Information and Pool Sap2000 Manuals English Problem 2 013 (1)

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EXAMPLE 2-013 SHELL –TEMPERATURE LOAD THAT IS CONSTANT THROUGH SHELL THICKNESS PROBLEM DESCRIPTION In this example a rectangular plate with irregularly shaped elements is subjected to a temperature load that is constant through the thickness of the plate. The geometry and properties for the plate are the same as those described for the patch test in MacNeal and Harder 1985. Joint displacements and stresses resulting from the temperature load are compared with hand calculated results. The original temperature for the example is 60 °F; the temperature load consists of raising the temperature to 160 °F, a 100 °F temperature increase. In SAP2000 the reference temperature is specified as 60 °F and the temperature load assigned to the shell elements is specified as 160 °F. Two different models are created for this example. The models are identical, except for the joint restraints. Model A has a fixed restraint at joint 1, thus allowing free expansion of the plate. Model B has pinned restraints at the four corner joints (joints 1, 2, 7 and 8), thus restraining the temperature expansion.

GEOMETRY, PROPERTIES AND LOADING 0.24" 2

8 4 1

4

6          "          2          1   .          0

5

3

Y Z

3

1 X

1

2

5 7

- Joint number - Area object object number number

Material Properties E = 1,000 1,000,0 ,000 00 lb/i lb/inn2  = 0.25  = Coeff. thermal thermal exp. exp. = 5.5E5.5E-06 06

Joint Coordinates (inches) Joint X Y 1 0 0 2 0 0.12 3 0.04 0.02 4 0.08 0.08 5 0.18 0.03 6 0.16 0.08 7 0.24 0 8 0.24 0.12

Z 0 0 0 0 0 0 0 0

Section Properties Thickness = 0.001 in Joint Restraint Model A: Joint 1 has Ux, Uy, Uz, Rx , Ry and Rz restrained Model B: Joints 1, 2, 7 and 8 have U x, Uy and Uz restrained EXAMPLE 2-013 - 1

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TECHNICAL FEATURES OF SAP2000 TESTED  Temperature loading for shell elements  Reference temperature for shell elements RESULTS COMPARISON The independent results are hand calculated based on Equation 1.3.4 on page 9 in Cook and Young 1985. The results for the thin plate option and the thick plate option are presented separately.

Thin Plate Option Model A

Free expansion

Output Parameter

SAP2000

Independent

Percent Difference

Ux (jt 8) in

0.000132

0.000132

0%

Uy (jt 8) in

0.000066

0.000066

0%

  (jt 8) lb/in

2

0

0

0%

  (jt 8) lb/in

2

0

0

0%

Ux (jt 8) in

0

0

0%

Uy (jt 8) in

0

0

0%

σxx σyy

B

Restrained

  (jt 8) lb/in

2

-733.33

-733.33

0%

  (jt 8) lb/in

2

-733.33

-733.33

0%

σxx σyy

EXAMPLE 2-013 - 2

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Thick Plate Option Model A

Free expansion

Output Parameter

SAP2000

Independent

Percent Difference

Ux (jt 8) in

0.000132

0.000132

0%

Uy (jt 8) in

0.000066

0.000066

0%

  (jt 8) lb/in

2

0

0

0%

  (jt 8) lb/in

2

0

0

0%

Ux (jt 8) in

0

0

0%

Uy (jt 8) in

0

0

0%

σxx σyy

B

Restrained

  (jt 8) lb/in

2

-733.33

-733.33

0%

  (jt 8) lb/in

2

-733.33

-733.33

0%

σxx σyy

COMPUTER FILES: Example 2-013a-thick, Example 2-013a-thin; Example 2-013b-thick, Example 2-013b-thin CONCLUSION The SAP2000 results show an exact comparison with the independent results for both the thin plate option and the thick plate option.

EXAMPLE 2-013 - 3

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HAND CALCULATION

EXAMPLE 2-013 - 4