f2 glue laminated roof beam
TRANSCRIPT
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F 2 GLUED LAMINATED ROOF BEAM
DESIGN D T I
Subject
It is required to check the adequacy of a glued laminated softwood timber beam for a restaurant
roof. The beams are at 3.0 m centres and have an effective span of 11.0 m. The permanent load,
excluding the self-weight of the beam, is 0.557 kN /mZ nd the snow load is 0.75 kN/m*.
Service class
,
Cl ause 3.1.5
Service class 1
GluIam strength class and properties
Glulam strength class GL24 prEN lY94
M at eri al roperti es or ghdam str ength l asses are given n prEN 1194
Bending strength f
m.0
Shear strength f
v.0
Compression strength perpendicular to grain ff,W,g,k
Mean modulus of elasticity parallel to grain &,__
Characteristic density of timber
P&k
=
24 N/mm*
=
2.8 N/mm*
= 5.5 N/mm*
/
= 11000 N/mm*
=
380 kg/m3
Section dimensions and properties
I
The dept h of a ghdam beam is normal ly mul ti ple of t he hi ckness f he am inati ons
usual l y 45 mm. The cross-secti onsmost ommonly vai lable n he UK are tabulat ed n
Tabl e 5 of he nt roducti on o he Design Exampl es.
GD3, Table 8
Breadth of beam section b
=
115 mm
Depth of beam section h = 540 mm
Span between bearing centres L =ll 000 mm
I
Bearing length 0
=
75 mm
he-camber u, = 20 mm
I
Cross-sectional area
A
= bh = 115x540 = 62 100 mm* 1
Section modulus about y-y
WY= bh2
= 115 x ? ?/E
= 5 589 000 mm3
6
Second moment of area about y-y 4 = z
= 115 x z = 1509000000 mm4
I I
For t he calculat i on f sel f-w ei ght, he mean densit y s used.
Cl ause 2.2.2.2 3)
prEN 1194 at he ime of w ri t i ng) iv es only characterist i c ensit ies. For glul am hese
may be convert ed o mean densit ies y div idi ng hem by a actor of 0.93.
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F 2 GLUED LAMINATED ROOF BEAM
pg.
mcpn
p&k=_
380
=
0.93
0.93 = 408.6 kg/m3
Beam self-weight
9.807
ps_,A 9.807
x 408.6 x 62 100
=
= 0.2488 kN/m
109
log
Actions
I
Dead weight of decking, insulation and ceiling = 0.557 kN/mz
= 0.557 x 3.0 = 1.671 kN/m
Beam self-weight
Therefore Gk = 1.671 + 0.249
snow load = 0.75 kNlm2
= 0.249 kN/m
= 1.920 kN/m
Therefore Q = 0.75 x 3.0
= 2.25Wm
The NALIstates that snow loads in the UK shoul d be considered as shor t-tern actions.
NAD Clause 3. . 6P 2)
Partial safety factors for unfavourable effects
Table
2.3.3.1
Permanent actions
YG
=
1.35
Variable actions
Material factor
YQ
= 1.5
Yu
= 1.3
ULTIMATE LIMIT STATE - Strength
Design value of actions
Gd =
YG
=
1.35
x
1.920 = 2.592 kN/m or N/mm
Qd = TQQ~
= 1.5 x 2.25
= 3.375 kN/m or N/mm
2.3.2.2a)
Strength modification factors
Guidance Document GD3, Table 5, l ists the modijku ion factors
applicable
to
character istic strength values.
=TRADA19 94.F
TRADA, HughendenValley, High Wycombe. Bucks. HP14 4ND. UK:
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F 2 GLUED LAMINATED ROOF BEAM
Load sharing
Beam is not part of a load-sharing assembly. Therefore $ = 1.0
Clause 5.4.6
Size factor
1
Fact or k,, may be used or glulam secti ons w i th ept hs n bending or w idt hs n ension f
l ess han 600 mm o ncrease he charact et i sti c ending and ension t rength al ues i ven
in prEN 1194.
Depth modification
Lateral stability
Beam is adequately
Therefore
Bearing length
Bearing length
kt, = (Y) = (E J = 1.02
restrained along compression edge by attached joists.
kimt
= 1.0
Clause 5.2. (4)
Cl ause 5.2.5
e
= 75mm
Distance between bearing members (clear span) 0, = L - 0 = 11 000 - 75 = 10 925 mm
Distance to end of bearing
a
= 1OOmm
(150
0 (150
-
earing factor
k&l = 1 +
= 1 +
75) = 1 44
170 170
PERMANENT LOAD
Design values
of effects of actions
Design bending moment
G,L* =
M, = _
2.592 x 11 ood
8
8
Design shear force
v, =
L
2.592 x 11 000
-=
2
2
Modification factor for actions of permanent duration
in Service class 1
knKd
= 0.6
Bending
stwngth
=
39200000Nmm
= 14260N
Tabl e 3.h.7
Design bending
stress
39 200
000
m.d,y
= - = = 7.01 N/mm*
wY 5 589 000
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TRADA, Hughenden Valley, High Wycumbe, Bucks. HP14 4ND. UK
0
TR&DA 1994. F
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F 2 GLUED LAMINATED ROOF BEAiM
Design bending strength fmay =
k,khkinrck&.t = 1x1.02x1x0.6x24 = 11_30N,_~
1.3
Shear strength
Design shear StresS
1.5 v*
Td = -
A
Design shear strength f,,d =
Uwdfv&k
Bearing
strength
Design compression stress
perpendicular to grain
uOU
Design compression strength
perpendicular to grain fqwA
Yhl
Fd
VC3
=?;I
Q4w
Bending strength
satisfactory
1.5 x 14 260
=
= 0.34 N/mm*
62 100
1 x0.6x2.8
=
1.3
14 260
=
115 x 75
PERMANENT + SEIORT-TERM LOADS
Design vah~es of effects of actions
1 x1.44x0.6x5.5
=
1.3
< fC,9oC
Design load on beam Fd
= G, + Q
= 2.592 + 3.375
Design bending moment Md
FaL
= _
= 5.967xllood
= 1.29 N/mm*
Shear strength
satisfactory
= 1.65 N/mm*
= 3.66 N/mm*
Section adequate in
benbrg,*tia
for permanent actions
= 5.967 N/mm
= 9025OOOONmm
Design shear force F,Lv, =-
= 5.967x11000
c)
L
Modification factor for short-term loading
in Service class 1
kmod
= 0.9
Bending strength
Design bending stress
QmAY =
M,
w =
2
90 250 000
5 589 000
Design bending strength fmAy
= lkwirQlkraodf~,k
YM
= 1x1.02x1x0.9x24
1.3
= 32 820N
Table 3.1.7
= I 16.15 N/mm*
= 16.95 N/mm*
Bending strength
satisfactory
BTRADA 1994. F o> TRADA, Hughenden Valley, High Wycombe, Bucks. HP14 4ND. UK
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Shear strength
Design shear
1.5
stress 1.5 x 32 820d = - v, = = 0.79
N/mm2
A
62 100
Design shear strength
fv,d =
4s sllcdfJC
1 x 0.9 x 2.8
YM
1.3
= 1.94 N/mm2
7d < f,d
Bearing strength
Design compression stress
perpendicular to grain
Design compression strength
perpendicular to grain
9O,d
f
c.90.d
SERVICEABILITY LIMIT STATE -
S@ar strength
satisfactory
Vd
32 820
=
=
iz
= 3.81 N/mm2
115 x 75
4skc9JLodfcso ~
i
=
YM
1 x1.44x0.9x5.5
=
= 5.48 N/mm2
1.3