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9. CALCULATION EXAMPLES OF LVL STRUCTURES
ULS design
Bending moment resistance
M_d = E_(d,ULS)∙s∙L^2/8 = 4,03kN/m^2∙0,4m∙〖(4,5m)〗^2/8 = 4,
σ_(m,d)=M_d/W=(4,1 kNm)/(4,32〖∙10〗^5 mm^3 )=9,5 N/mm^2
f_(m,0,edge,d)=k_mod/γ_M ∙k_h∙f_(m,0,edge,k)
(4.3)
f_(m,0,edge,d)=0,8/1,2∙1,034∙44 N/mm^2 =30,3 N/mm^2
σ_(m,d)≤f_(m,0,edge,d) →OK
Lateral torsional buckling is prevented by the fixing of the decking.
Shear resistance
V_d = E_(d,ULS)∙s∙L/2 = 4,03kN/m^2∙0,4m∙4,5m/2 = 3,6 kN
τ_(v,d)=〖3∙V〗_d/(2∙A)=(3∙3,6 kN)/(2 ∙10 800mm^2 )=0,5 N/mm^2
f_(v,0,edge,d)=k_mod/γ_M ∙f_(v,0,edge,k)=0,8/1,2∙4,2 N/mm^2 =2,8 N/mm^2
τ_(m,d)≤f_(v,0,edge,d) →OK
Compression perpendicular to the grain
F_(c,90,d) = V_d = 3,6 kN
σ_(c,90,d)=F_(c,90,d)/A_ef =F_(c,90,d)/(b∙(l_s
(4.14)
σ_(c,90,d)=3,6kN/(45 mm∙(45 mm+15mm
k_(c,90)∙f_(c,90,edge,d)=k_(c,90)∙k_mod/γ_M ∙
(4.13)
k_(c,90)∙f_(c,90,edge,d)=1,0∙0,8/1,2∙6 N/mm^2=4
(kc,90 Table 4.7)
σ_(c,90,d)≤k_(c,90)∙f_(m,0,edge,d) →OK
SLS design

Instantaneous deflection
w_inst = w_(inst,g) + w_(inst,q)
w_(inst,g)=(5〖∙g〗_(d,SLS)∙
(4.74)
d,SLS G 1,k 2,k G k (4.1)
d,SLS = 1,0 ∙ (0,6 kN/m2 + 0,3 kN/m2 ) + 1,0 ∙ 2,0 kN/m 2
d,SLS = 2,9 kN/m 2
d = d,ULS ∙ ∙ 2/8 = 4,03kN/m 2 ∙ 0,4 ∙ (4,5m) 2/8 = 4,1 kNm
m,d = d = 4,1 kNm 4,32 ∙ 105 mm3 = 9,5 N/mm2
m,0,edge,d = mod M∙ h ∙ m,0,edge,k (4.3)
m,0,edge,d = 0,8 1,2 ∙ 1,034 ∙ 44 Nmm2 = 30,3 N/mm2
m,d ≤ m,0,edge,d → OK
d = d,ULS ∙ ∙ /2 = 4,03kN/m2 ∙ 0,4m ∙ 4,5m/2 = 3,6 kN
d,SLS = G ∙ ( 1,k + 2,k) + G ∙ k (4.1)
d,SLS = 1,0 ∙ (0,6 kN/m2 + 0,3 kN/m2 ) + 1,0 ∙ 2,0 kN/m2
d,SLS = 2,9 kN/m2
d = d,ULS ∙ ∙ 2 /8 = 4,03kN/m2 ∙ 0,4m ∙ (4,5m) 2/8 = 4,1 kNm
m,d = d = 4,1 kNm 4,32 ∙ 105mm3 = 9,5 N/mm2
m,0,edge,d = mod M∙ h ∙ m,0,edge,k (4.3)
m,0,edge,d = 0,8 1,2 ∙ 1,034 ∙ 44 Nmm2 = 30,3 N/mm2
m,d ≤ m,0,edge,d → OK
d = d,ULS ∙ ∙ /2 = 4,03kN/m2 ∙ 0,4m ∙ 4,5m/2 = 3,6 kN
v,d = 3 ∙ d 2 ∙ = 3 ∙ 3,6 kN2 ∙ 10 800mm2 = 0,5 N/mm2
v,0,edge,d = mod M∙ v,0,edge,k = 0,8 1,2 ∙ 4,2 Nmm2 = 2,8 N/mm2
m,d ≤ v,0,edge,d → OK
c,90,d = d = 3,6 kN
c,90,d = c,90,d ef = c,90,d
∙� support +15 mm� (4.14)
c,90,d = 3,6kN
45 mm ∙ (45 mm + 15mm) = 1,35 N/mm2
c,90 ∙ c,90,edge,d = c,90 ∙ mod M∙ c,90,edge,k (4.13)
c,90 ∙ c,90,edge,d = 1,0 ∙ 0,8 1,2∙ 6 N/mm2 = 4N/mm2 (kc,90 Table 4.7)
c,90,d ≤ c,90 ∙ m,0,edge,d → OK
inst = inst,g + inst,q
inst,g = 5∙ d,SLS∙ ∙ 4
384∙ mean∙ + 6 5∙ d,SLS∙ ∙ 2
8∙ mean (4.74)
inst,g = 2,69 mm + 0,17 mm = 2,86 mm
inst,q = 5 ∙ d,SLS ∙ ∙ 4
384 ∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2
8 ∙ mean = 5,97 mm + 0,38 mm = 6,35 mm
d 2 ∙ k 1 0 0,5 N/mm
0 d ∙ 0 e k , 2
d 0 e ,d O
= d e c
∙ t
= ,9 ∙ 9 e k
c,9 ∙ 9 e d 0,8 1,2 N
g
3 4 6 5 ∙
m 6
∙ 8 + d S S = 5,97 mm + 0,38 mm = 6,35 mm
v,d = 3 ∙ d 2 ∙ = 3 ∙ 3,6 kN2 ∙ 10 800mm2 = 0,5 N/mm2
v,0,edge,d = mod M∙ v,0,edge,k = 0,8 1,2 ∙ 4,2 Nmm2 = 2,8 N/mm2
m,d ≤ v,0,edge,d → OK
c,90,d = d = 3,6 kN
c,90,d = c,90,d ef = c,90,d
∙� support+15 mm� (4.14)
c,90,d = 3,6kN
45 mm ∙ (45 mm + 15mm) = 1,35 N/mm2
c,90 ∙ c,90,edge,d = c,90 ∙ mod M∙ c,90,edge,k (4.13)
c,90 ∙ c,90,edge,d = 1,0 ∙ 0,8 1,2∙ 6 N/mm2 = 4N/mm2 (kc,90 Table 4.7)
c,90,d ≤ c,90 ∙ m,0,edge,d → OK
inst = inst,g + inst,q
inst,g = 5∙ d,SLS∙ ∙ 4
384∙ mean ∙ + 6 5∙ d,SLS∙ ∙ 2
8∙ mean (4.74)
inst,g = 2,69 mm + 0,17 mm = 2,86 mm
inst,q = 5 ∙ d,SLS ∙ ∙ 4
384 ∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2
8 ∙ mean = 5,97 mm + 0,38 mm = 6,35 mm
216 (255)
0,edge,d = 0,8 1,2 ∙ 1,034 ∙ 44 Nmm2 = 30,3 N/mm2
m,d ≤ m,0,edge,d → OK
Lateral torsional buckling is prevented by the fixing of the decking.
hear resistance
d d,ULS ∙ ∙ /2 = 4,03kN/m2 ∙ 0,4m ∙ 4,5m/2 = 3,6 kN
v,d = 3 ∙ d 2 ∙ = 3 ∙ 3,6 kN2 10 800mm 2 = 0,5 N/mm2
v,0,edge,d = mod M∙ v,0,edge,k = 0,8 1,2 ∙ 4,2 Nmm2 = 2,8 N/mm2
m,d ≤ v,0,edge,d → OK
ompression perpen icular to the grain
, ,d = d = 3,6 kN
c,90,d = c,90,d ef = c,90,d
∙� support+15 mm� (4.14)
c,90,d = 3,6kN
45 mm ∙ (45 mm + 15mm) = 1,35 N/mm2
c,90 ∙ c,90,edge,d c,90 ∙ mod M∙ c,90,edge,k (4.13)
, ∙ c,90,edge,d = 1,0 ∙ 0,8 1,2∙ 6 N/mm2 = 4N/mm2 (kc,90 Table 4.7)
c,90,d ≤ c,90 ∙ m,0,edge,d → OK
LS design
nstantaneous deflection
inst = inst,g + inst,q
i ,g 5 ∙ d,SLS ∙ ∙ 4
384 ∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2
8 ∙ mean = 2,69 mm + 0,17 mm = 2,86 mm
(4.74)
d,SLS 4 d,SLS 2
180 LVL Handbook Europe