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9.4 ROOF PURLIN
Single-span purlins of the roof of an unheated (service class 2) portal frame hall are 45x240 LVL 48 P beams.
Roof angle is 15°, span length is
L
= 4000 mm, spacing
s
= 900 mm and the purlins are perpendicular to the
roof plane having a side support line at the middle of the span. Support length is 45mm. Snow load
s
k
is 2,5 kN/
m
2
and own weight of the roof structure is 0,30 kN/m
2
. For simplification there is no wind load in the example.
The purlins are connected to the sides of the portal frame beams and they act also as lateral torsional buck-
ling supports. Therefore the purlins have an axial load of
N
k
= 3 kNmainly from snow load. Service class SC2.
Beam properties:
Bending strength edgewise
f
m,0,edge,k
= 44 N/mm
2
Bending strength flatwise
f
m,0,flat,k
= 48 N/mm
2
Shear strength edgewise
f
v,0,edge,k
= 4,2 N/mm
2
Compression parallel to grain
f
c,0,SC2,k
= 29 N/mm
2
Compression perpendicular to grain edgewise
f
c,90,edge,k
= 6 N/mm
2
Modulus of elasticity
E
0,k
= 11 600 N/mm
2
Modulus of elasticity
E
0,mean
= 13 800 N/mm
2
Modulus of rigidity
G
0,edge,k
= 600 N/mm
2
Modulus of rigidity
G
0,edge,mean
= 400 N/mm
2
Area of cross section
A
=
b∙h
= 10800 mm
2
Section modulus
W
y
=
b∙h
2
/6
= 4,32∙10
5
mm
3
Section modulus
W
z
=
h∙b
2
/6
= 8,10∙10
4
mm
3
Moment of inertia
I
y
=
b∙h
3
/12
= 5,18∙10
7
mm
4
Moment of inertia
I
z
=
h∙b
3
/12
= 1,82∙10
6
mm
4
Torsion moment of inertia
I
tor
= 0,3∙
h∙b
3
= 6,56∙10
6
mm
4
Moment stiffness of the joist
EI
y
= 13800 N/mm
2
∙ 6,56∙10
6
mm
4
= 7,15∙10
11
Nmm
2
Shear rigidity of the joist
GA
= 600 N/mm
2
∙ 40800 mm
2
= 6,48∙10
6
N
Modification factor
k
mod
for medium-term, SC2
= 0,8
Modification factor
k
def
for SC2
= 0,8
Material safety factor
γ
M
(default value in EC5)
=1,2
Size effect factor
k
h
= (300/240)
0,15
= 1,034
9. CALCULATION EXAMPLES OF LVL STRUCTURES
LVL Handbook Europe
191