Problem 4 003

Software Verification SAP2000 2

PROGRAM NAME: REVISION NO.:

EXAMPLE 4-003 ASOLID – ROTATING ANNULAR DISK PROBLEM DESCRIPTION In this example, a homogeneous annular disk rotates about its own axis, with a uniform angular velocity of 200 radians per second. The disk is modeled using a 2x20 mesh of asolid elements, with the incompatible bending modes option. A 10-degree segment of the disk is modeled. The disk has an inner radius of 10 inches, outer radius of 20 inches and is 1 inch thick. The disk is made of steel and its weight density is 0.28 lb/in3.

The radial stress at the middle of the disk (radius equal to 15 inches) and the radial deflection at the outer edge of the disk are compared with hand-calculated results.

GEOMETRY, PROPERTIES AND LOADING

Material Properties E = 29,000,000 lb/in2 ν=3 Weight density = 0.28 lb/in3

Y 200 rad/sec 20"

X 10"

20

Section Properties Inner radius = 10 in Outer radius = 20 in Thickness = 1 in

10°

Free

X Radius

Free

10

Y

A

A

Z Section A-A

EXAMPLE 4-003 - 1

Software Verification PROGRAM NAME: REVISION NO.:

SAP2000 2

TECHNICAL FEATURES OF SAP2000 TESTED  Analysis using asolid elements  Asolid rotate load RESULTS COMPARISON The hand-calculated results are based on equations presented in Item 8 on page 567 of Roark and Young 1975.

With Incompatible Bending Modes Output Parameter

SAP2000

Independent

Percent Difference

0.12040

0.12035

0%

45783

45891

0%

Radial displ in At outer edge, r = 20 in Radial stress psi At r = 15 in

COMPUTER FILE:

Example 4-003

CONCLUSIONS The SAP2000 results show an acceptable comparison with the independent results.

EXAMPLE 4-003 - 2

Software Verification PROGRAM NAME: REVISION NO.:

SAP2000 2

HAND CALCULATION

EXAMPLE 4-003 - 3

Software Verification PROGRAM NAME: REVISION NO.:

SAP2000 2

EXAMPLE 4-003 - 4