Asme Pressure Vessel Support

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011

Saddle Analysis Learning

Reference : 1. Deniss R Moss 2. ASME Sec.VIII Div.2 Legend

: Pink & red colour block are added reference text Other text are pv-elite output

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011 ASME Horizontal Vessel Analysis: Stresses for the Left Saddle (per ASME Sec. VIII Div. 2 based on the Zick method.) Horizontal Vessel Stress Calculations : Operating Case Note: Wear Pad Width (250.00) is less than 1.56*sqrt(rm*t) and less than 2a. The wear plate will be ignored.

Minimum Wear Plate Width to be considered in analysis [b1]: = min( b + 1.56*sqrt( Rm * t ), 2a ) = min( 220.000 + 1.56*sqrt( 1807.5001 * 9.0000 ), 2 * 1440.000 ) = 418.9688 mm.

Input and Calculated Values: Vessel Mean Radius Stiffened Vessel Length per 4.15.6 Distance from Saddle to Vessel tangent

Rm L a

1807.50 7200.00 1440.00

mm. Rm = (ID + Thk. + CA)/2 mm. L = Tan Line mm.

Saddle Width Saddle Bearing Angle

b theta

220.00 150.00

mm. degrees

Inside Depth of Head

h2

903.00

mm. h2 = Corroded ID /4

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011 Shell Allowable Stress used in Calculation Head Allowable Stress used in Calculation Circumferential Efficiency in Plane of Saddle Circumferential Efficiency at Mid-Span Saddle Force Q, Operating Case

1406.14 1406.14 1.00 1.00 121529.89

KG/CM2 KG/CM2

KG

From Step - 5

Horizontal Vessel Analysis Results: Actual Allowable ------------------------------------------------------------------Long. Stress at Top of Midspan 351.35 1406.14 KG/CM2 Long. Stress at Bottom of Midspan 416.61 1406.14 KG/CM2 Long. Stress at Top of Saddles 424.40 1406.14 KG/CM2 Long. Stress at Bottom of Saddles 343.56 1406.14 KG/CM2 Tangential Shear in Shell Circ. Compressive Stress in Shell Stiffener Circ. Stress at Shell Stiffener Circ. Stress at Tip

Basis of allow. stress ( ( ( (

SE SE SE SE

) ) ) )

122.26 85.33

1124.91 1406.14

KG/CM2 KG/CM2

(0.8S) (S)

1245.17 1624.91

1757.68 1757.68

KG/CM2 KG/CM2

(1.25 SE) (1.25 SE)

Intermediate Results: Saddle Reaction Q due to Wind or Seismic Step - 1 Saddle Reaction Force due to Wind Ft [Fwt]: = Ftr * ( Ft/Num of Saddles + Z Force Load ) * B / E = 3.00 * ( 4186.2 /2 + 0 ) * 2026.0000 / 3200.0000 = 3975.6 KG Fwt = Sum of wind load of all elements from wind load cal. Divided by 2 because it is taken by 2 saddles E is base plate length will play role in transverse load Ls length between saddle centrline will play role in long. load Ref. Deniss Moss page no.130

Step - 2 Saddle Reaction Force due to Wind Fl or Friction [Fwl]: = Max( Fl, Friction Load, Sum of X Forces) * B / Ls = Max( 3201.93 , 36822.13 , 0 ) * 2026.0000 / 4320.0000 = 17268.9 KG Fwl = calculated but not shown in detail in pv-elite calculation It is same as trasverse load only wind area is changing which is acting on single saddle See Ls length between saddle will play role in long. load

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011

Friction load = friction factor mu * saddle load from step – 2 i.e. friction load

= 0.45 * 81826 = 36821.7

Ref. Deniss Moss page no.181

Step – 3 Saddle Reaction Force due to Earthquake Fl or Friction [Fsl]: = Max( Fl, Friction Force, Sum of X Forces ) * B / Ls = Max( 41806.33 , 36822.13 , 0 ) * 2026.0000 / 4320.0000 = 19606.4 KG Fst is same as Fsl in case of earth quake because it does not depend up on direction as in case of Wind loading i.e. Fl = Ft = 41806

If we have specified any force in X or Z direction like bundle pulling force than it will come in sum of X force or Z force load Accordingly transverse & long. Load will change Ref. Deniss Moss page no.181

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011

Step - 4 Saddle Reaction Force due to Earthquake Ft [Fst]: = Ftr * ( Ft/Num of Saddles + Z Force Load ) * B / E = 3.00 * ( 41806 /2 + 0 ) * 2026.0000 / 3200.0000 = 39702.9 KG Fst is same as Fsl in case of earth quake because it does not depends up on direction as in case of Wind loading Step - 5 Load Combination Results for Q + Wind or Seismic [Q]: = Saddle Load + Max( Fwl, Fwt, Fsl, Fst ) = 81826 + Max( 17268 , 3975 , 19606 , 39702 ) = 121529.9 KG Saddle load 81826 is calculated by finding reaction at saddle as per SFBM calculation.

Step - 6 Summary of Loads at the base of this Saddle: Vertical Load (including saddle weight) Vertical load

122652.01

KG

= Q + Saddle weights from weight summary / 2 = 121529.9 + (2244.2/2)

Transverse Shear Load Saddle

20903.16

KG

Transverse load higher of wind or seismic from step – 1 or step – 4 divide by 2 Longitudinal Shear Load Saddle

41806.33

KG

Long. load higher of wind or seismic from step – 2 or step – 3

Formulas and Substitutions for Horizontal Vessel Analysis: Step -7 Note: Wear Plate is Welded to the Shell, k = 0.1 The Computed K values from Table 4.15.1: K1 = 0.1607 K2 = 0.7988 K3 = 0.4851 K5 = 0.6733 K6 = 0.0317 K7 = 0.0220 K9 = 0.2177 K10 = 0.0355 K1* = 0.2792

K4 K8

= 0.2952 = 0.3021

Please refer table 4.15.1 in ASME Sec.VIII Div 2 page no.531 Based on angles theta,alpha,bita,delta,rho various factor are calculated by pv-elite

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011 This factors will be utilised in calculation of moments at various points Which moments will be used for calculating stress at diff. points.

Note: Dimension a is greater than or equal to Rm / 2. Here a = 0.2* L = 1440 is greater than Rm/2 = 1807.5 / 2 =903.75 Step -7 : Calculating moment M1 & M2

Moment per Equation 4.15.3 [M1]: = -Q*a [1 - (1- a/L + (R²-h2²)/(2a*L))/(1+(4h2)/3L)] = -121529*1440.00[1-(1-1440.00/7200.00+(1807.500²-903.000²)/ (2*1440.00*7200.00))/(1+(4*903.00)/(3*7200.00))] = -37324.3 KG-M Moment per Equation 4.15.4 [M2]: = Q*L/4(1+2(R²-h2²)/(L²))/(1+(4h2)/( 3L))-4a/L = 121529*7200/4(1+2(1807²-903²)/(7200²))/(1+(4*903)/ (3*7200))-4*1440/7200 = 30131.7 KG-M

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011 Step -7 : Calculating Stress sigma 1 & sigma 2 at mid span due to moment M2 Longitudinal stress at midspan sigma 1 is in top which is compressive in nature & sigma 2 is in bottom which is tensile Longitudinal Stress at Top of Shell (4.15.6) [Sigma1]: = P * Rm/(2t) - M2/(pi*Rm²t) = 3.82 * 1807.500 /(2*9.00 ) - 30131.7 /(pi*1807.5²*9.00 ) = 351.35 KG/CM2 Compare with Allowable stress = SE = 1406.14 Here Longitudinal stress is combination of membrane stress + bending stress PR/2t = PD/4t = is longitudinal membrane stress acting on circumferntial joints PD/4t = Is circumferntial ( HOOP) membrane stress acting on long. Joint.Thk of shell is governing due to Hoop stress M/Z = Is bending stress where Z is section modulas of cylinder with thin wall

Longitudinal Stress at Bottom of Shell (4.15.7) [Sigma2]: = P * Rm/(2t) + M2/(pi * Rm² * t) = 3.82 * 1807.500 /(2 * 9.00 ) + 30131.7 /(pi * 1807.5² * 9.00 ) = 416.61 KG/CM2 Compare with Allowable stress = SE = 1406.14 Step - 8 : Calculating Stress sigma 3 & sigma 4 at saddle support due to moment M1 Longitudinal stress at midspan sigma 3 is in top which is tensile & sigma 4 is in bottom compressive in nature The values of these stresses depend on the rigidity of the shell at the saddle support. The cylindrical shell may be considered as suitably stiffened if it incorporates stiffening rings at, or on both sides of the saddle support, or if the support is sufficiently close defined as a ≤ 0.5R , to a torispherical or elliptical head (a hemispherical head is not considered a stiffening element), a flat cover, or tubesheet. Formulas for sigma 3 & sigma 4 are different for stiffened shell & unstiffned shell(Sigma3* & sigma 4*)Pv-elite will change formula as per criteria given in Div.2 Longitudinal Stress at Top of Shell at Support (4.15.8) [Sigma3]: = P * Rm/(2t) - M1/(pi * Rm² * t) = 3.82 * 1807.500 /(2 * 9.00 ) - -37324.3 /(pi * 1807.5² * 9.00 ) = 424.40 KG/CM2 Compare with Allowable stress = SE = 1406.14 Longitudinal Stress at bottom of Shell at Support (4.15.9) [Sigma4]: = P * Rm/(2t) + M1/(pi*Rm²t) = 3.82 * 1807.500 /(2*9.00 ) + -37324.3 /(pi*1807.5²*9.00 ) = 343.56 KG/CM2

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011 Compare with Allowable stress = SE = 1406.14

Where Sc Sigma3* & sigma 4*

= allowable compressive stress of shell material at design temp = longitudinal stress at saddle support if not considered shell as stiffened

Step - 9 : Calculating Shear Stress sigma due to shear force T So far we have calculated longitudinal bending stress Now its turn for shear stress There are four different cases in which shell shear stress is calculated Case – 1 Shell having single stiffner ring in plane of saddle Case – 2 Shell having two stiffner rings on both side of saddle support Case – 3 Shell without stiffening ring(s) & not stiffened by a formed head, flat cover, or tubesheet, (a > 0.5 Rm ) Case – 4 shell without stiffening ring(s) and stiffened by a torispherical or elliptical head, flat cover, or tubesheet, ( a 2 * t than compressive membrane plus bending stress at the ends of the reinforcing plate is calculated as shown in fig.b point G1,H1 fig. b fig.a

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011 Case – 2 Stiffening ring in plane of saddle a.find Sigma 6* = maximum compressive circ. stress at the base of saddle support Circ. Stress in shell w/ring in Plane of Saddle (4.15.32) [sigma6*]: = -K5 * Q * k/A = -0.673 * 121529 * 0.1 /9591.31 = -85.33 KG/CM2 Note: Single Ring in Plane of Saddle Outside the Shell. b.Claculte circumferential compressive membrane plus bending stress at Points G and H as shown in fig.a above case b -1 If internal stiffening ring is provided calculate sigma 8 = stress in shell sigma 9 = stress in ring case b - 2

If external stiffening ring is provided calculate sigma 8* = stress in shell sigma 9* = stress in ring

Circ. + Bending Stress in shell w/ring in Plane of Saddle (4.15.35) [sigma8*] = -K8 * Q/A + K6 * Q * Rm * c1/I = -0.3021*121529/9591.31+0.0317*121529*1807.50*104.94/44857792 = 1245.17 KG/CM2 Circ. + Bending Stress in ring w/ring in Plane of Saddle (4.15.36) [sigma9*]: = -K8 * Q/A - K6 * Q * Rm * c2/I = -0.3021*121529/9591.31-0.0317*121529*1807.50*80.06/44857788 = -1624.91 KG/CM2 Case – 3 cylindrical shell with stiffening rings on both sides of the saddle support a.find Sigma 6 = maximum compressive circ. stress at the base of saddle support b.Claculte circumferential compressive membrane plus bending stress at Points I and J as shown in fig.C below case b -1 If internal stiffening ring is provided calculate sigma 10 = stress in shell sigma 11 = stress in ring case b - 2

If external stiffening ring is provided calculate sigma 10* = stress in shell sigma 11* = stress in ring

Fig – C

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011

Step – 10 Calculate thermal expansion Free Un-Restrained Thermal Expansion between the Saddles [Exp]: = Alpha * Ls * ( Design Temperature - Ambient Temperature ) = 0.126E-04 * 4320.000 * ( 170.0 - 21.1 ) = 8.076 mm. Alpha shall be used from Part II D – alpha C Linear coefficient of thermal expansiom

Step-11 Check saddle in lateral loading in tension & bending Results for Vessel Ribs, Web and Base: Baseplate Length Baseplate Thickness Baseplate Width Number of Ribs ( inc. outside ribs ) Rib Thickness Web Thickness Web Location

Bplen Bpthk Bpwid Nribs Ribtk Webtk Webloc

Calculate MOI of saddle section as per Deniss moss reference method

3200.0000 22.0000 250.0000 4 30.0000 30.0000 Center

mm. mm. mm. mm. mm.

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011

Moment of Inertia of Saddle - Lateral Direction Shell Wearplate Web BasePlate Totals Value Value Value

Y 4. 17. 102. 189. 312.

A 4039. 4000. 4590. 5500. 18130.

C1 = Sumof(Ay)/Sumof(A) I = Sumof(Io) - C1*Sumof(Ay) As = Sumof(A) - Ashell

AY 18173. 68000. 465885. 1039500. 1591558. = = =

Io 109039. 1241329. 56241080. 196686640. 254278064. 88. 114550568. 14091.

mm. mm**4 sq.mm.

Find factor K1 from following table

K1 = (1+Cos(beta)-.5*Sin(beta)² )/(pi-beta+Sin(beta)*Cos(beta)) =

0.2594

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011 Fh = K1 * Q = 0.2594 * 121529.891 = 31521.4961 KG Tension Stress, St = ( Fh/As ) = Allowed Stress, Sa = 0.6 * Yield Str =

Where Q is taken from step - 5

223.7611 1529.5380

KG/CM2 KG/CM2

Where As = Saddle area is calualted in MOI step calculation d = B - R*Sin(theta) / theta Bending Moment, M = Fh * d

= =

672.5430 21195.4492

Bending Stress, Sb = ( M * C1 / I ) = Allowed Stress, Sa = 2/3 * Yield Str =

1625.0912 1699.4867

mm. KG-M

KG/CM2 KG/CM2

Bending stress = M/Z where Z = I / Y here Y is C1 calculated in MOI step Actual bending stress will be compare with allowable bending stress = 0.66 * Yield stress

Step -12 calculate Base plate thk Minimum Thickness of Baseplate per Moss : = ( 3 * ( Q + Saddle_Wt ) * BasePlateWidth / ( 4 * BasePlateLength * AllStress ))½ = ( 3 * (121529 + 1122 ) * 250.00 / ( 4 * 3200.000 * 1699.487 ))½ = 20.566 mm.

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011

Calculation of Axial Load, Intermediate Values and Compressive Stress Effective Baseplate Length [e]: = ( Bplen - Clearance ) / ( Nribs - 1) = ( 3200.0000 - 25.4 ) / ( 4 - 1 ) = 1058.2001 mm. Baseplate Pressure Area [Ap]: = e * Bpwid / 2 = 1058.2001 * 250.0000 / 2 = 0.1E+06 sq.mm. Axial Load [P]: = Ap * Bp = 132283.2 * 0.15 = 20094.2 KG Area of the Rib and Web [Ar]: = ( Bpwid - Clearance - Webtk ) * Ribtk + e/2 * Webtk = ( 250.000 - 25.4 - 30.000 ) * 30.000 + 1058.2001 /2 * 30.000 = 21712.348 sq.mm. Combined area of web & ribs will take axial load P Compressive Stress [Sc]: = P/Ar = 20094.2 / 21712.3477 = 92.5720 KG/CM2 Check of Outside Ribs: Inertia of Saddle, Outer Ribs - Longitudinal Direction Y A AY Rib 110.0 5769.4 634589.9 Web 110.0 15874.0 1746029.9 Values 110.0 21643.3 2380620.0

Ay² 0.0 0.0 0.0

Io 27463564.0 2380942.0 29844506.0

Bending Moment [Rm]: = Fl /( 2 * Bplen ) * e * rl / 2 = 41806.3 /( 2 * 3200.00 ) * 1058.200 * 1534.02 / 2 = 5300.864 KG-M Formula is like this Fl

* Effective base plate length * length of outer rib

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011 (2 * Base plate length ) Bending Momennt = 2 Fl = Logidudional shear load from Step – 6

We can rewrite this equation (l/k) = Sqrt ( 2*Pi^2*E*A / W) Cc

= Sqrt ( 2*Pi^2*E/Fy)

Where C = 2 for one end fixed & one end hinged Fy = W/A i.e. load / area KL/R how it is calculated is not clear so far ? KL/R < Cc ( 41.3750 < 125.6488 ) per AISC E2-1 Sca = (1-(Klr)²/(2*Cc²))*Fy/(5/3+3*(Klr)/(8*Cc)-(Klr³)/(8*Cc³) Sca = ( 1-( 41.38 )²/(2 * 125.65² )) * 2549 / ( 5/3+3*(41.38 )/(8* 125.65 )-( 41.38³)/(8*125.65³) Sca = 1350.19 KG/CM2 Allowable stress is calculated from following formula of AISC manual

AISC Unity Check on Outside Ribs ( must be No Uplift in Longitudinal direction) Bolt Area due to Shear Load [Bltarears]: = Fl / (Stba * Nbolts) = 41806.33 / (693.00 * 8.00 ) = 754.2833 sq.mm. Bolt Area due to Transverse Load Moment on Baseplate Due to Transverse Load [Rmom]: = B * Ft + Sum of X Moments = 2026.00 * 20903.16 + 0.00 = 42341.60 KG-M Eccentricity (e): = Rmom / QO = 42341.60 / 82949.07 = 510.55 mm. < Bplen/6 --> No Uplift in Transverse direction Bolt Area due to Transverse Load [Bltareart]: = 0 (No Uplift) Required of a Single Bolt [Bltarear]

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011 = max[Bltarearl, Bltarears, Bltareart] = max[0.0000 , 754.2833 , 0.0000 ] = 754.2833 sq.mm.

Same as left saddle Pv-elite will check right saddle Than for hydrotest case will check both saddle for hydro test condition