FE modeling of elastic buckling of stud walls September 2008 version O. Iuorio*, B.W. Schafer *This report was prepared while O. Iuorio was a Visiting Scholar with B.W. Schafer’s Thin-walled Structures Group at JHU. Summary: The following represents work in progress on the modeling of elastic buckling (and later collapse) of CFS stud walls with dis-similar sheathing.
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FE modeling of elastic buckling of stud walls
September 2008 version
O. Iuorio*, B.W. Schafer
*This report was prepared while O. Iuorio was a Visiting Scholar with B.W. Schafer’s Thin-walled Structures Group at JHU.
Summary: The following represents work in progress on the modeling of elastic buckling (and later collapse) of CFS stud walls with dis-similar sheathing.
1
4.4.3 ELASTIC BUCKLING OF SHEATHED STUD WALL.
Aim of this analysis is to study the behavior of walls sheathed with oriented
strand board (OSB) and gypsum board (GWB) panels when the wall is
subjected to vertical loads. It is well recognized that the strength of stud
wall can be improved by using sheathing material and that the connections
are key-points for the strength transmission. Hence, a parametric analysis
has been developed to study the wall behavior varying the screw spacing
and the sheathing material (OSB and GWB). In Table1 the parametric
analysis planning is summarized and geometrical and mechanical
components properties are defined in Table2.
Parametric analysis planning
symbol (mm) (inches)
Wall height h 2400 96
Stud 362S162-68 0,0713
Stud spacing d 300 12
50 2
75 3
100 4
150 6
200 8
304.8 12
609.6 24
Screw spacing s
1219 48
Table1. Parametric Analysis Planning
thickness Ex Ey G υx=υy
(inches) (ksi) (ksi) (ksi)
362S162-68 0.0713 29500 29500 11346.15 0.3
OSB// 0.35 638.2 754.2 203 0.3
2
GWB 0.5 384 384 108 0.3
Table2. Geometrical and Mechanical properties
The structure has been studied with Finite Strip Method (FSM) and the
Finite Element Method (FEM) and the results of CUFSM and Abaqus have
been compared.
In particular, in the finite element analysis, the components have been
modelled with isoparametric shell finite elements (S9R5) and a reference
stress equal to 1 has been considered placed at each node of the end stud
sections, whilst the panel has been considered totally unloaded.
In order to model the connections, three different conditions have been
analyzed:
1) connections with stiffness equal to zero
2) connections with infinite stiffness (rigid connections)
3) connections characterized by stiffness obtained by experimental
tests.
1) Connection with stiffness equal to 0 – (single stud)
In the first case, the wall can be identified as a system of two studs and two
panels without any connections. Hence, it corresponds to study a single
compressed stud. The buckling curve of the first model (96in length
member without panel) obtained with CUFSM is shown in Figure 1, whilst
Figure 2 shows the deformed shape corresponding to the first mode
obtained in Abaqus. The comparison between results of finite strip analysis
and finite element analysis show that the stud is subjected to global flexural
torsional buckling, as first mode, and the load factors obtained in CUFSM
and Abaqus are very closed (load factor = 11.125 CUFSM vs load factor =
11.325 with Abaqus).
Parametr ic analysis 3
Figure1. CUFSM buckling curve for the model without panel
Figure2. Global buckling of a single 362S162-68 stud ( model1) - FEM result
Moreover, the occurrence of the other buckling modes has been
investigated.
Table 3 compares the CFSM and Abaqus results for any buckling mode
and Figures from 3 to 5 show the deformed shape for each buckling mode.
Model Local
buckling Dist buckl Dist buckl
Global
flex
Global
flex-tors
CUFSM 60.33 73.63 150.5 11.13 11.61 Wall
sheathed
with GWB
panel Abaqus 59.46 76.35 166.26 11.33 11.80
Table3. Comparison between CUFSM and Abaqus results for the first model
4
Figure3. Local buckling of a single 362S162-68 stud
Figure4. Global Flexural buckling of a single 362S162-68 stud
Figure5. Global Flexural torsional buckling of a single 362S162-68 stud
Parametr ic analysis 5
Figure6. Distortional buckling (1) of a single 362S162-68 stud
Figure7. Distortional buckling (2) of a single 362S162-68 stud
2) Connections with infinite stiffness
2.1 General constraints in all directions.
The analysis continued considering rigid connections (second case,
connections with springs with infinite stiffness). In this case, the
compression loads acting on the studs are transferred to the panels by the
connections that have been modeled with general constraints. In particular,
in a first case general constraints acting in all direction have been
considered and the buckling curves obtained in CUFSM are shown in
Figure 8 and 9.
Figure 8: Buckling curve of a wall sheathed with OSB panel – CUFSM result.
6
Figure9: Buckling curves for modes from 1 to 4.
The buckling curve corresponding to the first mode identifies the load
factor corresponding to the local buckling (LF = 62.20) and for a half-
wavelength equal to 96” it identifies a flexural-torsional buckling (LF =
80.36). On the other hand, that buckling curve does not present any
minimum for distortional buckling; the latter starts to appear at the third
mode (Figure9). Hence, the minimum for the distortional buckling
corresponding to the third mode has been considered and it has been
referred as dist. 2. Moreover, the half-wavelength has been fixed and the
corresponding point on the first mode curve has been considered (this value
has been considered as dist.1).
Figure10. Definition of distortional buckling 1(dist1).
Finally, the Global Flexural buckling has been defined considering an
half-wavelenght equal to wall height (96”) and the third mode. All the
results are summarized in Table4.
Parametr ic analysis 7
Model Screw
spacing
Local
buckling
Dist
buckl1
Dist
buckl2
Global
flex-tors
Global
flex
Wall
sheathed
with
OSB
panel
CUFSM contin 62.3 118.87
mode1
236.98
mode3
80.36
mode1
length
96”
236.98
mode3
length
96”
Table4. CUFSM results for the model with rigid connection acting in all directions
The FEM model has been developed in order to study the behavior
varying the screw spacing and the results have been synthesized in Table5
and Table6.
Model Screw spacing CUFSM (Load
factor)
Abaqus (Load
factor)
Buckling mode
Without
connection
- 11.125 11.325 Global_ Flexural
continuous 62.38 64.18 Local _ Stud
2” 63.577 Local _ Stud
3” 62.441 Local _ Stud
4” 62.423 Local _ Stud
6” 62.342 Local _ Stud
8” 61.981 Global_ Panel
12” 29.037 Global_ Panel
Wall sheathed
with OSB
panels
24” 8.022 Global_ Panel
continuous 63.07 64.486 Local _ Stud
2” 63.627 Local _ Stud
3” 62.115 Local _ Stud
Wall sheathed
with GWB
panel
4” 62.139 Local _ Stud
8
6” 62.02 Local _ Stud
8” 62.047 Local _ Stud
12” 57.564 Global_ Panel
24” 16.053 Global_ Panel
Table5. Comparison between CUFSM and Abaqus results at 1st mode varying the screw
spacing.
Model Screw
spacing
Local
buckling
Dist
buckl1
Dist
buckl2
Global
flex-tors
CUFSM contin 62.3 118.87
mode1
236.98
mode3
80.36
mode1
length
96”
1 64.18 64.23
2 63.58 119.03 234.22 64.17
3 62.44 120.22 228.97 64.09
4 62.42 119.22 226.22 64.0
6 62.34 123.26 222.35 63.79
8 62.37 117.05 221.56 63.54
12 62.50 119.76 224.66 63
24 62.6 112.22 197.54 62.87
Wall
sheathed
with
OSB
panel Abaqus
48 62.98 53.74
Table6. Comparison between CUFSM and Abaqus results
Table5 shows that for screw spacing up to 6”, the local buckling of the stud
occurs as first mode (Figure11). Instead, for screw spacing between 8 and
48” the global buckling of the sheathing governs the behavior (Figure12)
and the number of sheathing waves depends on the number of connection
(8 waves for screw spacing equal to 12”, Figure12, and 4 waves for screw
spacing equal to 24” Figure13).
Parametr ic analysis 9
Figure11. Wall sheathed with OSB panels – first mode – Abaqus result
Figure12. Buckling behavior of wall sheathed with OSB panels and screw spacing equal
to 12” – First mode – Abaqus result
Figure13. Buckling behavior of wall sheathed with GWB panels and screw spacing equal
to 24” – First mode – Abaqus result
10
Figure14. Wall sheathed with OSB panels – Third mode – Abaqus result
2.2) General constraints in direction 1-2-4.
The comparison between CUFSM and Abaqus results showed a strange
panel behavior. Therefore, in a second time, the connections have been
modeled by general constraints that assure the same displacements and
rotations of the two connected point but leaving the vertical displacement
free. Both models have been studied varying the screw connection and all
the results, corresponding to the first mode, are summarized in Table 3.
Model Screw spacing CUFSM
(Load factor)
Abaqus
(Load
factor)
Buckling mode
Without
connection - 11.125 11.325 Global Flex-Tors
continuous 62.38 46,161 Global Flex-Tors
2” 46,288 Global Flex-Tors
3” 46,281 Global Flex-Tors
4” 46,272 Global Flex-Tors
6” 46,252 Global Flex-Tors
Wall sheathed
with OSB
panels
8” 46,231 Global Flex-Tors
Parametr ic analysis 11
12” 46,181 Global Flex-Tors
24” 45,924 Global Flex-Tors
48” 41,64 Global Flex-Tors
continuous 63.07 51,218 Global Flex-Tors
2” 51,21 Global Flex-Tors
3” 51,2 Global Flex-Tors
4” 51,19 Global Flex-Tors
6” 51,17 Global Flex-Tors
8” 51,15 Global Flex-Tors
12” 51,09 Global Flex-Tors
24” 50,818 Global Flex-Tors
Wall sheathed
with GWB
panel
48” 45,49 Global Flex-Tors
Table7. Wall 96”x12”: comparison between CUFSM and Abaqus results (1st mode) for the
three models varying the screw spacing.
Looking at the results, can be noticed that for both sheathing materials and
all the investigated screw spacing, the global flexural- torsional buckling
occurs as first buckling mode and that the CUFSM results are higher then
the Abaqus results. In particular, for both cases (OSB sheathed wall and
GWB sheathed wall), these global buckling is not influenced by the screw
spacing and only for an ideal screw spacing of 48” the load factor reduces
of a 0.06%.
Then in order to characterize the wall behavior, the occurrence of the other
buckling mode has been investigated. At this regards, the considerations
about the definition of the distortional buckling done above are still valid
(Figure 15 to 17).
12
Figure15. Buckling curve of a OSB wall studs (96”x12”)-CUFSM result.
Figure 16: OSB 96x12in – Buckling curves for higher modes
Figure 17: GWB 96x12in – Buckling curves
Taking into account all these consideration, a comparison among the
FSM and FEM results have been carried out and all the results are
summarized in Table 8 and 9.
Parametr ic analysis 13
Figure 18: deformed shape of a 96”x12” OSB wall corresponding to Global Flexural-
Torsional buckling – CUFSM result
Figure 19: deformed shape of a 96”x12” OSB wall corresponding to Global Flexural-
Torsional buckling – Abaqus result
Figure 20: deformed shape of a 96”x12” OSB wall corresponding to Local buckling –
CUFSM result
Figure 21: deformed shape of a 96”x12” OSB wall corresponding to Local buckling –
Abaqus result
14
Figure 22: deformed shape of a 96”x12” OSB wall corresponding to Distortional 1 –
CUFSM result
Figure 23: deformed shape of a 96”x12” OSB wall corresponding to Distortional
buckling (1) – Abaqus result
Figure 24: deformed shape of a 96”x12” OSB wall corresponding to Distortional (2) –
CUFSM result
Figure 25: deformed shape of a 96”x12” OSB wall corresponding to Distortional
buckling (2) – Abaqus result
Parametr ic analysis 15
Figure 26: deformed shape of a 96”x12” OSB wall corresponding to Flexural buckling –
CUFSM result
Figure 27: deformed shape of a 96”x12” OSB wall corresponding to Flexural buckling –
Abaqus result
Model Screw
spacing
Local
buckling
Dist
buckl
Dist
buckl
Global
flex-tors
Global
flex
CUFSM contin 62.19 114.40
mode1
235.62
mode3
54.03
mode1
length
96”
100.84
mode3
length
96”
contin 61.202 105.67 191.03 46.16 102.47
2” 60.77 102.72 187.99 46.29 102.46
3” 59.63 101.48 185.02 46.28 102.45
4” 59.65 101.33 182.11 46.27 102.43
6” 59.58 97.37 176.28 46.25 102.39
8” 58.58 86.76 161.01 46.23 102.35
12” 59.56 83.23 159.33 46.18 102.27
24” 59.52 81.05 142.01 45.92 101.9
Wall
sheathed
with GWB
panel
Abaqus
48” 59.50 77.27 155.24 41.64 70.21*
16
Table 8: OSB 96x12-constr1-2-4
Model Screw
spacing
Local
buckling
Dist
buckl
Dist
buckl
Global
flex-
tors
Global
flex
CUFSM contin 64.08 115.34
mode1
301
mode3
56.32
mode1
l.th96”
139.25
mode3
length
96”
contin 62.6 118.9 209.73 51.22 141.24
2” 61.59 116.49 204.54 51.21 141.22
3” 59.65 113.71 199.46 51.20 141.20
4” 59.75 110.82 194.85 51.19 141.18
6” 59.59 106.04 185.01 51.17 141.12
8” 59.59 105.53 171.7 51.15 141.04
12” 59.56 83.66 160.95 51.09 140.83
24” 59.52 78.33 139.19 50.82 139.66
Wall
sheathed
with GWB
panel Abaqus
48” 59.50 77.81 155.31 45.26 75.76*
Table 9: GWB 96x12-constr1-2-4
* In this case the wall is subjected to global flexural buckling + some
distortional.
Parametr ic analysis 17
Figure 30: deformed shape of a 96”x12” GWB wall corresponding to Flexural buckling –
Abaqus result
Results:
For all the models the wall is subjected first of all to Global Flexural-
Torsional buckling, and this independent on the screw spacing.
The local buckling occurs (for both material around an eigenvalues of
60) and it is independent on the screw spacing. CUFSM and FEM results
are pretty closed. This buckling mode interests all the section composed
with two studs plus sheathings.
In order to study the distortional buckling, two different kind of
distortional have been analyzed. In distortional 1 the FEM and CUFSM
results are very closed in case of little screw spacing, whilst FEM results
start to present lower values for screw spacing equal to 6” and reaching
very lower values for screw spacing equal to 12”, 24” and 48”.
For the second distortional buckling the FEM results are much lower
then the CUFSM, and this distortional buckling seems to be strongly
dependent on the screw spacing.
In order to study the Global Flexural Buckling, the CUFSM results
corresponding to length 96” and mode 3 have been compared with FEM
results. The values are almost coincident for screw spacing between the
continuous model and 24”, whilst in case of screw spacing equal to 48” it
seems not possible to find a “pure” Global Flexural Buckling. In this case
the Global Flexural-Torsional is associated to some Distortional forms
(Figure 30).
In conclusion, for these models, the screw spacing influences only the
Distortional buckling and the Global-Flexural buckling in case of wide
screw spacing.
The CUFSM results seems to be reliable for Local and Global Flexural
(this second for little screw spacing), whilst they overestimate of a 10% the
resistance for Global-Flexural buckling.
18
Moreover they seems to be not too much reliable for Distortional
buckling.
The diagrams in Figure 31 and 32 summarize the results for OSB and