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Timber Beam Calculator to AS1720.1's banner

Timber Beam Calculator to AS1720.1

Verified by the CalcTree engineering team on July 14, 2024

This calculator designs timber members in bending, like rafters and joists, by ensuring the beam meets flexural and shear requirements to Ultimate Limit State (ULS) methods.
All calculations are performed in accordance with AS 1720.1-2010.
Check out our Timber Design Standards - AS1720 and AS1684 for further explanation about timber design for flexural members.

Calculation

Assumptions

  1. Only applicable to solid sawn timber, i.e. excludes plywood, GLT and LVL members
  2. Only applicable to F-grade timber
  3. Input geometry is for rectangular and square sections only
  4. Bending is taken about the major axis only. Combined axis bending check is not included.
  1. Any applied wind,
    
    onto the beam is checked in both the wind pressure load case (1.2G + W + ΨcQ) and wind suction load case (0.9G + Wu)
  1. As per Cl 2.4.2 AS1720.1, seasoned timber has moisture content
    
    , unseasoned timber has moisture content
    
    and partially seasoned timber has moisture content
    
    -
    
    . For seasoned timber, the calculator takes
    
    as per Cl 2.4.2.3 AS1720.1 assuming it's average moisture content for 12 months is not expected to exceed 15%. For unseasoned timber, the calculator takes
    
    as per Cl 2.4.2.2 AS1720.1 assuming it will be subject to its full design load before being partially seasoned. For partially seasoned timber, the calculator uses Table 2.5 AS1720.1


Material Properties



Stress grade
:F27​



f'b
:67​



f's
:5.1​


Stress Grade

Timber used in structural applications are assigned a stress grade classification. These grades can be obtained from visual or machine grading. The grading specifies structural timbers' characteristic values of strength and stiffness and stress limits. Stress grades are generally known by either:
  1. F-Grades: F4 - F34 (i.e. F22 indicates that the bending stress timber is approximately 22 MPa, and it can withstand that force without excessive deflection). Most Hardwoods are ‘F’ graded, with the higher the grade, the stronger the timber. F-Grades for sawn timbers are given in Table H2.1 of Appendix H in AS1720.1, and F-grades for plywood as given in Table 5.1.
  1. Machine-graded pine (MGP): [excluded from this calculator]
  2. Australian Ash (A17-grade): [excluded from this calculator]
  3. Glue-Laminated Timber (GLT): [excluded from this calculator]


Type
:Softwood​



pb
:1.08​


Types

Wood from trees is typically classified as either hardwood or softwood. You can be forgiven for thinking that hardwood indicates the relative hardness of the wood, but this is often misleading as many hardwoods are relatively soft and vice versa. The the main characteristic differences between hardwoods and softwoods are shown below.

Whether the beam is hardwood or softwood affects the

material constant which affects k12.


Seasoned or unseasoned
:Seasoned​



Beam Geometry



d
:{"mathjs":"Unit","value":150,"unit":"mm","fixPrefix":false}​



b
:{"mathjs":"Unit","value":45,"unit":"mm","fixPrefix":false}​



Z
:168750​


Figure 3.1 AS1720.1



Lateral restraint conditions
:Discrete restraints to the compression edge​



L
:{"mathjs":"Unit","value":2000,"unit":"mm","fixPrefix":false}​



Lay
:{"mathjs":"Unit","value":2000,"unit":"mm","fixPrefix":false}​


If applicable:


Laφ
:{"mathjs":"Unit","value":2000,"unit":"mm","fixPrefix":false}​

Figure 3.2 AS1720.1


Loads



Type of live load
:Floors - Residential and Domestic​



G
:{"mathjs":"Unit","value":2,"unit":"kN / m","fixPrefix":false}​



Q
:{"mathjs":"Unit","value":5,"unit":"kN / m","fixPrefix":false}​



W
:{"mathjs":"Unit","value":5,"unit":"kN / m","fixPrefix":false}​



Ψc
:0.4​



Ψs
:0.7​



Ψl
:0.4​

Table for finding the live load factors



Modification Factors



k1
:0.8​


Load duration factor, k1

As per AS1720.1 Clause 2.4.1, the modification factor k1 describes the effect of duration of load on strength.

Since k1 changes for each load combination, we can determine which k1 will be most critical by determining w*/k1 for each load combination:


(0.9G + Wu)/k1
:6.8​



(1.2G + 1.5ΨcQ)/k1
:9.649122807017545​



(1.2G + Wu + ΨcQ)/k1
:9.4​



(1.35G)/k1
:4.7368421052631575​



(1.2G + 1.5Q)/k1
:12.375​



Most critical case
:1.2G + 1.5Q​




k4
:1.0​


Moisture content factor, k4

As per AS1720.1 Clause 2.4.2, k4 considers the effect of seasoning and moisture content. For seasoned & unseasoned timber, k4 = 1. If partially seasoned, k4 is taken from Table 2.5 of AS1720.1.



k6
:1​


Temperature Factor, k6

As per AS1720.1 Clause 2.4.3, k6 considers the effect of temperature. For timber structures that are covered and under ambient conditions, k6 equals 1. For seasoned timber structures in coastal regions of Queensland north of latitude 25S and all other regions of Australia north of latitude 16S, k6 shall be taken as 0.9.


s
:{"mathjs":"Unit","value":500,"unit":"mm","fixPrefix":false}​



n_com
:1​



n_mem
:1​



k9
:1​


Load sharing factor, k9

As per AS1720.1 Clause 3.4.2, k9 considers the effect of parallel timber members acting together as a combined, strength-sharing structural system. Parallel acting systems are classified as either combined systems or discrete systems. A combined parallel system consists of two or more elements that are effectively fastened together, where as a discrete parallel system has three or more members that are discretely spaced parallel to each other. These discrete members support the same set of overlying members or a structural sheathing material.



g31
:1​



g32
:1.0​


For rectangular sawn and round timbers, k9 is a function of the number of members in the system, and can be calculated using AS1720.1 Eq. 2.4.5.3 and Table 2.7. For plywood, GLT and LVL, k9 should be taken as 1.

k9=g31+(g32−g31)[1−2sL]≥1.0k_9 = g_{31} + (g_{32} - g_{31})[1 - \frac{2s}{L}] \ge 1.0



Continuous lateral restraint condition satisfied?
:NO​



k12
:0.6784161637422516​


Stability Factor, k12

As per AS1720.1 Clause 3.2.4, k12 considers the stability of the member. In bending
For bending, as per AS1720.1 Clause 3.2.4, k12 considers the effect of lateral and torsional restraints and member slenderness. The spacing of the lateral and torsional restraints govern how the member buckles under load, which affects its capacity.
k12 is given by:



S1
:15.214515486254601​

The slenderness factor for bending about the major axis, S1, is calculated differently depending on how the member is restrained:







ULS Flexural Checks



ϕ
:0.95​


Capacity reduction factor

As per Table 2.1 of AS1720.1.



M*
:4.95​



Md
:5.82946049099624​



Utilisation_b
:0.8491351828604738​



Design status_b
:PASS​


Md=ϕk1 k4 k6 k9 k12 fb′ Z×ncomM_d = \phi k_1 \space k_4 \space k_6 \space k_9 \space k_{12} \space f'_b \space Z \times n_{com}


V*
:9.9​



Vd
:11.8329347279924​



Utilisation_s
:0.8366479007595823​



Design status_s
:PASS​


Vd=ϕk1 k4 k6 fs′ AsV_d = \phi k_1 \space k_4 \space k_6 \space f'_s \space A_s


Related Resources

  1. Timber Design Standards - AS1720 and AS1684
  2. Timber Column Calculator to AS 1720.1
  3. Timber Beam Calculator to EC5

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