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9. CALCULATION EXAMPLES OF LVL STRUCTURES
The stiffness (EI)bracing of the bracing lines can be estimated according to EN1995-1-1, Annex BMechanical-
ly jointed beams. For simplification, also the top flange of the transverse bracing is modelled as a 22x100 C14
board and the stiffness of the 2 bracing lines are divided for the whole floor span length.
(EI)_bracing=n∙2∙E_(0,mean)∙((b_0∙〖h_0〗^3/12+γ∙b_0∙h_0∙(h/2+h_0/2)^2 ))/l_0
where
n
= number of bracing lines in each span = 2
E
0,mean
= mean modulus of elasticity of C14 flanges 7000 N/mm
2
b
0
= width of tension/compression chord = 100 mm
h
0
= thickness of tension/compression chord = 22 mm
h
= depth of joist = 240 mm
s
0
= Spacing of the nailing between blocking and flanges = 200 mm
l
0
= span length of the bracing line = width of the floor= 5 m
ρ
k
= characteristic density (C14: 350 kg/m
3
)
d
= diameter of the nail 2.5 mm for nails 2,5x60 mm
The deflection under
F
=1 kN point load
w=min{█((F∙l^2)/(42∙k_δ∙(EI)_l )@(F∙l^3)/(48∙s∙(EI)_l ))┤
(4.82)
k_δ=∜((EI)_b/(EI)_l =) ∜((3,11∙〖10〗^3)/(1,79∙〖10〗^6 ))=0,2
(4.84)
w=min{█((1kN∙(4,5m)^2)/█(42∙0,2∙1,79∙(〖10〗^6 Nm^2)/m@ )@(1kN∙(4,5m)^3)/(48∙0,4∙1,79∙(〖10〗^6
Nm^2)/m))┤=min{█(1,3 mm@ @2,7 mm)┤=1,3 mm
According to the Finnish national Annex of EC5, for the span length
L
= 4500mm the requirement is
w
≤ 0,6
mm and according to the Austrian national annex
w
≤ 0,5 mm which are not fulfilled by the structure.
The performance can be improved by transverse bracing by 2 blockings lines with tension boards close to
the centre of the span and cross battens 45x45 c/c 400 mm underneath the floor.
≤ 150
(
1
−1)
= 0,011 →
(4.78)
= min �
∙
2
42∙ ∙( )
l
∙
3
48∙ ∙( )
l
(4.82)
= �
( )
b
( )
l
=
4
�
3,11∙10
3
1,79∙10
6
4
= 0,2
(4.84)
= min
⎩⎪ ⎨ ⎪ ⎧ 1kN ∙ (4,5m)
2
42 ∙ 0,2 ∙ 1,79 ∙ 10
6
Nm
2
m
1kN ∙ (4,5m)
3
48 ∙ 0,4 ∙ 1,79 ∙ 10
6
Nm
2
m
= min � 1,3 mm 2,7 mm = 1,3 mm
( )
bracing
= ∙ 2 ∙
0,mean
∙ �
0
∙ ℎ
0 3
12 + ∙
0
∙ ℎ
0
∙ (ℎ/2 + ℎ
0
/2)
2
�
0
ser
=
k 1,5
∙
0,8
30 = 454 N/mm
=
1
2
∙
0
∙ ℎ
0
∙
0
∙
0 2
=
1
π
2
∙ 7000 N/mm
2
∙ 22 mm ∙ 100 mm ∙ 200 mm
2
= min
⎩⎪ ⎨ ⎪42 ∙ 0,2 ∙ 1,79 ∙ 10
6
Nm
2
m
1kN ∙ (4,5m)
3
48 ∙ 0,4 ∙ 1,79 ∙ 10
6
Nm
2
m
= min � 1,3 mm 2,7 mm = 1,3 mm
( )
bracing
= ∙ 2 ∙
0, ean
∙ �
0
∙ ℎ
0 3
12 + ∙
0
∙ ℎ
0
∙ (ℎ/2 + ℎ
0
/2)
2
�
0
ser
=
k 1,5
∙
0,8
30 = 454 N/mm
=
1
1 +
2
∙
0
∙ ℎ
0
∙
0
∙
0
ser
∙
0 2
=
1
1 + π
2
∙ 7000 N/mm
2
∙ 22 mm ∙ 100 mm ∙ 200 mm
454N/mm ∙ (5000 mm)
2
1. Decking panel, 2. Floor joists, 3. Transverse tension board (C18, min 22x100) under the joists fixed with 2,8x75 nails to the joists and
blockings, 4. Blocking
182
LVL Handbook Europe