Ce 164

TIMBER DESIGN Data: Type of wood: Bending and Tension(Fb) Shear(Fv) Compression(Fc) Modulus of Elasticity(E) Relative Density(G) Specific Gravity

= = = = = = =

Wn2

Yakal 23.10 MPa 1.72 MPa 15.40 MPa 1.46E+04 MPa 0.74 7.26 kN/m3

θ

Loadings: Wind Pressure Minimum Roof Live Load GI roofing Residential Live Load

= = = = =

0.96 kPa 0.80 kPa 0.15 kPa 2.00 kPa

= = =

0.60 m 3.70 m 0.50 m

Spacing: Purlins Truss Floor Joist

DESIGN OF PURINS Span Height Theta, θ;

= =

5.00 2.50

=

(+) Windward

26.57

Try: 50

x

150

;

I

=

1.41E+07 mm4

Loadings: Live load Roofing Purlin weight WDL+LL

= = = =

0.48 0.09 0.05 0.62

kN/m kN/m kN/m kN/m

Leeward: Pn = -0.5P (WW) Wn1 = Pn(Spacing) (LW) Wn1 = Pn(Spacing) Wn2 = WDL+LL(cosθ)

Load Combinations: Condition 1: DL + LL WDL+LL = 0.56 kN/m Condition 2: DL + LL + WL WDL+LL+WL = 0.32 kN/m

Wind Load: Windward: Pn = 1.3(sinθ - 0.5)P

governs!!

Wnt = WDL+LL(sinθ) WN = Wn1 + Wn2 Wt = Wnt

Moments:

5.59

Mn = Mx = 1/8(WnLx2)

=

1.75 KN-m

Mt = My = 1/12(WnLy2)

=

0.29 KN-m

5.00

Shear: Vx = (1/2)WnLx

=

1.40 kN

Vy = (1/2)WnLy

=

0.35 kN

=

6 Mx 6 My + 2 2 bh b h

Check for Bending: To be safe, Fb > Fact

= Check for Shear: To be safe, Fv > Fvact

13.96

MPa

<

23.10

MPa

safe

<

1.72

MPa

safe

3Vx 3Vy + 2bh 2bh

= =

0.35

MPa

6.64

mm

Check for Deflection: To be safe, Yall > Yact Yact = (5/384)(WLn4/EI) = Yallow = L/360

safe =

Therefore use

10.28

50

X

mm

150 mm thick purlins

DESIGN OF TRUSS

Load carried by the truss:

Try:

3" x 8 " for overall size of truss and me 75 x 200 ; = 5.00E+07 I Windward wind load = 1.62 kN

Loadings: = = = =

Weigth of truss Overall Length of Truss= Weight of Truss = Load carried by the ceiling: Ceiling Load

3.10 0.20 16.55 19.85

kN kN kN kN

0.72 1.45

GI roofing Wt. of Purlins Min. Roof LL

θ

1.62

=

-9.93

44.52 m 4.85 kN 24.70 kN

=

Leeward wind load

0.04 kN/m

8.88 θ

M L

w

N

K

O

J Ceiling load

A

B 1.00

0.25

C 1.25

D

E

1.25

1.25

F 1.25

G 1.25

1.25

10.00 m

Forces Due to DL + LL

9.88 kN 4.94 4.94

4.94

4.94

kN

M

kN

4.94

L

w

kN

kN

N

K 4.94

O

kN J Ceiling load

A

B 1.00

0.25

C 1.25

D 1.25

E 1.25

F 1.25

G 1.25

1.25

10.00 m

Forces Due to Wind Load

1.49 0.29

0.29

0.14

1.03 M

1.78 0.89

1.78

L 0.29

N

0.14

0.89 K

0.29

O

0.14 J

0.14 A

B 1.00

0.25

C 1.25

D 1.25

E 1.25

F 1.25

10.00 m

Support Reactions due to DL + LL

Axial Forces due to DL + LL

G 1.25

1.25

d load

Support Reactions Due to wind load

Axial Forces Due to wind load Summary of Bar Forces Top Chords AJ JK KL LM MN NO OP PI Bottom ChordS AB BC CD DE EF FG GH HI Verticals BJ KC DC

Length 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40

DL + LL

WL

4.20 -15.10 -17.40 15.70 15.70 -17.40 -15.10 4.20

0.60 0.60 0.80 1.00 -0.10 0.60 0.70 -2.30

1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25

-4.00 2.00 13.70 15.50 15.50 13.70 2.00 -4.00

4.40 4.00 4.20 4.00 2.10 1.20 2.10 3.00

0.63 1.25 1.88

-19.80 -6.50 -1.80

-0.30 0.00 0.20

ME NF OG HP Diagonals JC KD LE EN OF PG

2.50 1.88 1.25 0.63

3.60 -1.80 -6.50 -19.80

-1.60 -0.80 0.70 0.80

1.40 1.77 2.25 2.25 1.77 1.40

12.60 2.50 -2.00 -2.00 2.50 12.60

0.30 -0.30 -0.60 2.50 1.30 -1.00

Design of Truss Members Stresses Top Chord -17.40 Bottom chord 15.50 Vertical -19.80 / -0.30 Diagonal 12.60 / 0.30

Length 1.40 1.25 1.25 2.25

DESIGN OF TOP CHORD Try: 3" 75 P L L/d

mm

= =

-17.40 1400

=

18.67

X X

;

mm

I =

5.00E+07

kN mm

π  E K =    4 6 fc

=

8" 200

.5

   

9.87

since L/d>K and L/d>11

it is long column

To be safe: Fc >= fc

Fc =

Fc = fc = =

π2 E 2

L  36  d 

11.49 P/A 1.16 MPa

Therefore use

< 11.49 75

x

ok, SAFE

200 mm for TOP CHORD

mm4

DESIGN OF BOTTOM CHORD Try: 3" 75 P L L/d

mm

= =

15.50 1250

=

16.67

X X

;

mm

I =

5.00E+07

mm4

kN mm

π  E K =    4 6 fc

=

8" 200

.5

   

9.87

since L/d>K and L/d>11

it is long column

To be safe: Fc >= fc Fc =

Fc = Fc =

π2 E 2

L  36  d 

14.41

1.03 MPa

Therefore use

< 14.41 75

x

ok, SAFE

200 mm for BOTTOM CHORD

DESIGN OF VERTICALS Try: 3" 75 P L L/d

mm

= =

-19.80 1250

=

16.67

π  E K =    4 6 fc

=

X X / mm

8" 200

mm

;

-0.30 kN

.5

   

9.87

since L/d>K and L/d>11 To be safe: Fc >= fc

it is long column

I =

5.00E+07

mm4

Fc =

π2 E 2

L  36  d 

Fc = fc = =

14.41 P/A 1.32 MPa

Therefore use

< 14.41 75

x

ok, SAFE

200 mm for VERTICALS

Check for Stress Reversals: Fb

>= ft

Fb

=

ft =

To be safe:

23.10 MPa P (3 / 5) Ag

=

0.03

Since Fb > Ft, Use

<

75

x

23.10

SAFE

200 mm for VERTICALS

DESIGN OF DIAGONALS Try: 3" 75 P L L/d

X X

mm

= =

12.60 2250

=

30.00

/ mm

π  E K =    4 6 fc

=

8" 200

;

mm

I =

5.00E+07

mm4

0.30 kN

.5

   

9.87

since L/d>K and L/d>11

it is long column

To be safe: Fc >= fc

Fc =

π2 E 2

L  36  d 

Fc = fc = =

4.45 P/A 0.84 MPa

Therefore use

< 75

Check for Stress Reversals: Fb

>= ft

Fb

=

ft =

To be safe:

23.10 MPa P (3 / 5) Ag

4.45 x

ok, SAFE

200 mm for DIAGONALS MEMBERS

ft =

P

=

(3 / 5) Ag

Since Fb > Ft, Use

0.03

75

<

x

23.10

SAFE

200 mm for DIAGONALS MEMBERS

DESIGN OF POST

At Truss supports

DL + LL

WL

DL + LL + WL

-23.69 -23.69

-0.19 4.66

-23.88 -19.03

A B At Girder Supports

-17.27 USE, P = Try:

-17.27

95.52 8" 200

mm

96.39 X X

Length of column Weight of Column 4Pgirder L/d

0.00

Interior Post Carries 4 Girder 4P = 95.52

=

= PTotal

8" 200 = =

3.00 0.87 kN

=

96.39 kN

15.00

π  E K =    4 6 fc

=

mm

;

I =

Load Transmitted by the 4 Girder together w/ post weight….Center post

.5

   

9.87

since L/d > K and L/d > 11 it is long column To be safe: Fc > =fc Fc =

Fc =

π2 E 2

L  36  d 

17.79

1.33E+08

mm4

fc = =

P/A 2.41 MPa

Therefore use

< 17.79 200

x

ok, SAFE

200 mm for POST

DESIGN OF FASTENERS AND CONNECTORS

FOR TOP AND BOTTOM CHORD Determine the portion of the trus with largest P

3

P =

"

x

8

"

3

"

x

19.50 kN

k Diameter of Nail

P =1.25 KD 3 / 2

= = = = =

### 0.32 in 8.13 mm 0.008 m 0.17

115.75

8

"

DESIGN OF T&G Residential Live Load Specific Gravity Modulus of Elasticity

Wnt

= = =

2.00 kPa 7.26 kN/m3 1.46E+04 MPa

Try: 25

X

100

; I

=

2.08E+06 mm4

0.10

0.10

WDL+LL 0.025

T&G

T&G

FJ

0.50 Loadings: Dead Load (Weight of T&G) = Area X S.g. Live Load (Residential LL) WDL+LL (-) Leeward

MMAX = (1/8)WL2 VMAX = wL/2 Check for Bending: To be safe, Fb > Fact Fact = 6Mmax/bh2

= 0.16 MPa Since Fact is less than Fallowable, it is safe

=

0.08 kN/m

=

-0.48 kN/m

Check for Shear: To be safe, Fv > Fvact Fvact = (3/2)(Vmax/bh)

= =

0.05 kN/m -0.29

=

0.56 kN/m

=

0.28 kN/m

= =

0.61 kN/m 0.28 kN/m

2.50

= 0.03 MPa Since Fvact is less than Fvallowable, it is safe Check for Deflection: To be safe, Yall > Yact = 0.0058 = 1.39 Since Yact is less than Yallowable, it is safe Therefore use 25 mm X 100 mm T&G Yact = (5/384)(WLn4/EI) Yallow = L/360

DESIGN OF STAIRS

Design of Tread: Try: 2" 50 safe

safe

mm

X X

Width of stairs

8" 200 =

Loadings: Weigth of Tread Live Load TOTAL

= = w =

;

mm

1.10 m 1100 m 0.07 kN/m 0.40 kN/m 0.47 kN/m

Analytical Model: w

=

0.47

1.10 m Mmax = =

(1/8)wL2 0.07 kN-m

Vmax = (1/2)wL =

Check for Bending: To be safe, Fb > Fact Fact = 6Mmax/bh2 = Since Fact is less than Fallowable, it is safe

Check for Shear: To be safe, Fv > Fvact

Fvact = (3/2)(Vmax/bh) = Since Fvact is less than Fvallowable, it is s

ll size of truss and members 5.00E+07 mm4

Try: 2" 50

mm

X X

8" 200

;

mm

Considering the longest span of the stairs: No. of Stairs 0.14 / joint 0.29 / joint

18 @

0.20

Load carried by the tread

=

2.70 m

Fx = Fy =

=

9.93

Theta, θ Length of Carriage Weigth of Carriage

=

36.87 = 4.50 m = 0.07 kN/m

4.44 3.60 m Fx = Fy =

0.89 / joint 1.78 / joint

Analytical Model of Loadings:

P

Load by the Tread: H 1.25

I 0.25

1.00

0.38

0.

kN

44

4.94

Length of Carriage

kN 4.94

P

H 1.25

Vmax = Mmax =

=

4.50 m

kN

/m

0.98 kN 4.42 kN-m

I 0.25

1.00

Check for Bending: To be safe, Fb > Fact Fact = 6Mmax/bh2 = Since Fact is less than Fallowable, it is safe

0.89

1.78 0.89

1.78

P

Check for Shear: To be safe, Fv > Fvact

0.89 H 1.25

I 0.25

Fvact = (3/2)(Vmax/bh) = Since Fvact is less than Fvallowable, it is s

1.00

Check for Deflection: To be safe, Yall > Yact = Yact = (5/384)(WLn4/EI) Yallow = L/360 = Since Yact is less than Yallowable, it is saf

Therefore use

50 mm

X

200

DL + LL + WL 4.80 -14.50 -16.60 16.70 15.60 -16.80 -14.40 1.90 0.40 6.00 17.90 19.50 17.60 14.90 4.10 -1.00 -20.10 -6.50 -1.60

2.00 -2.60 -5.80 -19.00 12.90 2.20 -2.60 0.50 3.80 11.60

S MEMBERS

NALS MEMBERS

nterior Post arries 4 Girder 95.52 96.39 kN

Interior Post (carries 4 girders)

P =

19.50 kN

GN OF T&G

DESIG Specific Gravity Modulus of Elasticity Length of joist Joist Spacing Residential Live Load

0.10

0.10

T&G

1.46E+04

Try 50

T&G

= = = = =

X

175

; I

SECTION A-A: T&G

Floor Joist 0.50 m

Loadings: Dead Loads:

= = =

0.02 kN/m 0.20 kN/m 0.22 kN/m

=

0.007 kN-m

=

MPa le, it is safe

0.05 kN

Weight of joist = Specific Gra Load carried by the T&G Live Load: Floor LL WDL+LL

<

MPa < able, it is safe

Fb

23.10

MMAX = (1/8)WL2 VMAX = wL/2 Check for Bending: To be safe, Fb > Fact

Fv

0.0058 mm 1.39 mm le, it is safe m T&G

1.72 Fact = 6Mmax/bh

Since Fact is less than Fallo Check for Shear: To be safe, Fv > Fvact Fvact = (3/2)(Vmax

Since Fvact is less than Fva

N OF STAIRS

I =

3.33E+07

mm4

max = (1/2)wL 0.26 kN

0.21 MPa an Fallowable, it is safe

<

Fb

0.04 MPa < han Fvallowable, it is safe

Fv

23.10

1.72

I =

3.33E+07

mm4

m

0.47

θ

oad by the Tread: θ

0.28

0.47 kN Weight of Carriage: θ 0.

44

0.06 kN

0.07 kN/m

/m

13.25 MPa an Fallowable, it is safe

Landing is made up of concrete

<

Fb

23.10

0.04

0.15 MPa < han Fvallowable, it is safe

Fv

4.7851 mm 12.50 mm an Yallowable, it is safe

mm for Carriage

1.72

DESIGN OF FLOOR JOIST A

7.26 kN/m3 1.46E+04 MPa 3.60 MPa 0.50 m 2.00 kPa

Specific Gravity Modulus of Elastic Length of Girder Joist Spacing Residential Live L

T&G

FLOOR JOIST

FLOOR JOIST T&G

=

Try

2.23E+07 mm4

FLOOR JOIST

Weight of the girder A 2.08

0.18 0.50 m

0.050

f joist = Specific Gravity X Area of Joist = 0.06 kN/m ried by the T&G = 0.09 kN/m Check for Deflection: To be safe, Yall > Yact = 1.00 kN/m

17.27 At Mid span: 2.08

=

1.15 kN/m

= =

1.87 kN-m 2.08 kN

= 7.74E+00 mm = 10.00 mm Since Yact is less than Yallowable, it is safe Therefore use 50 mm X 175 mm Yact = (5/384)(WLn /EI) Yallow = L/360 4

Floor Joist 17.27

= 6Mmax/bh2

= 7.33 MPa < Fact is less than Fallowable, it is safe

Fb

23.10

Check for Bending To be safe, F Fact = 6Mmax/bh2 Check for Shear: To be safe, Fv >

= (3/2)(Vmax/bh)

= 0.36 MPa < Fvact is less than Fvallowable, it is safe

Fv

1.72

Check for Deflecti To be safe, Y

DESIGN OF GIRDER Specific Gravity Modulus of Elasticity Length of Girder Joist Spacing Residential Live Load

150

X

300

Weight of the girder:

= = = = =

; I

4.16 kN

0.50

=

3.38E+08 mm4

= Area X Specific Gravity =

2.08 kN

7.26 kN/m3 1.46E+04 MPa 4.00 MPa 0.50 2.00 kPa

0.33 kN/m 4.16 kN

0.50

4.16 kN

0.50

4.16 kN

0.50

4.16 kN

0.50

4.16 kN

0.50

4.16 kN

0.50

2.08

0.50

Weight of the girder 0.33 kN/m

4.00 m 17.27

kN

17.27

t Mid span: 2.08

4.16 0.50

4.16 0.50

4.16 0.50

0.33

2.08 0.50

kN/m

Mmax

=

17.93 kN-m

Vmax

=

17.27 kN

2.00 m 17.27

heck for Bending To be safe, Fb > Fact Fact = 6Mmax/bh2

=

7.97 MPa

<

23.10 MPa

SAFE

Check for Shear: To be safe, Fv > Fvact Fvact = (3/2)(Vmax/bh) = 0.58 MPa < Fv Since Fvact is less than Fvallowable, it is safe Check for Deflection: To be safe, Yall > Yact Yallow = L/360 = 11.11 mm Yactual =

1.72

5wl 4 Pa(3L −4a 2 ) PL3 + + 384 EI 24 EI 48 EI

Therefore use

= 150 x

6.90 mm 300 for Girder

<

11.11 mm

SAFE

2.08 kN

17.27

SAFE

kN