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Timber and Steel DesignTimber and Steel Design

Lecture Lecture 1010 Roof Design

Mongkol JIRAVACHARADETS U R A N A R E E INSTITUTE OF ENGINEERINGUNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL ENGINEERING

Types of RoofTypes of Roof

(a) Flat roof

(d) Gable

(b) Lean to

(e) Hip

(c) Butterfly

(f) Curve

RoofRoof RafterRafter

(RUN)

(SPAN)

(RISE)

..

1.0 1.2 .15 ../..10, 15, 20 ()

0.32 0.34 .50 ../..30 - 35 ()

1.0 2.0 .5 ../..MIN. 1 - 2 (Metal sheet)

(RUN) (SPAN)

(RISE)

P/2P

PP

P/2 RR

RL

10-1

4 m0.8 m 0.8 m

1.2 m

= 30 ../. = 50 ../. = 80 ../.

0.8 m

0.8 m

2 m

2 m

1 .

1 .

1.0 1.0 = 801.0 = 80 ../. = 10 ../. = 90 ../.

2 . 0.8 .

0.8 m RL RR2 m

w = 90 kg/m

72 kg 75.6 kg

104.4 kg

0.84 m

31.8 kg-m

28.8 kg-m

RL = (1/2) (90) (2.8)2 / 2.0 = 176.4 ..RR = (90) (2.8) 176.4 = 75.6 ..

Mmax = 31.8 ..-.Fb = 0.60(2,500) = 1,500 ../.2

S = Mmax/Fb = 31.8(100)/1,500 = 2.12 .3

5025 .. 1.6 .. (Sx = 2.81 .3)

10-2 1

4 m

4 m

0.5 m

0.5 m

4 m 4 m0.5 m

0.5 m

90 ../..

L

L

45

2 24 4= + = 5.66

2 20.5 0.5= + = 0.707 L = 4.0/2 = 2.0

wmax = 2L() = 2(2.0)(90)= 360 ../.

= 3(0.5)2(90) = 67.5 ..= (0.5)2(90) = 22.5 ..

:

:

RRRL5.66 m0.707 m

wmax = 360 kg/m67.5 kg

RRRL5.66 m0.707 m

wmax = 360 kg/m22.5 kg

RoofRoof TrussTruss

Truss

Free Support

Purlins

Top chord

Bottom chord

Sag rod

Truss

Fixed Support

Types of TrussesTypes of Trusses

King Post Truss Pratt Truss

Howe Truss

Fink Truss

Fan Truss

Howe TrussPratt Truss

King Post This is the most basic truss type. Primarily used for simple structures with short spans.

Fink Capable of longer spans than the King Post, adding further design flexibility.

Flat - Using this truss can reduce the amount of wall area that needs to be sheathed.

Double Pitch or Dual Pitch An asymmetrical truss used where the designer wants a change in roof appearance.

Gambrel This truss is often used in agricultural buildings and barns.

Hip This is one section of a hip roof system.

T-2

Sag rodPurlins Bracing

T-1

Bracing of TrussesBracing of Trusses

Roof Plan

1 25.00

35.00

45.00

55.00

65.00

75.00

85.00

95.00

105.00

A

B

10.0

0M

C

10.0

0M

Loading on TrussesLoading on Trusses

Purlins

Prim

ary

Trus

sS

econ

dary

Tru

ss

Trib

utar

y A

rea

=5

x 20

=10

0S

q.M

.

Loading on Loading on PurlinPurlin

s s

Primary Truss

C Purlins

L

s

s

s

Tributary Area

+ = ./.

s L

= x s ./.

= 6 ./.

q

q

sin,8

,

cos,8

,

2

0

2

wwlwMSM

f

wwwlw

MSMf

xx

yy

yby

yy

xx

xbx

===

+===

0.175.066.0

+=+y

by

y

bx

by

by

bx

bx

Ff

Ff

Ff

Ff

q

wwy

wx

Design of Design of PurlinsPurlins

Secondary TrussSecondary Truss

Primary Truss under Loading

Lower chordin Tension

Upper chordin Compression Lateral Buckling of upper

chord in primary trussLa

tera

l win

d lo

ad

Secondary Truss helps Primary Truss for

- Lateral wind load

- Lateral buckling of upper chord

- StabilityL

L

L/r

: = 30 ./.

= 14 ./.

= 44 ./.

1.0 5.0

= 44 x 1.0 = 44 ./.

= 6 ./.

= 44 + 6 = 50 ./.

m-kg1538

549kg/m,4904.14cos50

m-kg388

512kg/m,1204.14sin50

20

20

=

===

=

===

xy

yx

Mw

Mw

3cm27.9)500,2(66.0

)100(153===

bx

xx F

MS

C125x50x20x2.3 . (Sx = 21.9.3, Sy = 6.22.3, Ix =137.4, Iy=20.6.4, 4.51./.)

x :

y :

2kg/cm 6.6989.21

)100(153===

x

xbx S

Mf

2kg/cm 9.61022.6

)100(38===

y

yby S

Mf

OK( ) ( ) 0.175.0500,275.0

9.610500,266.06.698

75.066.0=+=+

y

by

y

bxF

fF

f

:)137)(101.2(384

)500)(100/49(53845

6

44

max

==DEI

wl

OK

==

= 60 x 5 x 0.5 = 150 .

T-1:

T-1 = 5

= 30 ../.

= 14 ../.

(+) = 6 ../.

() = 10 ./.

= 60 ../.

= 60 60 1 = 300 .. 150 ..

300 ..

(.) (.)L1L2 = L12L13 0 1.00L2L3 = L11L12 2200(T) 1.00L3L4 = L10L11 3000(T) 1.00L4L5 = L9L10 3240(T) 1.00L5L6 = L8L9 3200(T) 1.00L6L7 = L7L8 3000(T) 1.00

U1U2 = U12U13 2267(C) 1.03U2U3 = U11U12 3092(C) 1.03U3U4 = U10U11 3339(C) 1.03U4U5 = U9U10 3298(C) 1.03U5U6 = U8U9 3092(C) 1.03U6U7 = U7U8 2783(C) 1.03

Lower Chord:

Upper Chord:

VerticalBracing:

DiagonalBracing:

(.) (.)

L1U1 = L13U13 1800(C) 0.50L2U2 = L12U12 1100(C) 0.75L3U3 = L11U11 600(C) 1.00L4U4 = L10U10 240(C) 1.25L5U5 = L9U9 50(T) 1.50L6U6 = L8U8 300(T) 1.75

L7U7 1050(T) 2.00

L2U1 = L12U13 2460(T) 1.12L3U2 = L11U12 1000(T) 1.25L4U3 = L10U11 339(T) 1.41L5U4 = L9U10 64(C) 1.60L6U5 = L8U9 360(C) 1.80L7U6 = L7U8 604(C) 2.02

L4L5 L9L10 = 3240 . (T) 1.0

, Ft = 0.60Fy = 0.60(2,500) = 1,500 ./.2

, Ag = 3240/1500 = 2.16 .2

L50 x 50 x 4 . (Ag = 3.89 .2, rmin = 0.98 .)

A307 12 .

, Ae = 0.85Ag = 0.85(3.89) = 3.31

= 0.5FuAe = 0.5(4,000)(3.31)

= 6,620 . > 3,240 . OK

, L/r = 100/0.98 = 102 < 300 OK

:

U3U4 U10U11 = 3,339 ..() 1.03

, Fa = 1,000 ../.2

, A = 3,339/1,000 = 3.34 .2

L50 x 50 x 4 . (A = 3.89 .2, rmin = 0.98 .)

, L/r = 103/0.98 = 105

, Fa = 876.2 ../.2

= (3.89)(876.2) = 3,408 .. > 3,339 .. OK

:

L2U1 L12U13 = 2,460 .. 1.12

, Ft = 0.60Fy = 0.60(2,500) = 1,500 ../.2

, Ag = 2460/1500 = 1.64 .2

L40 x 40 x 3 . (A = 2.35 .2, rmin = 0.78 .)

:

A307 12 ..

, Ae = 0.85Ag = 0.85(2.35) = 2.00

= 0.5(4,000)(2.00) = 4,000 .. > 2,460 .. OK

, L/r = 112/0.78 = 143.6 < 300 OK

1) :

L7U6 L7U8 = 604 . 2.02

L65 x 65 x 6 . (A = 7.53 .2, rmin = 1.27 .)

= (4.70)(387.7) = 1,822 . > 600 . OK

L/r = 202/0.78 = 259 > 200 NG

2 L40 x 40 x 3 . (A = 2(2.35) = 4.70 .2)y

y

x x

Ix = 2 ( 3.45 ) = 6.90 .4

Iy = 2 ( 3.45 ) + 4.70 ( 1.07 )2 = 12.28 .4Control

min 6.90 / 4.70 1.21 cmr = =

L/r = 202/1.21 = 167 < 200 OK

, Fa = 387.7 ./.2

2) :

150 kg300 kg

300 kg300 kg

300 kg300 kg

300 kg

150 kg300 kg

300 kg300 kg

300 kg300 kg

12 m

FIXFREE

Max. Deflection:

From analysis,

Dmax = 1.64 cm

< [1200/300 = 4.0 cm] OK

Free (Roller) Support Design:

slot

= 12

a = 1210-6 /oc DT = 40 oCaDTL = 1210-6401,200 = 0.576 cm

Slot length = 2 0.576 + 1.6 = 2.75 cm USE 5 cm

BOLT 16 MM

5 cm

2 cm