verificari metal grinda cu zabrele

8/12/2019 verificari metal grinda cu zabrele

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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


24.963 * xr -2.774 * xr2

-35.498 = -26.375

xr=209

mmWe= Ix3/ymax= 119.88 cm3


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

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