Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 7

EXAMPLE 2-020 SHELL - PRESTRESS APPLIED TO AREA OBJECTS

EXAMPLE DESCRIPTION The SAP2000 prestress applied to area objects is verified in this example using a simply supported concrete beam with a parabolic prestressing tendon profile and different eccentricities at each end. The deflection, and the top and bottom stresses, at the beam center are compared with independent hand- calculated results.

SAP2000 has two options for modeling the effect of the prestress. One option models the prestress as loads applied to the structure. The other models the prestress tendon as internal tendon elements. Both options are verified in this example.

In SAP2000 the beam is modeled using a 4x10 area object mesh. Thus, each area object is 7.5 inches high by 36 inches long. This yields an aspect ratio of 4.8.

Two separate models are used in this analysis. Model A has the prestress modeled as loads. Models B treats the prestress as elements.

The effect of both wobble and curvature friction losses are included in the example as well as elastic shortening of the concrete beam. The tendon is stressed from the left end only.

Important Note: Shear deformations are included in this example.

EXAMPLE 2-020 - 1

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 7

GEOMETRY AND LOADING

Section A-A

CLCL

10" 3"

10"

30' = 360"

30"

18"Prestressing tendonT=220 k

Material PropertiesE = 3600 k/in2

ν = 0.2G= 1500 k/in2

Section Propertiesb = 18 ind = 30 inA = 540 in2

I = 40,500 in4

Av = 450 in2 (shear area)Prestressing Tendon Notes1.2.3.4.5.6.7.8.

T is the component of the tension force in the prestressing tendon before losses.The tendon is tensioned from the left end only.The cable drapes at the left end, center and right end of the beam are illustrated in the figure.The cable profile is parabolic.The friction loss coefficient for curvature is 0.15.The friction loss coefficient for wobble is 0.0001 / in.Consider losses due to friction and beam elastic shortening.Set the maximum tendon discretization length to 12 in.

Beam neutral axis

Prestress Properties

A

A

A = 1.5 in2E = 29000 k/in2ν = 0.3

TECHNICAL FEATURES OF SAP2000 TESTED Prestress tendon with parabolic tendon profile and different eccentricities at

the two ends Prestress tendon modeled using loads and applied to area objects Prestress tendon modeled as elements and applied to area objects Prestress losses

RESULTS COMPARISON Independent results are hand calculated using basic principles and using the unit load method described on page 244 in Cook and Young 1985. The results are presented separately for the thin plate option and the thick plate option.

Important Note: A simplifying assumption is made in the hand calculations that the distributed load the prestress imposes on the beam is uniform. Thus the SAP2000 and hand-calculated results are not expected to match exactly.

EXAMPLE 2-020 - 2

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 7

Thin Plate Option

Model Output

Parameter SAP2000 Independent Percent

Difference

A- By Loads Uz (center)

in

0.16485 0.16564

-0.5%

B- By Elements 0.16117 -2.7%

A- By Loads Avg. S11 (top center)

kip/in2

0.3707 0.3681

+0.7%

B- By Elements 0.3605 -2.1%

A- By Loads Avg. S11 (bot. center)

kip/in2

-1.1297 -1.1163

+1.2%

B- By Elements -1.1002 -1.4%

Thick Plate Option

Model Output

Parameter SAP2000 Independent Percent

Difference

A- By Loads Uz (center)

in

0.16485 0.16564

-0.5%

B- By Elements 0.16117 -2.7%

A- By Loads Avg. S11 (top center)

kip/in2

0.3707 0.3681

+0.7%

B- By Elements 0.3605 -2.1%

A- By Loads Avg. S11 (bot. center)

kip/in2

-1.1297 -1.1163

+1.2%

B- By Elements -1.1002 -1.4%

COMPUTER FILES: Example 2-020a-thick, Example 2-020a-thin, Example 2-020b-thick, Example 2-020b-thin

CONCLUSION The SAP2000 results and the independent results show an acceptable match.

EXAMPLE 2-020 - 3

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 7

HAND CALCULATION

EXAMPLE 2-020 - 4

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 7

EXAMPLE 2-020 - 5

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 7

EXAMPLE 2-020 - 6

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 7

EXAMPLE 2-020 - 7

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 7

EXAMPLE 2-020 - 8

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 7

EXAMPLE 2-020 - 9

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 7

EXAMPLE 2-020 - 10

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 7

EXAMPLE 2-020 - 11

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 7

EXAMPLE 2-020 - 12

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 7

EXAMPLE 2-020 - 13

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 7

EXAMPLE 2-020 - 14

Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 7

EXAMPLE 2-020 - 15