LVL Handbook EUROPE

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9. CALCULATION EXAMPLES OF LVL STRUCTURES
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Instantaneous deflection
w_inst = w_(inst,g) + w_(inst,q)
w_(inst,g)=(5〖∙g〗_(d,SLS)∙s∙L^4)/(〖384∙E〗_mean∙I)+〖〖6/5∙g〗_(d,
(4.74)
w_(inst,g)=1,30 mm+0,49 mm=1,79 mm
w_(inst,q)=(5〖∙q〗_(d,SLS)∙s∙L^4)/(〖384∙E〗_mean∙I)+(6/5∙〖q_(d,SLS)∙s∙L〗
mm+1,08 mm=3,95 mm
w_inst=1,79 mm+3,95 mm=5,5 mm
Final deflection
w_(net,fin) = (1+k_def)∙w_(inst,g) + (1+ψ_2∙k_def)∙w_(inst,q) (4.73)
Note: For the snow load in Finnish National annex: ψ2 = 0,2.
w_(net,fin) = (1+0,6)∙1,79 mm + (1+0,2∙0,6)∙3,95 mm = 7,3 mm
When the requirement is w_(net,fin)≤L/300=2300/300=7,7 mm→OK
The lintel beam fulfils the design requirements. However, in practice the required support lengths are quite
long and for windows a more strict deflection limit can be required. Therefore a double lintel 2x45x260 mm
or a 69x300 mm lintel from LVL 36 C could be a more suitable choice.
c,90,d 45mm ∙ (150mm + 15mm) 2
c,90 ∙ c,90,edge,d = c,90 ∙ mod M∙ c,90,edge,k = 1,0 ∙ 0,8 1,2 ∙ 6 N/mm 2 = 4 N/mm2
c,90,d ≤ c,90 ∙ m,0,edge,d → OK (4.13)
inst = inst,g + inst,q
inst,g = 5∙ d,SLS∙ ∙ 4
384∙ mean∙ + 6 5∙ d,SLS∙ ∙ 2
8∙ mean (4.74)
inst,g = 1,30 mm + 0,49 mm = 1,79 mm
inst,q = 5 ∙ d,SLS ∙ ∙ 4
384 ∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2
8 ∙ mean = 2,87 mm + 1,08 mm = 3,95 mm
= 1,79 mm + 3,95 mm = 5,5 mm
net,fin = (1 + def) ∙ inst,g + (1 + 2 ∙ def ) ∙ inst,q (4.73)
net,fin = (1 + 0,6) ∙ ,79 mm + (1 + 0,2 ∙ 0,6) ∙ 3,95 mm = 7,3 mm
When the requirement is net,fin ≤ L 300= 2300 300= 7,7 mm → OK
inst,g = 1,30 mm + 0,49 mm = 1,79 mm
inst,q = 5 ∙ d,SLS ∙ ∙ 4
384 ∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2
8 ∙ mean = 2,87 mm + 1,08 mm = 3,95 mm
= 1,79 mm + 3,95 mm = 5,5 mm
net,fin = (1 + def) ∙ inst,g + (1 + 2 ∙ def ) ∙ inst,q (4.73)
net,fin = (1 + 0,6) ∙ 1,79 mm + (1 + 0,2 ∙ 0,6) ∙ 3,95 mm = 7,3 mm
W e qui ent is net,fin ≤ L 300= 23 0 300= 7,7 mm → OK
SLS design
222 (253)
i t,g 5∙ d,SLS∙ ∙ 4
384∙ mean∙ + 6 5∙ d,SLS∙ ∙ 2
8∙ mean (4.74)
i st,g = 5 ∙ d,SLS ∙ ∙ 4
384 ∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2
8 ∙ mean = 1,30 mm + 0,49 mm = 1,79 mm
inst,g = 1,30 mm + 0,49 mm = 1,79 mm
inst,q = 5 ∙ d,SLS ∙ ∙ 4
384 ∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2
8 ∙ mean = 2,87 mm + 1,08 mm = 3,95 mm
= 1,79 mm + 3,95 mm = 5,5 mm
Final deflection
net,fin = (1 + def) ∙ inst,g + (1 + 2 ∙ def) ∙ inst,q (4.73)
Note: For the snow load in Finnish National annex: ψ2 = 0,2
net,fin = (1 + 0,6) ∙ 1,79 mm + (1 + 0,2 ∙ 0,6) ∙ 3,95 mm = 7,3 mm
When the requirement is net,fin ≤ L 300, 2300 300= 7,7 mm → OK
The lintel beam fulfils the design requirements. However, in practice the required support
lengths are quite long and for windows a more strict deflection limit can be required.
Therefore a double lintel 2x45x260 mm or a 69x300 mm lintel from LVL 36 C could be a
more suitable choice.
9.3 Double LVL 48 P ridge beam for roof
Single-span ridge beam of the roof in a one family house is LVL 48 P double beam 2x51x400
mm. Span length is L = 4000 mm, width of the loading area 6000 mm and roof rafters
connected to the sides of the beam at spacing s = 1200 mm. Support length is 120 mm.
Snow load sk is 2,5 kN/m2, own weight of the roof structure is 1,0 kN/m2 and own weigh of
the beam is 0,2 kN/m.
Beam properties:
Bending strength edgewise fm,0,edge,k = 44 N/mm2
Shear strength edgewise fv,0,edge,k = 4,2 N/mm 2
Compression perpendicular to grain edgewise fc,90,edge,k = 6 N/mm 2
Modulus of elasticity E0,k = 11 600 N/mm2
Modulus of elasticity E0,mean = 13 800 N/mm2
Modulus of rigidity G0,edge,k = 600 N/mm2
2
223 (255)
inst,g = 5∙ d,SLS∙ ∙ 4
384∙ mean∙ + 6 5∙ d,SLS∙ ∙ 2
8∙ mean (4.74)
inst,g = 5 ∙ d,SLS ∙ ∙ 4
384 ∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2
8 ∙ mean = 1,30 mm + 0,49 mm = 1,79 mm
inst,g 1,30 mm + 0,49 m = 1,79 m
inst,q 5 ∙ d,SLS ∙ ∙ 4
384 ∙ ean ∙ 6/5 ∙ d,SLS ∙ ∙ 2
8 ∙ mean = 2,87 m 1,08 m 3,95 m
1,79 m 3,95 m 5,5 mm
Final deflection
net,fin = (1 def) ∙ inst,g + (1 + 2 ∙ def ) ∙ inst,q (4.73)
Note: For the snow load in Finnish National annex: ψ2 = 0,2
net,fin = (1 0,6) ∙ 1,79 m + (1 + 0,2 ∙ 0,6) ∙ 3,95 mm 7,3 m
hen the re ire net,fin ≤ L 30, 230 mm 300 = 7,7 mm → OK
The lintel beam fulfils the design r quirements. However, in practice the required s pport
lengths are quite long and for windows a more strict deflection limit can be required.
Therefore a double lintel 2x45x260 mm or a 69x300 mm lintel from LVL 36 C could be a
more suitable choice.
9.3 Double LVL 48 P ridge beam for roof
Single-span ridge beam of the roof in a one family house is LVL 48 P double beam 2x51x400
mm. Span length is L = 4000 mm, width of the loading area 6000 mm and roof rafters
connected to the sides of the beam at spacing s = 1200 mm. Support length is 120 mm.
Snow load sk is 2,5 kN/m2, own weight of the roof structure is 1,0 kN/m2 and own weigh of
the beam is 0,2 kN/m. Service class SC1.
Beam properties:
Bending strength edgewise fm,0,edge,k = 4 N/m 2
Shear strength edg wise fv,0,edge,k = 4,2 N/mm 2
Compression perpendicular to grain edgewise fc,90,edge,k = 6 N/mm 2
Modulus of elasticity E0,k = 1 600 N/mm 2
Modulus of elasticity E0,mean = 13 800 N/ m 2
LVL Handbook Europe 187