problema 2-016

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Software Verification PROGRAM NAME: SAP2000REVISION NO.: 0

EXAMPLE 2-016 - 1

EXAMPLE 2-016S HELL OUT-O F-P LANE BUCKLING

EXAMPLE DESCRIPTION This example uses a flat plate to test out-of-plane buckling of shell elements. The

plate is 24 inches long, 24 inches wide and 1 inch thick. Unit shear and bendingstresses, and , respectively, are applied to the plate edges in two separate loadcases. The buckling loads, cr and cr , calculated by SAP2000 are compared withindependent results.

The modeling for this example is set up such that the automatic area meshingfeature of SAP2000 can be used. This makes it easy to test the model withdifferent mesh sizes. In this example both a 16x16 and a 64x64 mesh are used, inseparate models.

The automatic area meshing feature has a special option to add a restraint to adegree of freedom at a new joint (created by the meshing) along the edge of thearea object if both adjacent corners of the area object have that degree of freedomrestrained. This special option is used in this example.

The desired restraints for this example are as follows (see figure on next page): Joint 1: U x, Uy and U z Joints 2, 3: U z Joint 4: U x and U z (U x applied as spring, see discussion that follows) All other edge joints created by automatic meshing: U z

The U x restraint at joint 4 is applied as a spring with 1E9 kip/in stiffness. This isdone so that the automatic area meshing will only put a U z restraint on theintermediate joints along edge 1-4. If the U x restraint at joint 4 were specified asa joint restraint rather than a spring, the automatic area meshing would put bothUx and U z restraints on the intermediate joints along edge 1-4, which is not thedesired result.

Four frame objects are defined around the perimeter of the plate spanning fromone corner of the plate to the next. The property modifiers for those frame objectsare all set to zero so that they contribute no stiffness, mass or weight to thestructure. The frame objects are specified to be automatically subdivided atintermediate joints. All of the plate edge loading is applied to these dummyframe objects as distributed loads. Applying the load using those beams allowsthe edge load to be properly distributed when the automatic area meshing is used.

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EXAMPLE 2-016 - 2

GEOMETRY , P ROPERTIES AND LOADING 24"

NxN automaticinternal area mesh

1 2

34

2 4 "

Y

X

ZY

X

Z

-

-

Model Geometry

Load Case SHEAR

Load Case BEND

Material Properties

Section Properties

E = 29000 k/in2 = 0.3

Length = 24 inWidth = 24 inThickness = 1 in

Restraint at Joint 1Ux, Uy, Uz

Restraint at Joints 2 and 3Uz

Restraint at Joint 4Ux, Uz where Uxrestraint is appliedas a spring

Restraint at Other Edge JointsUz

Internal Meshing

Model A:16x16Model B: 64x64

Dummy beamsaround plate

perimeter used toapply loads

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EXAMPLE 2-016 - 3

TECHNICAL FEATURES OF SAP2000 TESTED Buckling analysis of shells Automatic area meshing (NxN) with added restraints Joint springs Frame property modifiers Frame distributed load Frame automatic subdivide at intermediate joints

RESULTS COMPARISON The independent result for the shear buckling stress, cr , is calculated usingequation 8-3 on page 320 and equation j together with Table 9-10 on page 382 ofTimoshenko and Gere 1961. The independent result for the bending bucklingstress, cr , is calculated using equation 8-3 on page 320 and equation j togetherwith Table 9-6 on page 377 of Timoshenko and Gere 1961. The results are

presented separately for the thin plate option and the thick plate option.

Note that the independent results do not include the effects of out-of-plane sheardeformations.

Thin Plate Option (1 Inch Plate Thickness)Output

ParameterModel and

Mesh SAP2000 IndependentPercent

Difference

A - 16 x 16 435 +2.4% cr k/in 2

B - 64 x 64 425425

0%

A - 16 x 16 1179 +1.2% cr k/in 2

B - 64 x 64 11631165

-0.2%

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EXAMPLE 2-016 - 4

Thick Plate Option (1 Inch Plate Thickness)

OutputParameter

Model andMesh SAP2000 Independent

PercentDifference

A - 16 x 16 416 -2.1% cr k/in 2

B - 64 x 64 408425

-4%

A - 16 x 16 1121 -3.8% cr k/in 2

B - 64 x 64 11121165

-4.5%

COMPUTER F ILE: Example 2-016a-thick, Example 2-016a-thin,Example 2-016b-thick, Example 2-016b-thin,Example 2-016c-thick, Example 2-016c-thin

CONCLUSION The SAP2000 results show an acceptable match with the independent results for

both the thin plate option and the thick plate option.The thick plate option converges to smaller buckling stress values than the thin

plate option and the theoretical results. The differences for the thick plate optionresults occur because the thick plate solution includes the effects of out-of-planeshear deformations, whereas neither the independent results nor the thin platesolution consider those effects.

This can be demonstrated by repeating the example with a smaller plate thicknesssuch that the effects of out-of-plane shear deformations are negligible comparedto bending deformations. Model C changes the plate thickness from 1 inch to0.01 inch. With this change, the thick plate and the thin plate results areessentially identical and show an acceptable comparison with the independentresults. The results for Model C are shown in the following table.

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EXAMPLE 2-016 - 5

Resul ts for Model C (0.01 Inch Plate Thickness and 64x64 mesh)

OutputParameter

ShellOption SAP2000 Independent

PercentDifference

Thin 0.0425 0% cr k/in 2

Thick 0.04250.0425

0%

Thin 0.1163 -0.2% cr k/in 2

Thick 0.11620.1165

-0.3%

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EXAMPLE 2-016 - 6

H AND C ALCULATION

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EXAMPLE 2-016 - 7

problema 2-016

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