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GEOMETRY OF TRUSS SYSTEM
Slope of roof, a=8. 53 m=0.15
Sina=0.148 cosa=0.989 tana=0.15
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O1 3.29 V1 1 D1 3.57 U1 6.5
O2 3.29 V2 1.98 D2 3.57 U2 7
O3 3.54 V3 1.98 D3 4.3 U3 6.5
O4 3.54 V4 1 D4 4.3
O5 3.29 D5 3.57
O6 3.29 D6 3.57
DIMENSIONS OF MEMBERS(M)
ANALYS OF LOADS
SELF WEIGHTS:
Roof coating : 12kg/m2 ( horizontal plane)
Purlin self weight : 10kg/m2 ( horizontal plane)
Stability connections :
= 2kg/m2 ( horizontal plane)
Wight of hardware : 15kg/m2 ( horizontal plane)
Weight of truss : 24kg/m2 ( horizontal plane)
Snow load : 184kg/m2(horizontal plane)
Wind load : 80kg/m2 (roof plane)
SNOW LOAD:
Pk= m x Po for a
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WIND LOAD:
Pr=c x q c =1.2 x 0.4
c = -0.222
Pr=-0.222 x 80 = -17.76 kg/m2
P pull= 0.4 x*80 = 32.00 kg/m2
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PURLIN DESIGN
Purlins made of I profiles. Roof coating materials are made of corrugated steel sheets and maximum space is
3.5 m which carry 196 kg/m2. Bottom and top steel sheet thicknesses are 0.7mm. Its
eps thickness is 70mm.
Distance between the purlins are changing,you can see this distance from the upperdrawings.
Maximum distance will be used for the purlin design and it is 3.5m.
Distance between two truss system is 4m.
Total q= dead loads +snow loads (wind loads is not calculated because of pulling !!)
Totalq=(12 + 10 + 2 + 184)x3.54 = 736.32 kg/m
Simple beam have 8.53 degree so we have qx qy .
Also we have two purlin braches for y axis.
qx = 736.32 x = 728.17 kg/m
qy = 736.32 x = 109.22 kg/m
Mx=
=
= 145.6 tcm
My =
=
(
)
= 2.43 tcm
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For I 180 Ix =1450cm4 Iy =81.3 cm
4
Wx =161 cm3
Wy =19.8 cm3
STRESS CONTROL:
s=
+
=
+
=1.02< 1.44 kg/m2
DISPLACEMENT CONTROL:
f = 6.20 x
( q=t/m , l= m , I=cm4 ) fmax =
fx = (6.20 x 0.728 x 44
) / 1450 fx = 0.799 cm
fy = (6.20 x 0.11 x (4/3)4) / 81.3 fy = 0.027 cm
f = (0.7992 + 0.0272) = 0.8 cm
fmax = 400/300 =1.33cm
f< fmax it is done
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TIE BAR CONTROL:
Z =
qy
qy = 3 x109.22 =327.66kg/m
Cos= 0.936
Z =4/(3x0.936) x 327.66
Z=466.74 kg
Chosen tie bar = 8
Fz = ( (0.86 x 0.8)2)/4 Fz=0.372 cm2
466.74/0.372= 1254 677 kg/cm2 < 1440 kg/cm2
Tie bar is checked and it is usefull
RESULTS:
Purlins are I 180 and purlins are design by two tie bars. Tie bars are 8
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ANALYS OF TRUSS SYSTEM
SELF WEIGT LOADING
FULL SNOW LOADING
HALF SNOW LOADING
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RIGHT WIND LOADING
LEFT WIND LOADING
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SELF WEIGT LOADING
Mb=0 , (0.41 x 20)+(0.83 x 16.75)+(0.86 x 13.5)+(0.89 x 10)+(0.86 x 6.5)+(0.83 x 3.25)
= 20 x A A = 2.55 t
Fy= 0 B = 2.55 t
USING RITTER METHOD, we can seperate the system from the O1 frame and equation is
like that;
-(0.41 x 3.25) + (2.55 x 3.25) = 1.49 U1 U1 = 4.67 t
From the firs node those equations are calculated;
U1 = 0.91 x D1 , (0.416 x D1) + V1 = 2.55 t
V1 = -0.42 t, D1 = -5 13 t
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First node
From the 2. Node O1 = 0 t
Calculation of 4. Node ( Ritter method)
(2.55 x 6.5)(0.41 x 6.5)( 0.83 x 3.25) +(1.95 x O2 ) = 0
O2 = - 5.75 t
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Calculation of 3. Node
D2 (horizontal) + 4.67 -5 67 = 0 D2 (horizontal) = 1 t
D2 (vertical) +0.83 +0.852.13 = 0 D2 (vertical) = 0.45 t
D2 = (12+ 0.452)(1/2) D2 = 1.1 t
From the geometry of truss system V2 = -0.86 t
U2 is calculated ritter metod, truss system seperated from O3 and moment values calculated to
the ridge point;
(2. 55 x 10)( 0.41 x 10)(0.83 x 6 75) - (80.86 x 3.5) ( U2 x2.5) = 0
U2 = 5.12 t
D3 is calculeted from the 5. Node and D3 = 0.69 t
Truss system is symmetric so the other ones are equal to those values.
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FRAME FORCES FOR THE OTHER LOAD PATTERN
LEFT WIND
Text Tonf
D1 1.7768
D2 -0.4733
D3 -0.0821
D4 -0.5104
D5 -0.3489
D6 2.207
O1 0.0175
O2 2.1214
O3 2.1577
O4 2.5101
O5 2.4446
O6 0.0315
U1 -1.5452
U2 -1.9087
U3 -2.0068
V1 0.1183
V2 0.2447
V3 0.4419
V4 0.2123
FULL SNOW
Text Tonf
D1 -14.9854
D2 3.2061
D3 2.0279
D4 2.0279
D5 3.2061
D6 -14.9854
O1 0
O2 -16.7263
O3 -16.7263
O4 -16.7263
O5 -16.7263
O6 0
U1 13.626
U2 14.8911
U3 13.626
V1 -1.211
V2 -2.513
V3 -2.513
V4 -1.211
DEAD LOADS
Text Tonf
D1 -5.1361
D2 1.0988
D3 0.6951
D4 0.6951
D5 1.0988
D6 -5.1361
O1 0
O2 -5.7327
O3 -5.7327
O4 -5.7327
O5 -5.7327
O6 0
U1 4.6702
U2 5.1037
U3 4.6702
V1 -0.4149
V2 -0.8613
V3 -0.8613
V4 -0.4149
HALF SNOW(RGHT)
Text Tonf
D1 -4.4729
D2 2.2648
D3 -1.6216
D4 3.6443
D5 0.9414
D6 0
O1 0
O2 -6.195
O3 -6.195
O4 -10.528
O5 -10.528
O6 0
U1 4.0671
U2 7.446
U3 9.5555
V1 0
V2 0
V3 -2.51
V4 -1.21
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