Checks are performed according to API 560 – Specification for steel chimneys
According to the values of wind load calculated on paragraph 0 following are calculated the value of loads and moments at the base of each section of the stack
Portion Thk.
I 12 1574 10000 46,2 3,48 34,83 174,16 108,80 1660,07 II 10 1570 10000 38,5 3,63 36,33 181,63 73,97 746,24
III 8 1566 10000 30,7 3,76 37,64 188,20 37,64 188,20
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According to what written in the previous paragraphs, the stack here described has the following characteristics:
Portion Thickness Corroded Thickness
Conical / cilindrical Top External Diameter
Portion Length
Lateral Surface
Casing Weight
mm mm mm mm m² Kg
I 12 10 1574 10000 49,4 4620,2
II 10 8 1570 10000 49,3 3845,2
III 8 6 1566 10000 49,2 3072,3
Total 30000 147,9 11537,7
Lining thickness = 50 mm Specific weight = 1400 daN/m3 Refractory weight calculation
Portion Refractory Density Portion lenght with refractory Refractory Thickness Refractory Weight
Kg/m³ mm mm Kg
I 1400,0 10000,0 50,0 3406,9 II 1400,0 10000,0 50,0 3406,9 III 1400,0 10000,0 50,0 3406,9
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Max. Height of stack: 30 m
The values above listed do not consider the effect of the corrosion on the stack walls.
The corrosion on the walls it will be considered later.
Material considered for Stack: JIS SS400 Overall Stack Height considered = 30 m
Young modulus E = 200000 N/mm² Yield stress for the material fy = 235 N/mm² Lining Thickness = 50 mm
Lining density = 1400 Kg/m³
Overall casing lateral surface 147,9 m²
Overall Casing weight 115,38 KN
Overall lining weight 102,21 KN
Overall extra weight for Equipments appended: 0 KN Overall extra steelwork, stiffening and flanges weight 53,23 KN Total platform surface considered 0 m² Overall structural platform weight 0 KN Live load considered on each platform surface 2 KN/m²
Overall non permanent live load 0 KN
Overall ladder length 0 m
Overall ladder weight 0 KN
Overall stack permanent weight 270,82 KN
Overall weight with 33% of live load 270,82 KN Maximum resulting shear at stack base 108,8 KN Maximum resulting moment at stack base 1660,08 KMn
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ANCHOR BOLTS AND GROUND RING
The design procedure described in this paragraph is written according to chapter 10 of the book :
“Process Equipment Design”
Written by: L.E. Brownell and E.H. Young Publisher: Wiley Publishing
Bearing plate thickness assumed t4 = 30 mm Compression plate thickness assumed t5 = 25 mm Gusset plate thickness assumed t6 = 12 mm
Base plate outer diameter De = 2074 mm
Base plate bolt circle diameter Db = 2060 mm
Base plate inner diameter Di = 1574 mm
Minimum vertical load on base plate Nmin = 270,82 KN Maximum vertical load on base plate Nmin = 270,82 KN Maximum shear load at stack base Vmax = 108,8 KN Maximum resulting moment at stack base Mmax = 1660,08 KNm
Number of bolts on base plate nb = 36 Nominal diameter of anchor bolts db = 30 mm Resistance section of anchor bolts Ares = 561 mm² Safety coefficient on yield stress n= 1,5 Admissible stress for parts resistance check σadm = 156,67 N/mm² Max load on anchor bolts is given by:
Nb =(-Nmin/nb)+(4Mmax/Nb*Db) = 82,02 KN
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Bearing plate design procedure:
Stress on net section of anchor bolt:
σb = Nb/Ab = 14,62 KN/cm2 VERIFIED
Maximum compression stress
σc = Nmax/(3,14*Db*c) + 4*Mmax/(3,14*Db2*c) = 0,22 KN/cm2
where:
c: Ring outer radius - medium shell radius = 1037 - 781 = 256 mm Base plate is defined as follows:
distance between stiffening bmin = 150 mm distance between stiffening bmax = 300 mm external width of base plate l = 250 mm
ratio (l/ b)max = 0,834 mm
thickness of bearing plate tb = (6*Mmax/σadm)0,5 = 29,6 mm Where Mmax is calculated with the formulas:
Mmax = c1*σb*b2 = 14,53 KNcm with c1 = 0,0765 by interpolation Mmax = c2*σb*b2 = 22,82 KNcm with c2 = -0,173 by interpolation
the value of “tb” has to be checked where the bolts are located In order to do this the maximum bolt load P is given by the formula:
P = sb*Ab = 87,9 KN
Where σb is the maximum stress admissible on bolts
The Maximum bending moment supported by bolts is given by:
Mmax = P*b/8 = 329,59 KN/cm
The bearing plate thickness calculated with the considerations above is:
tb=(6*Mmax/(lt-bhd)*σadm)0,5 = 24,2 mm THICKNESS t4 ASSUMED VERIFIED Where:
lt : overall bearing plate width = 250 mm bhd :bolt hole diameter in bearing plate = 33 mm
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Compression plate design procedure:
The thickness of the compression plate is calculated as follow:
Mymax = (P/4*π)*[(1,3*ln(2*l/π*e)+(1-g1)] = 15,95 KNcm Where:
Mmax: Maximum bending moment acting on compression plate P: Maximum bolt load calculated above
lc : Radial distance from outside of skirt to outer edge of compression plate e: One-half distance across flats of bolting nuts = 23 mm
g1: Constant = 0,472 (by interpolation) The thickness of the compression plate is:
tc =(6*Mymax/sigma_amm)0,5 = 24,7 mm THICKNESS t5 ASSUMED VERIFIED
Vertical gussets plate design procedure:
The vertical gusset plated equally spaced may be considered to react as a vertical column.
From empirical calculations it comes that the minimum thickness required for the gusset plates is given by the equation:
18000*l*tg³-P*tg²-h²*P/1500=0
Where:
l: is the width of the gussets (inches) h: is the height of the gussets (inches) tg: is the thickness of the gussets (inches)
P: is the Maximum value of bolt load calculated (lbs)
According to the values above listed the minimum thickness required for the gussets is:
tg = 6,25 mm THICKNESS t6 ASSUMED VERIFIED
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INTERMEDIATE RING FLANGES STRESS CHECK Flange Stress Check
The procedure considered for the stress check of the flanges is the following:
The maximum pressure on flange due to vertical load is given by:
()
The uniform load on middle flange diameter due to Pmas-V is given by:
⎟⎟
Assuming that the neutral axis for maximum moment passes from the section axis and assuming that the highest pressure value is located on bolt circle diameter, the maximum pressure on flange due to wind is given by:
()
Assuming that this pressure is uniformly distributed on compressed side of the flange it can be calculated the uniform load on middle flange diameter due to this pressure:
⎟⎟
P: is the maximum vertical load calculated at the base of the section considered Mmax is the maximum moment calculated at the base of the section considered Dpe & Dpi are the Outside and the Inside flange diameters
Dcb is the Bolt Circle diameter
the worst load combination is given in the position where the two loads add one to the other:
With the geometry assumed it follows that the distance between the stiffness on bolt circle diameter is given by:
s
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Now each flange can be assumed as a beam simply supported in the position where it joins to the stiffness, so the maximum moment calculated between the two supports is given by:
The stress check of the flange is verified if
f
In order to check the maximum stress of the stiffness placed on each flange they are calculated the maximum shear load and the maximum moment acting at the base of each stiffness.
In order to do this, the flange is considered as a beam uniformly loaded and supported by each stiffness.
From this consideration the maximum reaction and the maximum moment calculated under the stiffness are given by the equations:
max
From these values it is easy to calculate the maximum shear and bending stresses:
s The stress of the stiffness is verified if
f
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Following are listed all the geometric data and the resulting value calculated according to the procedure above described.
Flange at base of
Section Bolt Circle diameter Nr. of stiffness on interm. flange Stiffness Height Stiffness Thk
Dcb Ns hs ts section base due
to wind or
II 169,84 746,24 0,20 31,26 0,52 82,66 113,92 III 81,02 188,20 0,09 14,95 0,13 20,89 35,84
Section distance between the stiffness Max Bending moment on flange Max stress on flange Check
bmax Mf sMf
mm KNm N/mm2
II 189,46 0,51 17,99 OK
III 203,06 0,18 6,07 OK
Section Max reaction under stiffness
Max moment under stiffness
Max bending stress on Stiffness
Max shear stress on Stiffness
Max ideal stress
on Stiffness Check
Rmax-s Mmax-s smax-s tmax-s sid-s
KN KNm N/mm2 N/mm2 N/mm2
II 26,98 0,29 3,45 13,49 23,62 OK III 9,10 0,10 1,25 4,55 7,98 OK
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Flange bolts stress check
The flange bolts considered in the following procedures are in class 8.8 with the following values for admissible stress:
σadm-b = 373 N/mm2 τadm-b = 264 N/mm2
The procedure considered for the stress check of the flange bolts is the following:
The maximum axial load on each bolt is given by the difference of the axial load due to bending moment at the base of each section and the minimum vertical load calculated in the same section.
The maximum axial load on worst stressed bolt is given by:
b
From this follows that the highest axial stress on bolts is given by:
res
The maximum shear stress on each bolt is given by:
b
Nmin is the minimum vertical load calculated at the base of the section considered Vmax is the maximum shear load calculated at the base of the section considered Mmax is the maximum bending moment calculated at the base of the section considered
Dcb is the bolt circle diameter
nb is the total number of bolts considered on the flange Ares is the resistance section of the bolts considered The bolt are verified if
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The data and the results of the procedure applied to each intermediate flange are following listed:
Section Stack Ext. Dia. section base due
to wind or
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