PROJETO DA MADEIRADados:

Tipo da madeira: = YakalBending and Tension(Fb) = 23.10 MPaShear(Fv) = 1.72 MPaCompression(Fc) = 15.40 MPaModulus of Elasticity(E) = 1.46E+04 MPaRelative Density(G) = 0.74Specific Gravity = 7.26 q

Loadings:0.025

Wind Pressure = 0.96 kPaMinimum Roof Live Load = 0.80 kPaGI roofing = 0.15 kPaResidential Live Load = 2.00 kPa

=Spacing:

Purlins = 0.60 m Truss = 3.70 mFloor Joist = 0.50 m

DESIGN OF PURINS

Span = 5.00Height = 2.50 (+) Windward (-) Leeward

= 26.57Try:

50 x 150 ; I = 1.41E+07

Loadings: Wind Load:Windward:

Live load = 0.48 kN/m = 0.08 kN/mRoofing = 0.09 kN/m Leeward:Purlin weight = 0.05 kN/m = -0.48 kN/m

= 0.62 kN/m(WW) = 0.05 kN/m

Load Combinations: (LW) = -0.29Condition 1: DL + LL = 0.56 kN/m

= 0.56 kN/m governs!! = 0.28 kN/mCondition 2: DL + LL + WL

= 0.32 kN/m = 0.61 kN/m= 0.28 kN/m

Moments: 5.59

2.50= 1.75 KN-m

= 0.29 KN-m 5.00

Wn2

Wnt

kN/m3

WDL+LL

Theta, q;

mm4

Pn = 1.3(sinq - 0.5)P

Pn = -0.5PWDL+LL

Wn1 = Pn(Spacing) Wn1 = Pn(Spacing) Wn2 = WDL+LL(cosq)

WDL+LL Wnt = WDL+LL(sinq)

WDL+LL+WL WN = Wn1 + Wn2

Wt = Wnt

Mn = Mx = 1/8(WnLx2)

Mt = My = 1/12(WnLy2)

DESIGN OF STAIRSShear:

= 1.40 kN

= 0.35 kN

Check for Bending:=

= 13.96 MPa < 23.10 MPa safe

Check for Shear:=

= 0.35 MPa < 1.72 MPa safe

Check for Deflection:

= 6.64 mm

safe

= 10.28 mm

Therefore use 50 X 150 mm thick purlins

Vx = (1/2)WnLx

Vy = (1/2)WnLy

To be safe, Fb > Fact

To be safe, Fv > Fvact

To be safe, Yall > Yact

Yact = (5/384)(WLn4/EI)

Yallow = L/360

6Mx

bh2+6My

b2h

3Vx2bh

+3Vy2bh

DESIGN OF TRUSS

Load carried by the truss: Try: 3 " x 8 " for overall size of truss and members75 x 200 ; I = 5.00E+07

Loadings: WindwardGI roofing = 3.10 kN wind load = 1.62 kNWt. of Purlins = 0.20 kNMin. Roof LL = 16.55 kN 0.72

= 19.85 kN

1.45

q 1.62

Weigth of trussOverall Length of Truss= 44.52 m Fx = 0.14 / jointWeight of Truss = 4.85 kN Fy = 0.29 / joint

24.70 kNLoad carried by the ceiling: Leeward

Ceiling Load = 0.04 kN/m wind load = -9.939.93

8.88q

4.44

Fx = 0.89 / jointM Fy = 1.78 / joint

L N

K O

J P

Ceiling load

A B C D E F G H I

1.00 0.25 1.25 1.25 1.25 1.25 1.25 1.25 0.25 1.00

10.00 m

Forces Due to DL + LL 9.88 kN

4.94 kN 4.94 kN

4.94 kN M 4.94 kN

L N

4.94 kN 4.94 kNK O

4.94 kN 4.94J P

Ceiling load

A B C D E F G H I

mm4

w

w

1.00 0.25 1.25 1.25 1.25 1.25 1.25 1.25 0.25 1.00

10.00 m

Forces Due to Wind Load 1.49

0.29 1.03 1.78

0.29 0.14 M 0.89 1.78

L N

0.29 0.14 0.89 1.78K O

0.29 0.14 0.89 1.78J P

0.14 0.89

A B C D E F G H I

1.00 0.25 1.25 1.25 1.25 1.25 1.25 1.25 0.25 1.00

10.00 m

Support Reactions due to DL + LL

Axial Forces due to DL + LL

Supp

ort R

eacti

ons

Due

to w

ind

load

Supp

ort R

eacti

ons

Due

to w

ind

load

Axia

l For

ces

Due

to w

ind

load

Axia

l For

ces

Due

to w

ind

load

Summary of Bar Forces

Top Chords Length DL + LL WL DL + LL + WLAJ 1.40 4.20 0.60 4.80JK 1.40 -15.10 0.60 -14.50KL 1.40 -17.40 0.80 -16.60LM 1.40 15.70 1.00 16.70MN 1.40 15.70 -0.10 15.60NO 1.40 -17.40 0.60 -16.80OP 1.40 -15.10 0.70 -14.40PI 1.40 4.20 -2.30 1.90

Bottom ChordSAB 1.25 -4.00 4.40 0.40BC 1.25 2.00 4.00 6.00CD 1.25 13.70 4.20 17.90DE 1.25 15.50 4.00 19.50EF 1.25 15.50 2.10 17.60FG 1.25 13.70 1.20 14.90GH 1.25 2.00 2.10 4.10HI 1.25 -4.00 3.00 -1.00

VerticalsBJ 0.63 -19.80 -0.30 -20.10KC 1.25 -6.50 0.00 -6.50DC 1.88 -1.80 0.20 -1.60ME 2.50 3.60 -1.60 2.00NF 1.88 -1.80 -0.80 -2.60OG 1.25 -6.50 0.70 -5.80HP 0.63 -19.80 0.80 -19.00

DiagonalsJC 1.40 12.60 0.30 12.90KD 1.77 2.50 -0.30 2.20LE 2.25 -2.00 -0.60 -2.60EN 2.25 -2.00 2.50 0.50OF 1.77 2.50 1.30 3.80PG 1.40 12.60 -1.00 11.60

Design of Truss MembersStresses Length

Top Chord -17.40 1.40

Bottom chord 15.50 1.25Vertical -19.80 / -0.30 1.25Diagonal 12.60 / 0.30 2.25

DESIGN OF TOP CHORD

Try:3 " X 8 "

75 mm X 200 mm ; I = 5.00E+07

P = -17.40 kNL = 1400 mm

L / d = 18.67

= 9.87

since L/d>K and L/d>11 it is long column

To be safe:Fc >= fc

Fc = 11.49fc = P/A

= 1.16 MPa < 11.49 ok, SAFE

Therefore use 75 x 200 mm for TOP CHORD

DESIGN OF BOTTOM CHORD

Try:3 " X 8 "

75 mm X 200 mm ; I = 5.00E+07

P = 15.50 kNL = 1250 mm

L / d = 16.67

= 9.87

mm4

mm4

K=( π4 )( E6 fc ). 5

Fc= π2E

36( Ld )2

K=( π4 )( E6 fc ). 5

since L/d>K and L/d>11 it is long column

To be safe:Fc >= fc

Fc = 14.41Fc

= 1.03 MPa < 14.41 ok, SAFE

Therefore use 75 x 200 mm for BOTTOM CHORD

DESIGN OF VERTICALS

Try:3 " X 8 "

75 mm X 200 mm ; I = 5.00E+07

P = -19.80 / -0.30 kNL = 1250 mm

L / d = 16.67

= 9.87

since L/d>K and L/d>11 it is long column

To be safe:Fc >= fc

Fc = 14.41fc = P/A

= 1.32 MPa < 14.41 ok, SAFE

Therefore use 75 x 200 mm for VERTICALS

mm4

Fc= π2E

36( Ld )2

K=( π4 )( E6 fc ). 5

Fc= π2E

36( Ld )2

Check for Stress Reversals:

>= To be safe:

= 23.10 MPa

= 0.03 < 23.10 SAFE

Since Fb > Ft, Use 75 x 200 mm for VERTICALS

DESIGN OF DIAGONALS

Try:3 " X 8 "

75 mm X 200 mm ; I = 5.00E+07

P = 12.60 / 0.30 kNL = 2250 mm

L / d = 30.00

= 9.87

since L/d>K and L/d>11 it is long column

To be safe:Fc >= fc

Fc = 4.45fc = P/A

= 0.84 MPa < 4.45 ok, SAFE

Therefore use 75 x 200 mm for DIAGONALS MEMBERS

Check for Stress Reversals:

>= To be safe:

= 23.10 MPa

= 0.03 < 23.10 SAFE

Since Fb > Ft, Use 75 x 200 mm for DIAGONALS MEMBERS

Fb ft

Fb

mm4

Fb ft

Fb

f t=P

(3 /5 ) Ag

K=( π4 )( E6 fc ). 5

Fc= π2E

36( Ld )2

f t=P

(3 /5 ) Ag

DESIGN OF POST

At Truss supports DL + LL WL DL + LL + WL

A -23.69 -0.19 -23.88B -23.69 4.66 -19.03

At Girder Supports Interior PostCarries 4 Girder

-17.27 0.00 -17.27 4P = 95.52

USE, P = 95.52 96.39 kNTry:

8 " X 8 "200 mm X 200 mm ; I = 1.33E+08

Length of column = 3.00Weight of Column = 0.87 kN

= = 96.39 kN

L / d = 15.00

= 9.87

since L/d > K and L/d > 11 it is long column

To be safe:Fc > = fc

Fc = 17.79fc = P/A

mm4

4Pgirder PTotal

K=( π4 )( E6 fc ). 5

Fc= π2E

36( Ld )2

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

Interior Post(carries 4 girders)

= 2.41 MPa < 17.79 ok, SAFE

Therefore use 200 x 200 mm for POST

DESIGN OF FASTENERS AND CONNECTORS

FOR TOP AND BOTTOM CHORD

Determine the portion of the trus with largest P

3 " x 8 " 3 " x 8 "

P = 19.50 kN P = 19.50 kN

k = ###Diameter of Nail = 0.32 in

= 8.13 mm= 0.008 m

= 0.17

115.75

P=1.25KD3/ 2

DESIGN OF T&G DESIGN OF FLOOR JOIST

Residential Live Load = 2.00 kPa Specific GravitySpecific Gravity = 7.26 Modulus of ElasticityModulus of Elasticity = 1.46E+04 MPa Length of joist

Joist SpacingTry: Residential Live Load

25 X 100 ; I = 2.08E+06

0.10 0.10 0.10 0.10 Try

0.025 T&G T&G T&G T&G SECTION A-A:

FJ

0.50 m Loadings:

Loadings:

Dead Load (Weight of T&G) = Area X S.g. = 0.02 kN/mLive Load (Residential LL) = 0.20 kN/m

= 0.22 kN/m

= 0.007 kN-m= 0.05 kN

Check for Bending:

= 0.16 MPa < Fb 23.10Since Fact is less than Fallowable, it is safe

Check for Shear:Check for Bending:

= 0.03 MPa < Fv 1.72Since Fvact is less than Fvallowable, it is safe

Check for Deflection:

= 0.0058 mm Check for Shear:= 1.39 mm

Since Yact is less than Yallowable, it is safeTherefore use 25 mm X 100 mm T&G

kN/m3

mm4

WDL+LL

MMAX = (1/8)WL2

VMAX = wL/2

To be safe, Fb > Fact

Fact = 6Mmax/bh2

To be safe, Fv > Fvact

Fvact = (3/2)(Vmax/bh)

To be safe, Yall > Yact

Yact = (5/384)(WLn4/EI)Yallow = L/360

DESIGN OF STAIRS

Design of Tread:

Try:2 " X 8 "

50 mm X 200 mm ; I = 3.33E+07

Width of stairs = 1.10 m1100 m

Loadings:Weigth of Tread = 0.07 kN/mLive Load = 0.40 kN/mTOTAL w = 0.47 kN/m

Analytical Model:w = 0.47

1.10 m

Mmax = Vmax = (1/2)wL= 0.07 kN-m = 0.26 kN

Check for Bending:

= 0.21 MPa < Fb 23.10Since Fact is less than Fallowable, it is safe

Check for Shear:

= 0.04 MPa < Fv 1.72Since Fvact is less than Fvallowable, it is safe

mm4

(1/8)wL2

To be safe, Fb > Fact

Fact = 6Mmax/bh2

To be safe, Fv > Fvact

Fvact = (3/2)(Vmax/bh)

Try:2 " X 8 "

50 mm X 200 mm ; I = 3.33E+07

Considering the longest span of the stairs:

No. of Stairs = 18 @ 0.20 m

Load carried by thetread = 0.47

m2.

70

= 36.87Length of Carriage = 4.50 mWeigth of Carriage = 0.07 kN/m

q

3.60 m

Analytical Model of Loadings:Load by the Tread:

q 0.28

0.380.47 kN

Weight of Carriage:

q 0.04

0.060.07 kN/m

Length of Carriage = 4.50 m

Vmax = 0.98 kNMmax = 4.42 kN-m

Landing is made upof concrete

mm4

Theta, q

0.44kN/m

Check for Bending:

= 13.25 MPa < Fb 23.10Since Fact is less than Fallowable, it is safe

Check for Shear:

= 0.15 MPa < Fv 1.72Since Fvact is less than Fvallowable, it is safe

Check for Deflection:

= 4.7851 mm= 12.50 mm

Since Yact is less than Yallowable, it is safe

Therefore use 50 mm X 200 mm for Carriage

To be safe, Fb > Fact

Fact = 6Mmax/bh2

To be safe, Fv > Fvact

Fvact = (3/2)(Vmax/bh)

To be safe, Yall > Yact

Yact = (5/384)(WLn4/EI)Yallow = L/360

DESIGN OF FLOOR JOIST DESIGN OF GIRDER

A

Specific Gravity = 7.26 Specific GravityModulus of Elasticity = 1.46E+04 MPa FLOOR JOIST Modulus of ElasticityLength of joist = 3.60 MPa

T&G

Length of GirderJoist Spacing = 0.50 m Joist SpacingResidential Live Load = 2.00 kPa Residential Live Load

FLOOR JOIST

T&G

TryTry

50 X 175 ; I = 2.23E+07FLOOR JOIST Weight of the girder: = Area X Specific Gravity

SECTION A-A: A

T&G

0.182.08

Floor Joist0.50 m

Loadings:

0.050Dead Loads:

Weight of joist = Specific Gravity X Area of Joist= 0.06 kN/m

Load carried by the T&G 17.27= 0.09 kN/m

Live Load: Check for Deflection: At Mid span: Floor LL = 1.00 kN/m

2.08= 1.15 kN/m = 7.74E+00 mm

= 10.00 mm= 1.87 kN-m Since Yact is less than Yallowable, it is safe= 2.08 kN Therefore use 50 mm X 175 mm

Floor JoistCheck for Bending:

17.27

= 7.33 MPa < Fb 23.10 Check for BendingSince Fact is less than Fallowable, it is safe

Check for Shear:Check for Shear:

= 0.36 MPa < Fv 1.72Since Fvact is less than Fvallowable, it is safe

Check for Deflection:

kN/m3

mm4

To be safe, Yall > Yact

WDL+LL Yact = (5/384)(WLn4/EI)Yallow = L/360

MMAX = (1/8)WL2

VMAX = wL/2

To be safe, Fb > Fact

Fact = 6Mmax/bh2

To be safe, Fb > Fact

Fact = 6Mmax/bh2

To be safe, Fv > Fvact

To be safe, Fv > Fvact

Fvact = (3/2)(Vmax/bh)

To be safe, Yall > Yact

DESIGN OF GIRDER

Specific Gravity = 7.26Modulus of Elasticity = 1.46E+04 MPaLength of Girder = 4.00 MPaJoist Spacing = 0.50Residential Live Load = 2.00 kPa

150 X 300 ; I = 3.38E+08

Weight of the girder: = Area X Specific Gravity

= 0.33 kN/m

2.08 kN 4.16 kN 4.16 kN 4.16 kN 4.16 kN 4.16 kN 4.16 kN 4.16 kN 2.08 kN

0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50

Weight of the girder0.33 kN/m

4.00 m17.27 kN 17.27 kN

At Mid span:

2.08 4.16 4.16 4.16 2.08

0.50 0.50 0.50 0.50

0.33 kN/m= 17.93 kN-m

= 17.27 kN2.00 m

17.27

Check for Bending

= 7.97 MPa < 23.10 MPa SAFE

Check for Shear:

= 0.58 MPa < Fv 1.72Since Fvact is less than Fvallowable, it is safe

Check for Deflection:

= 11.11 mm

= 6.90 mm < 11.11 mm SAFE

kN/m3

mm4

Mmax

Vmax

To be safe, Fb > Fact

Fact = 6Mmax/bh2

To be safe, Fv > Fvact

Fvact = (3/2)(Vmax/bh)

To be safe, Yall > Yact

Yallow = L/360

Y actual=5wl4

384 EI+Pa(3L−4 a2 )24 EI

+ PL3

48 EI

Therefore use 150 x 300 for Girder