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EXAMPLE 2-010 - 1

EXAMPLE 2-010

SHELL CYLINDER WITH INTERNAL PRESSURE

PROBLEM DESCRIPTION

In this example a cylinder is analyzed for an internal pressure load. The resulting

radial outward displacement, vertical displacement at the top of the cylinder and

11 stress are compared with hand calculated results based on formulas presentedin Roark and Young 1975.

The cylinder is 200 inches tall and has a 60 inch radius. The wall thickness is 1inch.

The applied load is a uniform radial pressure of 1 k/in2

on the inside face of theentire cylinder.

The local axes of all joints are oriented such that axis 1 points radially outward

and axis 3 points upward. The joints at the base of the cylinder are restrained

against translation in the local 2 and 3 directions. All other joints are restrained

against translation in the local 2 direction.

The local axes of all area objects (shells) are oriented such that axis 3 points

radially outward and axis 2 points upward.

Two different models are created for the analysis. The models are identical

except for the shell element mesh. Model A uses an 8x16 mesh (height x

circumference) and Model B used a 24x48 mesh.

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EXAMPLE 2-010 - 2

GEOMETRY, PROPERTIES AND LOADING

E = 29,000 k/in2

= 0.3

G= 11,154 k/in2

Material Properties

Shape of Cylinder

height = 200 inradius = 60 inthickness = 1 in

Loading

Uniform radial pressureon inside of cylinderp = 1k/in2

Base

Top

200"

X

Z

Y

3

12

Restraints

Base joints: U2, U3All other joints: U2

Typical area object local axesare oriented with axis 3pointing radially outward andaxis 2 pointing up

1

23

Typical joint local axes areoriented with axis 1 pointradially outward and axis 3pointing up

TECHNICAL FEATURES OF SAP2000 TESTED

Three-dimensional analysis using shell elements

Surface pressure load applied to shell elements Joint local axes

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EXAMPLE 2-010 - 3

RESULTS COMPARISON

The independent results are calculated using formulas presented in Item 1b in

Table 29 on page 448 of Roark and Young 1975. The SAP2000 results arepresented separately for the thin plate option and the thick plate option.

Thin Plate Option

Output

Parameter

Modeland

Mesh SAP2000 Independent

Percent

Difference

A 8 x 16 0.12175 -1.9%U1 (at any jt)

in B 24 x 48 0.123870.12414

-0.2%

A 8 x 16 -0.12175 -1.9%U3 (at top jt)

in B 24 x 48 -0.12387-0.12414

-0.2%

A 8 x 16 58.85 -1.9%11 (anywhere)

k/in2

B 24 x 48 59.8760

-0.2%

Thick Plate Option

OutputParameter

Modeland

Mesh SAP2000 IndependentPercent

Difference

A 8 x 16 0.12175 -1.9%U1 (at any jt)

in B 24 x 48 0.123870.12414

-0.2%

A 8 x 16 -0.12175 -1.9%U3 (at top jt)in B 24 x 48 -0.12387

-0.12414-0.2%

A 8 x 16 58.85 -1.9%11 (anywhere)

k/in2 B 24 x 48 59.8760

-0.2%

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EXAMPLE 2-010 - 4

COMPUTER FILES: Example 2-010a-thick, Example 2-010a-thin,Example 2-010b-thick, Example 2-010b-thin

CONCLUSIONS

The SAP2000 results show an acceptable comparison with the independentresults for both the thin plate and thick plate options. Increasing the meshing

improves the comparison.

The percentage difference for the 8x16 mesh is consistently 1.9% and for the

24x48 mesh is consistently 0.2%. It can be shown that the difference between the

SAP2000 results and the independent results is related to how well the SAP2000model approximates a true circular cylinder. For

example, with an 8x16 mesh, a cross section

through the cylinder is an octagon rather than atrue circle.

Consider the sketch shown to the right that

shows a plan view of a single shell element. The

sketch shows the radius of the cylinder, R, and

the distance from the center of the cylinder to theactual center of the shell element, a. The distance

from the center of the cylinder to the theoreticalcenter of the shell element (located on the dashedcircular arc) is equal to the radius, R. Thus the

percent error in the location of the center of the

shell element can be determined from thefollowing equations.

=

=

2cos60

2cos

Ra

=

=

=2

cos1100100*60

2cos6060100*

R

aRerrorPercent

The calculated percent error using the preceding formula for Models A and B isshown in the following table.

a

/2

/2

Plan View

Theoretical shell elementlocation following circularcurve shown dashed

Actual shell elementlocation shown solid

Center ofcylinder

R=60"

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EXAMPLE 2-010 - 5

Model and Mesh (degrees) a (in) Percent Error

A 8 x 16 22.5 22.5 1.9%

B 24 x 48 7.5 7.5 0.2%

The percent error shown for the location of the center of the shell element in the

preceding table is the same as the percent error found in the analysis results.

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EXAMPLE 2-010 - 6

HAND CALCULATION