Contents Problem 1 006

Problem 1-006 Problem 1-006

User Manual: Problem 1-006

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EXAMPLE 1-006
FRAME - NON-PRISMATIC SECTIONS AND AUTOMATIC FRAME SUBDIVISION
EXAMPLE DESCRIPTION
This example tests the SAP2000 non-prismatic frame section property. In
SAP2000 the axial (A), torsion (J), weight, and mass properties can vary linearly,
and the bending property (I) variation can be linear, parabolic or cubic. The
variation of the moment of inertia is defined in SAP2000 as follows:
I
2
where,
n = 1 for linear variation,
n = 2 for parabolic variation, and
n = 3 for cubic variation,
x
I
1
( ) ( )
n
nn
L
x
I
L
x
IxI
+
−=
/1
2
/1
1
1)(
L
The example model consists of a complex, non-prismatic frame section that is
made up of four segments, assigned to a cantilever beam, and subjected to seven
load cases, each with a different type of loading. An applicable deformation
component at the free end of the cantilever is compared with independent hand
calculated results for each load case.
Important Note: Only bending and axial deformations are considered in the
analysis. Shear deformations are ignored. In SAP2000 this is achieved by setting
the property modification factor for shear area to 0.
This example also tests the frame automatic subdivide feature of SAP2000. The
automatic frame subdivide option internally divides the frame object into a user-
specified number of elements for the analysis. The analysis results are combined
and reported for the entire frame object, not the subdivided elements.
In this example two models are run. Model A has no automatic subdivision.
Model B has automatic subdivision that divides the frame object up into 10 equal
length elements. The results are compared for each model.
EXAMPLE 1-006 - 1
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GEOMETRY, PROPERTIES AND LOADING
144"
Seg. 2 Seg. 3 Seg. 4
36" 36" 36" 36"
Seg. 1
FSec 4
FSec 3
FSec 2
FSec 2
FSec 3
FSec 1
FSec 1
FSec 2
Z
X
Y
Material Properties
E=3,600 k/in
2
ν=0.2
G=1,500 k/in
2
Unit weight = 0.15 k/ft
3
Segment Definitions
Segment 1 Segment 2 Segment 3 Segment 4
Start Section FSec4 FSec2 FSec3 FSec1
End Section FSec3 FSec2 FSec1 FSec2
Length, in 36 36 36 36
Axial (A) Variation Linear Constant Linear Linear
Bending (I33) Variation Linear Constant Parabolic Cubic
Bending (I22) Variation Linear Constant Parabolic Cubic
Torsion (J) Variation Linear Constant Linear Linear
EXAMPLE 1-006 - 2
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Section Properties
FSec1 FSec2 FSec3 FSec4
Width b, in 12 12 12 12
Depth d, in 12 18 24 30
Area A, in2 144 216 288 360
Bending I33, in4 1728 5832 13824 27000
Bending I22, in4 1728 2592 3456 4320
Torsion J, in4 2,920.32 6,085.12 9,492.12 12,934.73
Loading
Load Case Load Type Value
1 Self weight Not Applicable
2 Fx at free end (axial) 500 k
3 Fy at free end 5 k
4 Fz at free end -5 k
5 Mx at free end (torsion) 5,000 k-in
6 My at free end 5,000 k-in
7 Mz at free end 5,000 k-in
EXAMPLE 1-006 - 3
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TECHNICAL FEATURES OF SAP2000 TESTED
Structural behavior of a non-prismatic frame section
Self weight calculations
Linear variation of section area
Linear, parabolic and cubic variation of moment of inertia
Linear variation of section torsional constant
Automatic frame subdivision
RESULTS COMPARISON
Independent results are hand calculated using the unit load method described on
page 244 in Cook and Young 1985.
Results for Model A (With No Automatic Subdivision)
Load
Case Output
Parameter SAP2000 Independent Percent
Difference
1 My (fixed end)k-in -184.950 -184.950 0%
2 Ux (free end) in 0.09087 0.09087 0%
3 Uy (free end) in 0.43120 0.43120 0%
4 Uz (free end) in -0.14335 -0.14335 0%
5 Rx (free end) rad 0.07987 0.07987 0%
6 Ry (free end) rad 0.03742 0.03742 0%
7 Rz (free end) rad 0.07634 0.07634 0%
EXAMPLE 1-006 - 4
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Results for Model B (With Automatic Subdivision into Ten Elements)
Load
Case Output
Parameter SAP2000 Independent Percent
Difference
1 My (fixed end)k-in -184.950 -184.950 0%
2 Ux (free end) in 0.09087 0.09087 0%
3 Uy (free end) in 0.43120 0.43120 0%
4 Uz (free end) in -0.14335 -0.14335 0%
5 Rx (free end) rad 0.07987 0.07987 0%
6 Ry (free end) rad 0.03742 0.03742 0%
7 Rz (free end) rad 0.07634 0.07634 0%
COMPUTER FILE: Example 1-006a, Example 1-006b
CONCLUSION
The SAP2000 results show an exact match with the independent results for both
models A and B.
EXAMPLE 1-006 - 5
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HAND CALCULATION
EXAMPLE 1-006 - 6
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EXAMPLE 1-006 - 7
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EXAMPLE 1-006 - 8
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EXAMPLE 1-006 - 9
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EXAMPLE 1-006 - 10
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EXAMPLE 1-006 - 11
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EXAMPLE 1-006 - 12
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EXAMPLE 1-006 - 13
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EXAMPLE 1-006 - 14
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EXAMPLE 1-006 - 15
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EXAMPLE 1-006 - 16
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EXAMPLE 1-006 - 17
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EXAMPLE 1-006 - 18

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