Download - Planilha Treliça de Madeira
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