Bending and Shear Capacity

Python code for the following examples are available in the Github repository examples folder. Several examples on this page are sourced from the Timber Design Handbook (Standards Australia HB 108 - 2013), written by Geoffrey Boughton and Keith Crews.

Bending Capacity

The design bending capacity of timber member as per AS1720.1 Clause 3.2.1 is: $$ M_{d} = \phi k_1 k_4 k_6 k_9 k_{12} f_b Z $$

Input and evaluation of bending design parameters using timberas is detailed further with reference to the following example.

Example 5.1, Timber Design Handbook (page 333):

Check the bending design capacity of a formwork bearer. The bearer spans 2.7m, is a nominal 250 mm x 50 mm section, and is made from unseasoned F11 messmate timber. Joists are skew-nailed to the top edge of the bearer at 450mm centres.

Solution:

from timberas.geometry import TimberSection as TS
from timberas.material import TimberMaterial as TM
from timberas.member import (
    BoardMember,
    ApplicationCategory,
    DurationFactorStrength,
    RestraintEdge,
)

sec = TS.from_library("Nominal 250x50")
mat = TM.from_library("F11 Unseasoned Hardwood")
mat.update_from_section_size(sec.d)
member_dict = {
    "sec": sec,
    "mat": mat,
    "application_cat": ApplicationCategory.PRIMARY_MEMBER,
    "k_1": DurationFactorStrength.FIVE_DAYS,
    "r": 0,
    "L": 2700,
    "L_a": {"x": None, "y": 450},
    "restraint_edge": RestraintEdge.COMPRESSION,
}
member = BoardMember(**member_dict)
member.report(["S1", "k_12_bend", "M_d", "L_CLR", "CLR"])

#(ANS: k_12_bend = 1.0, M_d = 9.75kNm)

Bending design parameters are derived from member inputs as follows:

$\phi$, $k_1$, $k_4$, $k_6$ as described for previous capacities.
Section modulus $Z$ is a TimberSection derived attribute.
Characteristic bending strength $f_b$ is a TimberMaterial attribute.
Strength sharing factor $k_9$ (Ref. Cl 2.4.5) is implemented in TimberMember child classes:
- For GlulamMember, $k_9$ always equals 1.0.
- For BoardMember, $k_9$ is evaluated from additional input n_mem (number of members spaced parallel to each other) and s (member spacing). Parameter n_com (number of elements fastened together in member) is a TimberSection attribute.
Stability factor for bending $k_{12}$ (Ref. Cl 3.2.4) is derived from:
- Material constant $\rho_B$ - requires a load-dependent ratio parameter $r$ (temporary design action / permanent design action).
- Slenderness coefficient $S1$ - requires lateral restraint information (distance between restraint and restrained edge condition).

Distance between lateral restraints on the tension or compression edge is $L_{ay}$, using the same input as for lateral restraint against compressive buckling:

"L_a": {"x": None, "y": 450}

The restraint edge condition is specified with the restraint_edge attribute. This accepts a string value (e.g. "compression" for compression edge) or a RestraintEdge enum class attribute; the latter gives type-safe input of available restraint edge conditions.

"restraint_edge": RestraintEdge.COMPRESSION,

The timber member will self-evaluate whether the distance between lateral restraints is sufficient to provide continuous lateral restraint (CLR). If $L_{ay}<=L_{CLR}$, the member is considered continuously restrained (CLR = True). If not, it is considered as having discrete restraints (CLR=False).

For the special case of continuous tension edge restraint with discrete torsional restraint, distance between torsional restraints is provided with a phi key in the L_a input dictionary:

"restraint_edge": RestraintEdge.TENSION_AND_TORSIONAL,
"L_a": {"x": None, "y": 450, "phi" = 900}

Bending capacity is currently evaluated about the x-axis only, using $S1$ if the $x$ direction is the major axis ($k_{12}<=1.0$), or $S2$ otherwise if $x$ is the minor axis ($k_{12}=1.0$).

Shear Capacity

The design shear capacity of timber member as per AS1720.1 Clause 3.2.5 is: $$ M_{d} = \phi k_1 k_4 k_6 f_s A_s $$ Input and evaluation of shear design parameters using timberas is detailed further with reference to the following example.

Example 5.6, Timber Design Handbook (page 401):

Evaluate the design bending and shear capacities of a GL12 floor beam member under a: (a) permanent and short-term (5 day) load case; and (b) permanent load case
The floor beam has a 4 m design span and supports an office floor in a building in Victoria. Joists are attached to the top of the beam with nailed straps at 450 mm spacing. Solution:

from timberas.geometry import TimberSection as TS
from timberas.material import TimberMaterial as TM
from timberas.member import (
    GlulamMember,
    ApplicationCategory,
    DurationFactorStrength,
    RestraintEdge,
)

#(a) Permanent and short-term (5 day) load case"
sec = TS.from_library("GL395x85")
mat = TM.from_library("GL12")
mat.update_from_section_size(sec.d)
member_dict = {
    "sec": sec,
    "mat": mat,
    "application_cat": ApplicationCategory.PRIMARY_MEMBER,
    "k_1": DurationFactorStrength.FIVE_DAYS,
    "r": 0.25,
    "L": 4000,
    "L_a": {"x": None, "y": 450},
    "restraint_edge": RestraintEdge.COMPRESSION,
}
member = GlulamMember(**member_dict)
member.report(["S1", "k_12_bend", "M_d", "V_d"])
#(ANS: k_12_bend = 1.0, M_d = 41.7 kNm, V_d = 71.6 kN)

#(b) Permanent load case
member.update_k_1(DurationFactorStrength.FIFTY_YEARS)
member.report(["M_d", "V_d"])
#(ANS: M_d = 25.3 kNm, V_d = 43.5 kN)

Shear design parameters are derived from member inputs as follows:

$\phi$, $k_1$, $k_4$, $k_6$ as described for previous capacities.
Shear plane area $A_s$ is a TimberSection attribute, calculated as a reduction from gross area depending upon section shape type (e.g. single_board shapes have $A_s=2/3 A_g$)
Characteristic shear strength $f_s$ is a TimberMaterial attribute.