Timber Beam Calculator to AS 1720.1: Bending, Shear and Deflection of a Joist, Rafter or Purlin
Check a sawn timber member for bending, shear and deflection.
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How this calculator works
Enter the span, the spacing of the members, the design and service loads, the section size and the grade properties f'b, f's and E.
The calculator finds the design moment and shear, the bending capacity Md = phi k1 k4 k6 k9 k12 f'b Z (clause 3.2.1.1) and the shear capacity Vd = phi k1 k4 k6 f's As (clause 3.2.5).
It also finds the deflection under the service load against the limit of the span divided by a number, and reports if the member passes.
Formulas used
- M_d = \phi\,k_1k_4k_6k_9k_{12}\,f'_bZ
- V_d = \phi\,k_1k_4k_6\,f'_sA_s,\ \ A_s = \tfrac23bd
- \delta = \frac{5wL^4}{384EI}
- Z = \frac{bd^2}{6}
Worked example
With the default numbers in the calculator above:
- Design load along the member: 0.90 kN/m
- Design bending moment and shear force (simply supported): 1.01 kN m and 1.35 kN
- Section modulus: 270750.00 mm3
- Design capacity in bending (AS 1720.1 cl 3.2.1.1): 2.95 kN m (utilisation 34.37 percent)
- Design capacity in shear (AS 1720.1 cl 3.2.5): 9.12 kN (utilisation 14.80 percent)
- Deflection under the service load (the elastic formula; add the creep factor j2 of AS 1720.1 for long-term loads): 1.97 mm, which is span/1524.22
- Deflection limit: 10.00 mm
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
Which standard is it?
AS 1720.1:2010 Timber structures: Design methods, with the capacity factor from Table 2.1 and the duration of load factor from Table 2.3. The grade properties come from Table H2.1 or the maker.
Why use AS 1684 for a house?
AS 1684 gives span tables for the common cases of house framing that allow for load sharing, bearing and fixing, so a member from the table does not need a separate calculation.
What is k1?
The duration of load factor. Timber is weaker under a load that lasts a long time, so k1 is 0.57 for a permanent load and up to 1.14 for a load of 5 seconds.
Does it check lateral stability?
Only through the factor k12 that you enter. A deep member that is not braced needs a smaller factor.
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Further reading: AS 1720.1:2010 Timber structures: Design methods; AS 1684 Residential timber-framed construction; AS/NZS 1170.0 Structural design actions: General principles.
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