low tank stiffness

FE/Pipe Version 4.111 September 25, 2003 www.paulin.com

Copyright 2003, Paulin Research Group 1.5.1

Generating Low Tank Stiffnesses for a Pipe Stress Analysis

Generating a reasonable low tank model for a piping analysis is problematic for several reasons:

1) The exact stiffness of the shell connection to the baseplate is not known.

2) Rotations are strongly tied to translations.

3) Initial translations and rotations occur when the tank is filled.

The modeling approach described below addresses each of these issues. The resulting beam

model is intended to be used in a CAESAR type piping stress analysis and should give the user

reasonable values for loads and stresses in the low tank connection, as well as predicting the

loads due to movement of the nozzle when the tank is filled. The procedure will be illustrated

with an example. The model geometry is shown below:

The lower course is broken down into two courses in the FE/Pipe model so that the mesh around

the nozzle is uniform. The 96 inch, 0.679 inch, lower course is entered as one 66 course and one

30 course. If only a single course had been entered, the mesh would appear as shown below:

Slightly Distorted Elements

The element shapes are somewhat distorted. Breaking the lower course down into two unequal

length courses of the same thickness as shown above solves this problem.



A single FE/Pipe run can be used to compute two stiffness coefficients. Three coefficients are

sought for each nozzle: axial (transverse), inplane (longitudinal, rotational) and outplane

(circumferential, rotational), therefore at least two runs will be needed to get a full set of the

desired stiffnesses. Additionally, the initial rotation and displacement of the nozzle when the

tank is filled must be found to be used as a boundary condition. The following runs will be

made:

Run1: Axial Load and Inplane Moment. (Base rigid)

Run2: Outplane Moment (Base Rigid)

Run3: Axial Load and Inplane Moment (Base Simply Supported)

Run4: Outplane Moment (Base Simply Supported.)

Run5: Tank full to get initial displacements and rotations (Base Rigid)

Run6: Tank full (Base simply supported.)

The displacements due to the Run1 axial load are shown below:

A 1E6 lb. axial load was applied to the nozzle. A rotation and a translation is observed. (Not just

a translation.) It is this combined effect that should be included in the local CAESAR model of

the nozzle stiffness. (Coupled rotations can produce high bending stresses in close coupled,

tight, piping systems.) There are several ways to simulate the interaction between the

translational and rotational stiffness coefficients. The method shown below is one of the

simplest.

To collect exact data from the FE/Pipe plot, contour mapping should be enabled. This is done on

the contour controls screen shown below.

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onlineText BoxBoth axial load and inplane moment in the same run?)



Next a contour plot of the displacements should be generated. For the operating load case 2, the

Z displacement plot is shown below:

Of interest is the deflection in the Z direction at the center of the nozzle. This is the point that

will be described by a beam model of the low tank nozzle. The Z movement on the nozzle end

due to the axial load is shown on the following plot.

The point at the centerline is moving 3.33 inches in the Z direction due to the load. The rotation

about the X axis can also be read from a similar plot of the RX rotations.

The rotation about the X axis is essentially constant as would be expected since the endcap is

numerically rigid. The displacements and rotations due to a circumferential moment are shown

below: The Z displacements are labeled on the plot.



Rotation magnitudes are shown below:

The displacements due to an operating hydrostatic head is shown below:

Fixed Base Hydrostatic Load Simply Supported Base Hydrostatic Loads

The collected data from each of the runs described above is given below:

Run Load Fixity DZ RX RY Run1 Z Load Base Fixed 3.385 in. 0.316 rad. 0.0

MX Load 0.3094 in. 0.0432 rad.

Run2 MY Load Base Fixed 0.0 0.0 0.0223 rad.

Run3 Z Load Base Simply Supported 11.16 in. 0.7082 rad. 0.0

MX Load 0.6795 in. 0.0632 rad. 0.0

Run4 MY Load Base Simply Supported 0.0 0.0 0.0371 rad.

Run5 Hydrostatic Base Fixed 0.0878 in. 0.0101 rad. 0.0

Run6 Hydrostatic Base Simply Supported 0.2203 in. 0.0154 rad. 0.0

Stiffnesses will be generated for the CAESAR type beam model shown below:

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onlineText BoxIs it in the same Run1 with Z-Load?



The distance from 5 to 10 is the length of the nozzle from the tank wall penetration to the face-

of-flange. The distance from 10 to 15 is the centerline height of the nozzle above the baseplate.

The elements from 5-to-10 and from 10-to-15 are rigid. Three translational and three rotational

stiffnesses are inserted between the nodes 15 and 20. Each of the three translational stiffnesses

are rigid.

The stiffnesses should be based on the rigid base model, and the movement should be based on

the simply supported model to be conservative. Values will be estimated based on both to show

the possible variation in the values selected. (The actual interaction between the tank base and

the shell is unknown, but will be somewhere in between the completely fixed case, and the

simply supported case.)

Two stiffnesses will be found for the above rigid element model. One will be the RX stiffness

between nodes 15 and 20. This stiffness will be used to simulate both the axial and rotational

coupling of the nozzle connection at 5. A stiffness in the RY direction between nodes 15 and 20

will be used to simulate the circumferential flexibility of the nozzle connection. The RZ or

torsional rigidity of the local nozzle connection will be assumed rigid. The RX stiffness is the

most interesting, because it will be used to simulate both the axial and rotational coupling of the

nozzle. The RX stiffness can be calculated from each of the Z axial and MX bending load cases:

Run 1 Z Load K=M/O= (1E6)(13.5)/(0.316) * (pi/180/12) = 62.135 ft.lb./deg.

Run 1 MX Load K=M/O= (1E6)/(0.0432) * (pi/180/12) = 33,667 ft.lb./deg.

Run 3 Z Load K=M/O= (1E6)(13.5)/(0.7082) * (pi/180/12) = 27,725 ft.lb./deg.

Run 3 MX Load K=M/O= (1E6)/(0.0632) * (pi/180/12) = 23,013 ft.lb./deg.

The most conservative value for the RX stiffness is 62,135 ft.lb./deg. The RY stiffness can be

estimated in a similar manner.

Run 2 MY Load K=M/O = (1E6)/(0.0223) * (pi/180/12) = 65,221 ft.lb./deg.

Run 4 MY Load K=M/O = (1E6)/(0.0371) * (pi/180/12) = 39,203 ft.lb./deg.

An MY stiffness of 65,211 ft.lb./deg. will be used.



There is some justification for using these higher values, in that stress stiffening, not included in

a linear stiffness calculation will tend to stiffen the shell. If the solution proves to be sensitive to

the high-end stiffness values computed above, i.e. the nozzle or piping is O.K. if the low stiffness

is used and overstressed if the high stiffness is used, then further investigation is certainly

warranted, but this tends not to be the case. The biggest difference in practice tends to occur

because the user has selected a flexible vs. numerically rigid nozzle connection.

The largest rotation due to filling comes from the Run #6 hydrostatic result. The translational

displacement is s/R = 0.2203/13.5 = 0.0163 radians. This compares favorably to 0.0154 radians

in the same run. This will be the initial movement for an operating fluid level.

The BEAM-type piping model will be:

NODE 15 CNODE 20 TYPE = X STIF = RIGID

NODE 15 CNODE 20 TYPE = Y STIF = RIGID

NODE 15 CNODE 20 TYPE = Z STIF = RIGID

NODE 15 CNODE 20 TYPE = RX STIF = 62,135 ft.lb./deg.

NODE 15 CNODE 20 TYPE = RY STIF = 65,221 ft.lb./deg.

NODE 15 CNODE 20 TYPE = RZ STIF = RIGID

NODE 20 DISP X=0, Y=0, Z=0, RX=0.0163 radians, RY=0, RZ=0.

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onlineText Box?

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onlineText BoxWhere is the displacement 0.2203 measured?at nozzle end or shell-nozzle interface?How to measure displacement or rotation at shell-nozzle interface?

low tank stiffness

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