Saddle Analysis

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

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20018698Text boxReference : 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


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 Rm 1807.50 mm. Rm = (ID + Thk. + CA)/2 Stiffened Vessel Length per 4.15.6 L 7200.00 mm. L = Tan Line Distance from Saddle to Vessel tangent a 1440.00 mm.

Saddle Width b 220.00 mm. Saddle Bearing Angle theta 150.00 degrees

Inside Depth of Head h2 903.00 mm. h2 = Corroded ID /4

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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 1406.14 KG/CM2 Head Allowable Stress used in Calculation 1406.14 KG/CM2 Circumferential Efficiency in Plane of Saddle 1.00 Circumferential Efficiency at Mid-Span 1.00

Saddle Force Q, Operating Case 121529.89 KG From Step - 5

Horizontal Vessel Analysis Results: Actual Allowable Basis of allow. stress -------------------------------------------------------------------

Long. Stress at Top of Midspan 351.35 1406.14 KG/CM2 ( SE ) Long. Stress at Bottom of Midspan 416.61 1406.14 KG/CM2 ( SE ) Long. Stress at Top of Saddles 424.40 1406.14 KG/CM2 ( SE ) Long. Stress at Bottom of Saddles 343.56 1406.14 KG/CM2 ( SE )

Tangential Shear in Shell 122.26 1124.91 KG/CM2 (0.8S) Circ. Compressive Stress in Shell 85.33 1406.14 KG/CM2 (S)

Stiffener Circ. Stress at Shell 1245.17 1757.68 KG/CM2 (1.25 SE) Stiffener Circ. Stress at Tip 1624.91 1757.68 KG/CM2 (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

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Friction load = friction factor mu * saddle load from step 2

i.e. friction load = 0.45 * 81826 = 36821.7


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


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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) 122652.01 KG

Vertical load = 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 K4 = 0.2952 K5 = 0.6733 K6 = 0.0317 K7 = 0.0220 K8 = 0.3021 K9 = 0.2177 K10 = 0.0355 K1* = 0.2792

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

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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 + (R-h2)/(2a*L))/(1+(4h2)/3L)] = -121529*1440.00[1-(1-1440.00/7200.00+(1807.500-903.000)/ (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(R-h2)/(L))/(1+(4h2)/( 3L))-4a/L = 121529*7200/4(1+2(1807-903)/(7200))/(1+(4*903)/ (3*7200))-4*1440/7200 = 30131.7 KG-M

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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*Rmt) = 3.82 * 1807.500 /(2*9.00 ) - 30131.7 /(pi*1807.5*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 * Rm * t) = 3.82 * 1807.500 /(2 * 9.00 ) + 30131.7 /(pi * 1807.5 * 9.00 ) = 416.61 KG/CM2


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 * Rm * t) = 3.82 * 1807.500 /(2 * 9.00 ) - -37324.3 /(pi * 1807.5 * 9.00 ) = 424.40 KG/CM2


Longitudinal Stress at bottom of Shell at Support (4.15.9) [Sigma4]: = P * Rm/(2t) + M1/(pi*Rmt) = 3.82 * 1807.500 /(2*9.00 ) + -37324.3 /(pi*1807.5*9.00 ) = 343.56 KG/CM2

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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 = allowable compressive stress of shell material at design temp Sigma3* & sigma 4* = 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

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------- Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011 For case 1 tau1 is calculated For case 2 & 3 tau2 is calculated For case 4 tau3 is calculated

If we have placed saddle like case 4 such that a = 8 * Rm find Sigma 7 Case b1 if L = Tan to tan line length < 8 * Rm find Sigma 7*

c. If wear plate has been provided as per min. width required as per code clause 4.15.3.1.C Above stress can be calculated as per given formula Sigma 6r Sigma 7r Sigma 7*r where r indicates it is considering reinforcement (wear) plate

d. if provided wear plate thk. tr > 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

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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

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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 Bplen 3200.0000 mm. Baseplate Thickness Bpthk 22.0000 mm. Baseplate Width Bpwid 250.0000 mm. Number of Ribs ( inc. outside ribs ) Nribs 4 Rib Thickness Ribtk 30.0000 mm. Web Thickness Webtk 30.0000 mm. Web Location Webloc Center Calculate MOI of saddle section as per Deniss moss reference method

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Moment of Inertia of Saddle - Lateral Direction

Y A AY Io Shell 4. 4039. 18173. 109039. Wearplate 17. 4000. 68000. 1241329. Web 102. 4590. 465885. 56241080. BasePlate 189. 5500. 1039500. 196686640. Totals 312. 18130. 1591558. 254278064.

Value C1 = Sumof(Ay)/Sumof(A) = 88. mm. Value I = Sumof(Io) - C1*Sumof(Ay) = 114550568. mm**4 Value As = Sumof(A) - Ashell = 14091. sq.mm.

Find factor K1 from following table

K1 = (1+Cos(beta)-.5*Sin(beta) )/(pi-beta+Sin(beta)*Cos(beta)) = 0.2594

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Fh = K1 * Q = 0.2594 * 121529.891 = 31521.4961 KG Where Q is taken from step - 5

Tension Stress, St = ( Fh/As ) = 223.7611 KG/CM2 Allowed Stress, Sa = 0.6 * Yield Str = 1529.5380 KG/CM2

Where As = Saddle area is calualted in MOI step calculation

d = B - R*Sin(theta) / theta = 672.5430 mm. Bending Moment, M = Fh * d = 21195.4492 KG-M

Bending Stress, Sb = ( M * C1 / I ) = 1625.0912 KG/CM2 Allowed Stress, Sa = 2/3 * Yield Str = 1699.4867 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 )) = ( 3 * (121529 + 1122 ) * 250.00 / ( 4 * 3200.000 * 1699.487 )) = 20.566 mm.

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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 Ay Io Rib 110.0 5769.4 634589.9 0.0 27463564.0 Web 110.0 15874.0 1746029.9 0.0 2380942.0 Values 110.0 21643.3 2380620.0 0.0 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

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(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*Cc))*Fy/(5/3+3*(Klr)/(8*Cc)-(Klr)/(8*Cc) Sca = ( 1-( 41.38 )/(2 * 125.65 )) * 2549 / ( 5/3+3*(41.38 )/(8* 125.65 )-( 41.38)/(8*125.65) Sca = 1350.19 KG/CM2

Allowable stress is calculated from following formula of AISC manual

AISC Unity Check on Outside Ribs ( must be

PV Elite 2011 Licensee: L&T - Chiyoda Limited FileName : 7030-TK-3100-------------------------------------- Horizontal Vessel Analysis (Ope.) : Step: 9 4:00p Sep 7,2011 Rib 112.3 5838.4 655607.4 0.0 28324862.0 Web 112.3 31748.0 3565075.8 0.0 2380942.0 Values 112.3 37586.3 4220683.5 0.0 30705804.0

KL/R < Cc ( 8.8600 < 125.6488 ) per AISC E2-1 Sca = (1-(Klr)/(2*Cc))*Fy/(5/3+3*(Klr)/(8*Cc)-(Klr)/(8*Cc) Sca = ( 1-( 8.86 )/(2 * 125.65 )) * 2549 / ( 5/3+3*(8.86 )/(8* 125.65 )-( 8.86)/(8*125.65) Sca = 1501.95 KG/CM2

AISC Unity Check on Inside Ribs ( must be QL --> 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]

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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

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Saddle Analysis

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