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PURLINS
1. Constructive Scheme
Student Number: 1
D= 24 m
t= 9 m
H= 10 m
d= 2.4 m
p= 0.1
= 5.71
2. Calculus Scheme
3. Loads, Load Factors, Load Combinations
Loads Nominal Load Safety
(KN/m2) Factor
Permanent 0.2 1.35
Loads (P) 0.15 1.35
0.1 1.35
Variable 1.14 1.5Loads (V)
s0,k= 1.5 KN/m2
Ce= 0.8
Ct= 1
1= 0.8
2= 0.95
Roof weigth
Purlin weigth
Technological load
Snow load
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The horizontal distributed (surface) load on the roof
ULS: Qc= 2.32 KN/m
2 (roof weight is divided by cos)
SLS: Qn= 1.59 KN/m
2
The vertical distributed (linear) load acting on the current purlin
ULS: qc= Q
c*d = 5.58 KN/m
SLS: qn
= Qn
*d = 3.82 KN/mthe parallel component
ULS: qfc= q
c*sin = 0.55 KN/m
SLS: qfn= q
n*sin = 0.38 KN/m
the normal component
ULS: qwc= q
c*cos = 5.55 KN/m
SLS: qwn= q
n*cos = 3.81 KN/m
4. Calculus of bending moment and shear force (elastic range)
ULS 5.55
SLS 3.81
KN
KNm
35.05 14.83 20.67
24.35
19.72
30.21 23.67 24.96
26.21 24.96 24.96
M KNm
24.05 10.17 14.18
M
47.18 35.50 35.50
T
32.37 24.35
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5. Cross Section Sizing
5.1 Sizing for Deflection Checking
fallowable= t/200 = 4.5 cm 1= 49.6 2= 59.52
Inecd1
= 1706.47 cm2
Inecd2
= 831.215 cm2
5.2 Sizing for Resisting Bending Moment
Cross section shape I
Material type: OL 37 R = 220 N/mm2
Required section modulus:
M*
= 29.37 KNmW
*= M
*/R = 133.519 cm
3
Web dimensions
propose tw= 3 mm
hw= 242.61 mm we use hw= 250 mm
Flanges dimensions
propose tf= 6 mm
Strength modulus
W1= 161354 mm3
W2= 214458 mm3
W3= 93953.2 mm3
Flange areas
Af1= 525.42 mm2
Af2= 737.83 mm2
Af3= 255.81 mm2
bf1= 87.5696 mm bf1= 90 mm
bf2= 122.972 mm we use bf2= 130 mm
bf3= 42.6355 mm bf3= 60 mm
current spans
first span and current supports
first support
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6. Verifications for the Sized Cross Section
A1= 18.3 cm2 A2= 23.1 cm
2 A3= 14.7 cm2
Ix1= 2160.42 cm4 Ix2= 2947.00 cm
4 Ix3= 1570.49 cm4
6.1 Verifications of ULS
Check for resistance
M T * e
Section KNm KN N/mm2
N/mm2
N/mm2
N/mm2 check
1 35.50 24.96 215.247 33.2845 205.388 213.326 ok
2 47.18 30.21 209.728 40.2743 200.123 211.932 ok
3 20.67 0 172.413 0 164.516 164.516 ok
Check for local buckling
for compressed flange7.25 15
b'/tf15 10.5833 15 (OL 37)
4.75 15
for web
83.3333 107.471
6.1 Verification of SLS
Check for deflection
first span
factual,1= 3.55 cm
current span
factual,2= 2.38 cm
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7. Purlin Cross Section Variation on the Length of the Beam
second support
We= Ix3/ymax= 119.88 cm3
Me= We*R = 26.37 KNm
26.212 * xr -2.774 * xr2
-47.181 = -26.375
xr= 875 mm
We= Ix1/ymax= 164.92 cm3Me= We*R = 36.28 KNm
30.206 * xl -2.774 * xl2
-47.181 = -36.282
xl= 374 mm
x1= 1000 mm
current support
We= Ix3/ymax= 119.88 cm3
Me= We*R = 26.37 KNm
24.963 * xr -2.774 * xr2
-35.498 = -26.375
xr=209
mmWe= Ix3/ymax= 119.88 cm3
Me= We*R = 26.37 KNm
23.665 * xl -2.774 * xl2
-35.498 = -26.375
xl= 221 mm
x1= 300 mm
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8. Purlin Splice Design
second support
Design Stress
M= 47.18 KNm H= M/h = 180.08 KN
Cover plates sizing
Acpn= H/R = 818.54 mm
2
top flange cover plate
propose bcpt= b-20mm
bcpt= 110 mm
tcpt= 7.44 mm we use tcp
t= 7 mm
= 233.87 N/mm2
aw 0.7*tmin tmin= min(tf, tcp)
aw= 4.2 mm
lw= 140 mm 60*aw= 252 mm
bottom cover cover plate
tcpb=tf= 6 mm
bcpt= 140.00 mm
= 214.38 mm
lw= 160 mm 60*aw= 252 mm
current support
Design Stress
M= 35.50 KNm H= M/h = 135.49 KN
Cover plates sizing
Acpn= H/R = 615.86 mm
2
top flange cover plate
propose bcpt= b-20mm
bcpt= 70 mm
tcpt= 8.80 mm we use tcp
t= 6 mm
= 322.59 N/mm2
aw 0.7*tmin tmin= min(tf, tcp)
aw= 4.2 mm
lw
=80 mm 60*aw= 252 mm
bottom cover cover plate
tcpb=tf= 6 mm
bcpt= 110.00 mm
= 205.285 mm
lw= 130 mm 60*aw= 252 mm
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TRUSS
Loads for truss analysis
Loads Nominal Load Safety
(KN/m2) Factor
Permanent 0.2 1.35
Loads (P) 0.15 1.35
0.1 1.35
Variable 1.14 1.5
Loads (V)
s0,k= 1.5 KN/m2
Ce= 0.8
Ct= 1
1= 0.8
2= 0.95
The horizontal distributed (surface) load on the roof
ULS: Qc= 2.32 KN/m
2 (roof weight is divided by cos)
SLS: Qn= 1.59 KN/m
2
The vertical distributed (linear) load acting on the current purlin
ULS: qc= Q
c*d*t = 50.18 KN/m
SLS: qn= Q
n*d*t = 34.42 KN/m
the parallel component
ULS: qfc= q
c*sin = 4.99 KN/m
SLS: qfn= q
n*sin = 3.43 KN/m
the normal component
ULS: qwc= q
c*cos = 49.93 KN/m
SLS: qwn= q
n*cos = 34.25 KN/m
Purlin weigth
Technological load
Snow load
Roof weigth
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COLUMN
1. Loads for column analysis
Loads
Permanent Roof weigth 0.2 KN/m2
Loads (P) Purlin weigth 0.15 KN/m2
Truss weigth 0.15 KN/m2
Quasipermanent Industrial dust 0.25 KN/m2
Loads (C) Technological dust 0.1 KN/m2
Variable Snow load 1.14 KN/m2
Loads (V)
s0,k= 1.5 KN/m2
Ce= 0.8
Ct= 1
1= 0.8
2= 0.95
Wind load
(wind surface pressure)
(reference wind pressure)
= 1.25 Kg/m3 (air density for standard air)
Uref= 28.9 m/s (reference air velocity-10min)
qref= 0.522 KPa
(exposure factor)
(gust factor)
g = 3.5 (peak factor)
(wind turbulence intensity
for reference heigth 10m)
2.35
z0= 0.3 (roughness length)
I(10) = 0.27
cg(z) = 2.88
(roughness factor)
kr(z0) = 0.22 (factor for terrain category)
cr(z) = 0.60ct(z)= 1 (topograhic factor)
ce(z)= 1.71
cp (aerodynamic pressure
cp1= 0.7 coefficient)
cp2= -0.3
pressure: 0.626 KN/m2
suction: -0.268 KN/m2
Nominal Load
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Earthquake load
1= 1 (building of importance class III)
ag= 0.08 g (for Cluj)
0= 2.75
q = 4Sd(T) = 0.540 m/s
2
m = q*t*D = 28233.26 kg (mass of a frame)
= 0.85
12.95 KN
Load Combinations
a b c a b c
Permanent 0.5 KN/m2 1.35 1.35 1 0.68 0.68 0.50
Cvasipermanent 0.35 KN/m2 1.35 1.35 1 0.47 0.47 0.35
Variable snow 1.14 KN/m2 1.5 1.05 0.4 1.71 1.20 0.46
wind pressure 0.626 KN/m2 0.66 0.94 0.00
suction -0.268 KN/m2 -0.28 -0.40 0.00
12.95 KN 0 0 1 0.00 0.00 12.95
Loads a b c
gravitational Q = 309.054 253.517 141.166
lateral w1= 5.911 8.445 0.000
w2= -2.533 -3.619 0.000
W1= 7.093 10.133 0.000
W2= -3.040 -4.343 0.000
Fb,frame= 0.000 0.000 12.948
N T M
a 309.054 57.844 282.89
b 253.517 82.641 404.15
c 141.66 6.475 64.75
0
Load Nominal Value
1.05 1.5
Load factor Factored Load
Max Sectional Efforts
Earthquake
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2. Cross Section Sizing
Cross section shape I
Material type: OL 37 R = 220 N/mm2
Required section modulus:
2076.31 cm3
A - an aproximate area of the CS (A = 10000mm2)
Web dimensions
propose tw= 8 mm
hw= 585.87 mm we use hw= 590 mm
Flanges dimensions
propose tf= 10 mm
Af= 2763.97 mm2
bf= 276.397 mm we use bf= 280 mm
3. Verifications for the Sized Cross Section
A = 10320 mm2
Ix= 63260.1 cm4
3.1 Check for resistance
M T N * e
Case KNm KN KN N/mm2
N/mm2
N/mm2
N/mm2 check
a 282.89 57.84 309.054 166.339 12.255085 161.867 163.253 ok
b 404.15 82.64 253.517 219.421 17.508686 213.032 215.18 ok c 64.75 6.48 141.66 44.9451 1.371822 43.9215 43.9858 ok
W = M/(R-N/A) =
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3.2 Check for overall buckling
-
-
-
-
Ii(cm4) A (cm
2) ri(cm) li(cm) lfi (cm) i
x 63260.1 24.759 1500 60.59 0.875
y 3661.18 5.956 500 83.950.664
Ir= 287360 cm4
= 0.1056 i= 8.87 => 0.997
cx= 0.85
NEx= 5827.29 KN
210.678 N/mm2 => ok
3.3 Check for slenderness
120 83.95 < 120 => ok
3.4 Check for local buckling
Plate slenderness
for flange:
b'/tf15 13.6 < 15 => ok
for web:
= -213.03 N/mm
2
' = 163.90 N/mm2
= 1.769 => k3= 50.873
= 17.51 N/mm2 => = -0.29268
= -0.29268
73.75 151.013 => ok
103.2 1000 0.664
max= max(x,y)
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3.5 Anchorage bolts check
M= 404.15 KNm N = 253.517 KN
use gr 5.6 => Rib= 180 N/mm
2
propose M38 => d = 38 mm
hb1= 381 mm4 bolts with 2d spacing=> 201.811 KN
Rbolt= Nb/Ab Ab= 1121.1724 mm2 d = 37.78 mm
Rb= 20 N/mm2 (C16/20)
H = 914 mm
Bmin= bf+70mm => B = 350.00 mm
Tension in the bolts (4 bolts)
Nb= M*hi/hj2-N/4 =
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ROOF BRACING
1. Loading
a. wind pressure on transverse cladding
pwp= 0.626 KN/m
2 pws= 0.268 KN/m
2
0.938 KN/m2 0.402 KN/m
2
W1p= 70.9343 KN W1
s= 30.4004 KN
W2p= 131.735 KN W2
s= 56.4579 KN
W3p= 81.0677 KN W3
s= 34.7433 KN
b. wind friction
pwf= 0.007 KN/m2
0.0105 KN/m2
W1f= 0.7938 KN
W2f= 0.9072 KN
W3f= 1.4742 KN
11.35 KN
S1= 0
S2= S3= 11.35 KN
Bracing loading for diagonal members design (wind pressure + wind friction)
71.7281 KN
143.99 KN
93.89 KN
Bracing loading for bracing chord design
31.19 KN
68.71 KN
47.57 KN
2. Determination of stresses in the members of the transverse bracing
a. stresses in the bracing chord
110 KN
b. stresses in the diagonal member
D = (H2/2-H1/2)*1/sin = 57.326 KN
= arctg(2*a/(0.5*t)) = 0.729
pwc= 1.5*pw =
pwfc= 1.5*pw =
c. S 2%*Tmax =
pwc= 1.5*pw =
H3= W3s+W3
f+S3=
Nmax= Mmax/h =
H1= W1p+W1
f=
H2= W2p+W2
f+S2=
H3= W3p+W3
f+S3=
H1= W1s+W1
f=
H2= W2s+W2
f+S2=
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3. Design of compression members of the bracing (bracing chord + diagonal)
Used CS: round hollow section
Material type: OL 37
Bracing Chord 88.9 t=3.2mm R = 220 N/mm2
lbx= lby= 3.29 m rx= ry= 3.03 cm A = 1070 mm2
x= lbx/rx= 108.581 => x= 0.546
y= lby/ry= 108.581 => y= 0.488
=> 209 210.663 220
Diagonal Members 76.1 t=4mm
ld= 5.8 m rx= ry= 2.55 cm A = 906 mm2
x= 0.5*lbx/rx= 113.725 => x= 0.653 0.586
y= 0.7*lby/ry= 159.216 => y= 0.303 0.368
209 208.824 220