LVL Handbook EUROPE

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9. CALCULATION EXAMPLES OF LVL STRUCTURES
Loading combinations
Snow load at roof level qk = μ1∙ Ce ∙ sk. Form factor μ1=0,8, when roof angle is less than 30° and in normal
conditions Ce = 1,0 → qk = 0,8 ∙ 1,0 ∙ 2,75 N/m2 = 2,2 kN/m2.
The most critical ultimate limit state (ULS) load combination:
E_(d,ULS )= γ_G∙g_k+ γ_Q∙q_k (4.1)
E_(d,ULS )= 1,15∙(5m∙1,0 kN/m^2 )+1,5∙5m∙2,2 kN/m^2=22,3 kN/m
Note: Safety factors γG and γQ are according to Finnish National annex of Eurocode 0.
The most critical serviceability limit state (SLS) load combination:
E_(d,SLS) = γ_G∙g_k + γ_Q∙q_k (4.1)
E_(d,SLS) = 1,0∙(5m∙1,0 kN/m^2+1,0∙5m∙2,2kN/m^2=16,0 kN/m
ULS design
Bending moment resistance
M_d= E_(d,ULS)∙s∙L^2/8 = 22,3kN/m∙〖(2,3m)〗^2/8 = 14,7 kNm
σ_(m,d)=M_d/W=(14,7 kNm)/(6,75〖∙10〗^6 mm^3 )=21,8 N/mm^2
f_(m,0,edge,d)=k_mod/γ_M ∙k_h∙f_(m,0,edge,k)=0,8/1,2∙1,00∙44 N/mm^2 =29,3 N/mm^2
σ_(m,d)≤f_(m,0,edge,d) →OK
Lateral torsional buckling
The lintel beam is laterally supported to wall studs in 600mm spacing and the load is applied via them.
Therefore the effective length is Lef = 600mm (See table 4.9).
σ_(m,crit)=M_(y,crit)/W_y =(π√(E_0,05 I_z G_0,05 I_tor ))/(l_ef W_y ) (4.42)
σ_(m,crit)= (π√(10600 N/mm^2∙2,28∙〖10〗^6 mm^4∙400N/mm^2 ∙8,20∙〖10〗^6∙
〗^5 mm^3 )
σ_(m,crit)=72,2 N/〖mm〗^2
λ_rel=√(f_(m,k)/σ_(m,crit) )=√((44 N/mm^2)/(72,2N/mm^2 ))= 0,78
(4.41)
when 0,75<λ_(rel,m)≤1,4 ,k_crit=1,56-0,75∙λ_(rel,m)=1,56-0,75∙0,78=0,97
d,ULS = G ∙ k + Q ∙ k (4.1)
d,ULS = 1,15 ∙ �5m ∙ 1,0 kNm2� + 1,5 ∙ 5m ∙ 2,2 kN/m2 = 22,3 kN/m
d,SLS = G ∙ k + Q ∙ k (4.1)
d,SLS = 1,0 ∙ (5m ∙ 1,0 kN/m2 + 1,0 ∙ 5m ∙ 2,2kN/m2 = 16,0 kN/m
d = d,ULS ∙ ∙ 2/8 = 22,3kN/m ∙ (2,3m)2 /8 = 14,7 kNm
m,d = = 14,7 kNm 6,75 ∙ 106mm3 = 21,8 N/mm2
m,0,edge,d = mod M∙ h ∙ m,0,edge,k = 0,8 1,2 ∙ 1,00 ∙ 44 Nmm2 = 29,3 N/mm2
m,d ≤ m,0,edge,d → OK
m,crit = y,crit y = � 0,05 z 0,05 toref y (4.42)
m,crit = π�10600 N/mm2 ∙ 2,28 ∙ 106mm4 ∙ 400Nmm2 ∙ 8,20 ∙ 106 ∙ mm4
600mm ∙ 6,75 ∙ 10 5mm3
m,crit = 72,2 / 2
= � m,k m,crit= � 44 N/mm2
72,2N/mm2 = 0,78 (4.41)
when 0,75 < rel,m ≤ 1,4 , crit = 1,56 − 0,75 ∙ rel,m = 1,56 − 0,75 ∙ 0,78 = 0,97
crit ∙ m,d = 0,97 ∙ 29,3 N/mm2 = 28,6 N/mm2
m,d ≤ crit ∙ m,d →
d = d,ULS ∙ ∙ /2 = 22,3kN/m ∙ 2,3m/2 = 25,6 kN
d,ULS = G ∙ k + Q ∙ k (4.1)
d,ULS = 1,15 ∙ �5m ∙ 1,0 kNm2� + 1,5 ∙ 5m ∙ 2,2 kN/m2 = 22,3 kN/m
d,SLS = G ∙ k + Q ∙ k (4.1)
d,SLS = 1,0 ∙ (5m ∙ 1,0 kN/m2 + 1,0 ∙ 5m ∙ 2,2kN/m2 = 16,0 kN/m
d = d,ULS ∙ ∙ 2/8 = 22,3kN/m ∙ (2,3m)2 /8 = 14,7 kNm
m,d = = 14,7 kN 6,75 ∙ 106mm3 = 21,8 N/mm2
m,0,edge,d = mod M∙ h ∙ m,0,edge,k = 0,8 1,2 ∙ 1,00 ∙ 44 Nmm2 = 29,3 N/mm2
m,d ≤ m,0,edge,d → OK
m,crit = y,crit y = � 0,05 z 0,05 toref y (4.42)
m,crit = π�10600 N/mm2 ∙ 2,28 ∙ 106mm4 ∙ 400Nmm2 ∙ 8,20 ∙ 106 ∙ mm4
600mm ∙ 6,75 ∙ 10 5mm3
m,crit = 72,2 / 2
= � m,k m,crit= � 44 N/mm2
72,2N/mm2 = 0,78 (4.41)
when 0,75 < rel,m ≤ 1,4 , crit = 1,56 − 0,75 ∙ rel,m = 1,56 − 0,75 ∙ 0,78 = 0,97
crit ∙ m,d = 0,97 ∙ 29,3 N/mm2 = 28,6 N/mm2
m,d ≤ crit ∙ m,d →
d = d,ULS ∙ ∙ /2 = 22,3kN/m ∙ 2,3m/2 = 25,6 kN
d,UL = G ∙ k + Q ∙ k (4.1)
d,ULS = 1,15 ∙ �5m ∙ 1,0 kNm2� + 1,5 ∙ 5m ∙ 2,2 kN/m2 = 22,3 kN/m
d,SLS = G ∙ k + Q ∙ k (4.1)
d,SLS = 1,0 ∙ (5m ∙ 1,0 kN/m2 + 1,0 ∙ 5m ∙ 2,2kN/m2 = 16,0 kN/m
d = d,ULS ∙ ∙ 2/8 = 22,3kN/m ∙ (2,3m)2 /8 = 14,7 k
m,d = = 14,7 kNm 6,75 ∙ 106mm3 = 21,8 N/mm2
m,0,edge,d = mod M∙ h ∙ m,0,edge,k = 0,8 1,2 ∙ 1,00 ∙ 44 Nmm2 = 29,3 N/mm2
m,d ≤ m,0,edge,d → OK
m,crit = y,crit y = � 0,05 z 0,05 toref y (4.42)
m,crit = π�10600 N/mm2 ∙ 2,28 ∙ 106mm4 ∙ 400Nmm2 ∙ 8,20 ∙ 106 ∙ mm4
600mm ∙ 6,75 ∙ 10 5mm3
m,crit = 72,2 / 2
= � m,k m,crit= � 44 N/mm2
72,2N/mm2 = 0,78 (4.41)
when 0,75 < rel,m ≤ 1,4 , crit = 1,56 − 0,75 ∙ rel,m = 1,56 − 0,75 ∙ 0,78 = 0,97
crit ∙ m,d = 0,97 ∙ 29,3 N/mm2 = 28,6 N/mm2
m,d ≤ crit ∙ m,d →
d = d,ULS ∙ ∙ /2 = 22,3kN/m ∙ 2,3m/2 = 25,6 kN
d,ULS = G ∙ + ∙ ( . )
, S = , 5 ∙ 5 ∙ , m2 , ∙ ∙ , 2 ,
,S S ∙ + ∙ ( . )
,S S , ∙ ( ∙ , 2 , ∙ ∙ , 2 ,
d,U S ∙ ∙ 2 8 2, (2, )2/ 4,
m, = 1 , kNm ,75 ∙ 106 3 , / 2
m,0,e ge,d ∙ ∙ ,0,e ge, 0,8 1,2 ∙ , ∙ Nmm2 , / 2
, ,0,e ge,
,crit = y,crit y = � 0,05 z 0,05 toref y (4.42)
,crit 6 m2 ∙ ,2 ∙ 06 4 ∙ 4 0m 2 ∙ , ∙ 6 ∙ 4
∙ , ∙ 5 m3
,crit 2,2 2
m,k ,crit � 44 / 2
72,2 / 2 , ( . )
, 5 rel, ≤ , , crit = , , ∙ rel, , , ∙ , ,
crit ∙ , = , 7 ∙ , 2 , 2
, crit ∙ ,
, S ∙ ∙ , m ∙ , ,
LVL Handbook Europe 185