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k_crit∙ f_(m,d)=0,97 ∙29,3 N/mm^2=28,6 N/mm^2
σ_(m,d)≤k_crit∙ f_(m,d)→OK
Shear resistance
V_d = E_(d,ULS)∙s∙L/2 = 22,3kN/m∙2,3m/2 = 25,6 kN
τ_(v,d)=〖3∙V〗_d/(2∙A)=(3∙25,6 kN)/(2 ∙13500mm^2 )=2,84 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) →NOT OK
The design shear force may be reduced by determining it from a distance of the beam height h from the
support edge:
rel,m crit rel,m
crit ∙ m,d = 0,97 ∙ 29,3 N/mm2 = 28,6 N/mm2
m,d ≤ crit ∙ m,d →
d = d,ULS ∙ ∙ /2 = 2 , / ∙ 2,3m/2 = 25,6 kN
v,d = 3 ∙ d 2 ∙ = 3 ∙ 25,6 kN2 ∙ 13500mm2 = 2,84 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 → NOT OK
red,d = d ∙ �1 − 2ℎ + support � = 25,6kN ∙ �1 − 2 ∙ 300mm + 150mm2300mm �
red,d = 17,2kN
v,d = 3 ∙ d 2 ∙ = 3 ∙ 17,2 kN2 ∙ 13500mm2 = 1,92 N/mm2
m,d < v,0,edge,d → OK
c,90,d = d = 25,6 kN
c,90,d = c,90,d ef = c,90,d
∙� support+15 mm� (4.14)
c,90,d = 25,6kN
45mm ∙ (150mm + 15mm) = 3,4 N/mm2
c,90 ∙ c,90,edge,d = c,90 ∙ mod M∙ c,90,edge,k = 1,0 ∙ 0,8 1,2 ∙ 6 N/mm2 = 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)
9. CALCULATION EXAMPLES OF LVL STRUCTURES
V_(red,d)=V_d∙(1-(2h+l_support)/l)=25,6kN∙(1-(2∙300mm+150mm)/2300mm)
V_(red,d)=17,2kN
τ_(v,d)=〖3∙V〗_d/(2∙A)=(3∙17,2 kN)/(2 ∙13500mm^2 )=1,92 N/mm^2
τ_(m,d)<f_(v,0,edge,d) →OK
Compression perpendicular to grain
F_(c,90,d) = V_d = 25,6 kN
σ_(c,90,d)=F_(c,90,d)/A_ef =F_(c,9 ,d)/(b∙(l_support+15 mm) )
(4.14)
σ_(c,90,d)=25,6kN/(45mm∙(150mm+15mm))=3,4 N/mm^2
k_(c,90)∙f_(c,90,edge,d)=k_(c,90)∙k_mod/γ_M ∙f_(c,90,edge,k)=1,0∙0,8/1,2∙6 N/mm^2=4 N/m
σ_(c,90,d)≤k_(c,90)∙f_(m,0,edge,d) →OK
(4.13)
2 1 A
red
h
V V
  
    
 
l
l
v,d = 3 ∙ d 2 ∙ = 3 ∙ 25,6 kN2 ∙ 13500mm2 = 2,84 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 → NOT OK
re ,d = d ∙ �1 − 2ℎ + support � = 25,6kN ∙ �1 − 2 ∙ 300mm + 150mm2300mm �
red,d = 17,2kN
v,d = 3 ∙ d 2 ∙ = 3 ∙ 17,2 kN2 ∙ 13500mm2 = 1,92 N/mm2
m,d < v,0,edge,d → OK
c,90,d = d = 25,6 kN
c,90,d = c,90,d ef = c,90,d
∙� support+15 mm� (4.14)
c,90 d = 25,6kN
45mm ∙ (150mm + 15mm) = 3,4 N/mm2
c,90 ∙ c,90,edge,d = c,90 ∙ mod M∙ c,90,edge,k = 1,0 ∙ 0,8 1,2 ∙ 6 N/mm2 = 4 N/mm2
c,90,d ≤ c,90 ∙ m,0,edge,d → OK (4.13)
inst = inst,g + inst,q
d,SLS 4 6 5∙ d,SLS∙ ∙ 2 (4.74)
v,d = 3 ∙ d 2 ∙ = 3 ∙ 25,6 kN2 ∙ 13500mm2 = 2,84 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 → NOT OK
red,d = d ∙ �1 − 2ℎ + support � = 25,6kN ∙ �1 − 2 ∙ 300mm + 150mm2300mm �
red,d = 17,2kN
v,d = 3 ∙ d 2 ∙ = 3 ∙ 17,2 kN2 ∙ 13500mm2 = 1,92 N/mm2
m,d < v,0,edge,d → OK
, ,d = d = 25,6 kN
c,90, = c,90,d ef = c,90,d ∙� support+15 mm� (4.14)
c,90,d = 25,6kN
45mm ∙ (150mm + 15mm) = 3,4 N/mm2
c,90 ∙ c,90,edge,d = c,90 ∙ mod M∙ c,90,edge,k = 1,0 ∙ 0,8 1,2 ∙ 6 N/mm2 = 4 N/mm2
c,90,d ≤ c,90 ∙ m,0,edge,d → OK (4.13)
inst = inst,g + inst,q
v,d = 3 ∙ d 2 ∙ = 3 ∙ 25,6 kN2 ∙ 13500mm2 = 2,84 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 → NOT OK
red,d = d ∙ �1 − 2ℎ + support � = 25,6kN ∙ �1 − 2 ∙ 300mm + 150mm2300mm �
red, = 17,2kN
v,d = 3 ∙ d 2 ∙ = 3 ∙ 17,2 kN2 ∙ 13500mm2 = 1,92 N/mm2
m,d < v,0,edge,d → OK
c,90,d = d = 25,6 kN
c,90,d = c,90,d ef = c,90,d
∙� support+15 mm� (4.14)
c,90,d = 25,6kN
45mm ∙ (150mm + 15mm) = 3,4 N/mm2
c,90 ∙ c,90,edge,d = c,90 ∙ mod M∙ c,90,edge,k = 1,0 ∙ 0,8 1,2 ∙ 6 N/mm2 = 4 N/mm2
c,90,d ≤ c,90 ∙ m,0,edge,d → OK (4.13)
inst inst,g inst,q
186 LVL Handbook Europe