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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