

Let’s try a 240 x 45 section.

$Z=(b*d^2)/6=(45*240^2)/6=432,000mm^3$

The minimum section modulus needs to be 711,000 cubic millimeters, so we will need to increase the grade of the timber.

Let’s try a grade of F27.

$Z≥M_d/(φ*k_1*k_4*k_6*k_9*k_12*f_b^{'} )≥(2,565,000 )/(0.9*0.57*0.7*1.0*1.25575*1.0*27)≥210,671mm^3$

Using F27 grade timber, we find the 240 x 45 section size suitable.

The spacing of the joists can also be adjusted by making them closer together to achieve smaller minimum section modulus requirements. To adjust the joist size, return to Step 3 and complete the process again.

Step 7: Check deflection:

To ensure the serviceability of the floor, we must check deflection as per AS 1170.1-2002 - Structural Design Actions Part 1: Permanent, Imposed, and Other Actions. This standard specifies limits on deflection for different floor spans based on floor use.

In our example, the floor span is 5 meters, and we take a maximum allowable deflection of $L/250$ (where L is the span length).

Maximum Allowable Deflection $= 5000mm/250 = 20mm$

Second Moment of Area

$I_x=(bd^3)/12=(45*240^3)/12=51,840,000mm^3$

$δ=((5wL^4))/((384EI))=((5*1.2825*5000^4))/((384*18500*51,840,000))=11mm$

The deflection is within the limits. The selected joist size is suitable for the residential project as per Australian standards.

Please note that this example provides a simplified outline of the design process, and in a real-world scenario, a qualified structural engineer should perform a comprehensive analysis considering all applicable factors and standards for accurate and safe design.

Always consult the relevant Australian standards and seek professional advice when designing structural elements for a project.

Timber Floor Joist Design to Australian Standards Using ClearCalcs

The Timber Beam Calculator to AS 1720.1:2010 enables you to do quick and powerful design and analysis for simple and continuous timber beams, with unlimited supports and loads.

The member selector tool, which has a library of thousands of common timber sections, allows you to get instant results for moment, deflection, and shear, which means that engineers don’t have to iteratively perform calculations as with the worked example by hand above which saves heaps of time!

Step 1: Enter the Key Properties

From our example above, we have a joist length of 4000mm that is simply supported. So we'll just need to enter the total beam length and the support positions into the support table.

Step 2: Enter the Loads

Live load: 1.5 kPa (15 kg/m²)

This includes the weight of furniture, occupants, etc. AS1170.1 Chapter 3 Table 3.1 details the imposed actions (live loads) that need to be considered for various building types. For a self-contained dwelling, a uniformly distributed action of 1.5kPa should be considered.

Dead load: 0.5 kPa (5 kg/m²)

This includes the weight of the floor finish, building services, subfloor, and other fixed loads.

Floor joists only bend about the major axis.

Step 3: Check the Design Criteria, Member Properties and Modifications Factors

By default, the ClearCalcs Timber Calculator already has the Design Criteria, Member Properties, and Modifications Factors prefilled based on the inputs provided in the Key Properties and Loads.

Some of these can be manually changed, and clicking on each input will provide a description of the parameter as well as the relevant Australian Standard to refer to for further information.

For example, if you would like to know more about the Equilibrium Moisture Content (EMC) value used in the calculation, the calculator shows that it is based on Clause 2.4.2.3 of the AS 1720.1:2010.

Step 4: Assess Summary Outputs

The summary outputs provide immediate feedback for the design and detail the utilization of the moment, shear, bearing, and deflection capacity.

Step 5: Optimise the Design

The member selector tool has thousands of standard grades and sizes of timber and provides immediate feedback on the utilization of their moment, shear, bearing, and deflection capacity.

Users can use this tool to provide the most efficient design possible, ensuring that members aren’t unnecessarily oversized (utilization <50%) or undersized (utilization>100%).

This can help reduce material costs for the builder and is also environmentally efficient.

Timber Floor Joist Case Studies & Best Practices

Case Study 1: Open-Concept Multi-Level Living Space

Description

In this residential project, the design called for an open-concept living space with multiple levels and a seamless connection between different areas. Timber floor joists were creatively used to achieve a visually appealing and functional interior.

Innovative Use

Cantilevered Timber Floor Joists

Best Practices

• Structural Analysis: Before implementing cantilevered timber floor joists, a thorough structural analysis was conducted to ensure that the selected timber species and grade could support the intended loads without compromising safety and stability. Shear and deflection become critical for cantilevered members.
• Expert Engineering: A qualified structural engineer worked closely with the architect and construction team to design the cantilevered floor system. The engineer accounted for factors like deflection, vibration, and load distribution to ensure the best possible performance.
• Timber Selection: High-quality, durable timber with the appropriate strength and structural properties was chosen. The timber species and grade were carefully selected to meet the design requirements and comply with relevant Australian standards.

Case Study 2: Sustainable Commercial Building

Description

A commercial office building aimed to be environmentally friendly and promote sustainability throughout its design. Timber floor joists played a crucial role in achieving this objective.

Innovative Use

Glue-Laminated Timber (Glulam) Floor Joists

Best Practices

• Sustainable Material: Glulam, made from laminated layers of sustainably sourced timber, was used as an eco-friendly alternative to traditional solid timber or steel. The building's sustainability goals were met by reducing the carbon footprint associated with construction materials.
• Fire Resistance: The glulam timber used in the floor joists was treated with fire-retardant coatings to enhance fire resistance, making it compliant with relevant fire safety regulations.
• Quality Control: Quality control measures were implemented throughout the manufacturing process of glulam timber to ensure uniformity and structural integrity. Adherence to Australian standards for glulam production was paramount.

Case Study 3: Adaptive Reuse of Industrial Space

Description

An old industrial building was repurposed into a modern co-working space that preserved its industrial charm. Timber floor joists were an essential component in the adaptive reuse of the space.

Innovative Use

Exposed Timber Floor Joists

Best Practices

• Structural Evaluation: The existing timber floor joists were thoroughly inspected by structural engineers to assess their condition and capacity. Any damaged or weak joists were repaired or replaced, ensuring safety and stability.
• Architectural Aesthetics: The original timber floor joists were left exposed, adding character and a rustic ambiance to the co-working space. Careful consideration was given to their arrangement to create visually appealing patterns.
• Acoustic Treatment: To control noise transmission between different areas of the co-working space, acoustic treatments were incorporated into the design. Sound-absorbing materials were strategically placed to minimize noise disruptions.

Overall Best Practices for Timber Floor Joists:

• Compliance with Standards: All designs and installations should comply with relevant Australian standards for timber structures, ensuring safety and meeting legal requirements.
• Professional Expertise: Qualified structural engineers and architects should be involved in the design process to ensure proper analysis, selection of suitable timber, and adherence to best practices.
• Regular Maintenance: Timber floor joists should undergo regular inspections and maintenance to identify any issues and prolong their service life.
• Sustainable Sourcing: Use sustainably sourced timber or timber alternatives to promote environmental consciousness in construction projects whenever possible.
• Fire Safety: Implement appropriate fire-retardant treatments and measures as building codes and regulations require.

By applying these best practices and embracing innovative uses, timber floor joists can be utilized effectively and safely to create unique and sustainable spaces in various construction projects.