Upz

15 mm

1. Beam geometric properties

Depth of the beam, h

Clear span of the beam, lc

Bearing length of the beam at each end, 4

Design span of the beam, I

Notch depth at each end of beam, hn Notch inclination, i (including dimension correction factor required by mathcad)

Beam depth at each end, hef Ratio of hef/h, a

Length of the notch from the centre line of the end support, x

Section modulus of the beam about the y-y axis, Wy b = 63 mm h = 225 mm 4 = 3100 mm 4 = 85 mm

2. Timber properties

Table 1.3, strength class C24 (BS EN 338:2003, Table I):

Characteristic bending strength, fm.k

Characteristic shear strength, fv k

Characteristic bearing strength, fc.90.k

Fifth-percentile modulus of elasticity parallel to the grain, E0.05

Mean modulus of elasticity parallel to the grain, E0.mean Mean shear modulus, G0.mean Mean density of the beam timber, pm

fv.k = 2.5N/mm2 fc.90.k = 2.5N/mm2 E0.05 = 7.4kN/mm2

3. Partial safety factors

Table 2.8 (UKNA to BS EN 1990:2002, Table NA.AI.2(B))) for the ULS

Permanent actions, yg.uls Yg.uls = 1.35

Variable actions, Yq.uls Yq.uls = 1.5

Table 2.2 (UKNA to BS EN 1990:2002, Table NA.AI.I - Category A

Factor for the quasi-permanent value = 0.3 of the variable action, f2

Material factor for solid timber at the ym = 1-3 ULS, Ym

4. Actions

Characteristic self-weight of the beam, Gk swt

(1) Design action from the self-weight of the beam, Fd.swt

Characteristic permanent action due to the point load, Gk.p

(2) Design permanent action due to the point load, Fd.p

Characteristic permanent action due to the udl, Gk.udl

Characteristic medium-term action due to the udl, Qk.udl

(3) Design action due to the permanent action udl, Fd p udl

(4) Design action due to the variable action udl, Fd.q udl

5. Modification factors

Factor for medium-duration loading and service class 2, kmod.med, (Table 2.4 (EC5, Table 3.1))

Size factor for depth greater than 150 mm, kh (Table 2.11; EC5, equation (3.1))

Lateral stability of the beam: kcrit, (Table 4.3 (EC5, 6.3.3))

Reduction factor for the notch, kv, (equation (4.19) (EC5, Clause 6.5.2))

Shear factor for solid timber, kn (incorporating the dimension factor for Mathcad)

Reduction factor for notched beams, kv

Fd.swt = Kg.uls ■ Gk.swt Fd,wt = 0.08 kN/m G kp = 1.00 kN

Fd.p = Kg.uls ■ Gk.p Fd.p = 1.35 kN G k.udl = 1.0 kN/m Q k.udl = 2.5 kN/m

Fd.q.udl = Kq.uls ■ Qk.udl Fd.q.udl = 3.75 kN/m kmod.med = 0.8 kh = 1.0

kcrit 1

0 0