elastic buckling of stud walls xjhu

Transcription

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
Stud spacing
d
Screw spacing
0,0713
s
300
12
50
2
75
3
100
4
150
6
200
8
304.8
12
609.6
24
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).
Par ametr 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.
Local
Model
Wall
buckling
Dist buckl
Dist buckl
Global
Global
flex
flex-tors
CUFSM
60.33
73.63
150.5
11.13
11.61
Abaqus
59.46
76.35
166.26
11.33
11.80
sheathed
with GWB
panel
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
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.
5
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 halfwavelength 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.
7
Model
Screw
Local
Dist
Dist
Global
Global
spacing
buckling
buckl1
buckl2
flex-tors
flex
80.36
236.98
118.87
236.98
mode1
mode3
mode1
mode3
length
length
96”
96”
Wall
sheathed
with
CUFSM
contin
62.3
OSB
panel
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
Without
Screw spacing
CUFSM (Load
Abaqus (Load
Buckling mode
factor)
factor)
-
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
24”
8.022
Global_ Panel
64.486
Local _ Stud
2”
63.627
Local _ Stud
3”
62.115
Local _ Stud
4”
62.139
Local _ Stud
connection
Wall sheathed
with OSB
panels
Wall sheathed
with GWB
panel
continuous
63.07
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
Local
Dist
Dist
Global
spacing
buckling
buckl1
buckl2
flex-tors
80.36
CUFSM
contin
118.87
236.98
mode1
mode1
mode3
length
62.3
96”
Wall
sheathed
with
OSB
panel
Abaqus
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
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).
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
Without
connection
Wall sheathed
with OSB
panels
Screw spacing
CUFSM
(Load factor)
Abaqus
(Load
Buckling mode
factor)
-
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
8”
46,231
Global Flex-Tors
11
12”
46,181
Global Flex-Tors
24”
45,924
Global Flex-Tors
48”
41,64
Global Flex-Tors
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
48”
45,49
Global Flex-Tors
continuous
Wall sheathed
with GWB
panel
63.07
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 flexuraltorsional 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.
13
Figure 18: deformed shape of a 96”x12” OSB wall corresponding to Global FlexuralTorsional buckling – CUFSM result
Figure 19: deformed shape of a 96”x12” OSB wall corresponding to Global FlexuralTorsional 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
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
CUFSM
Wall
sheathed
Screw
Local
Dist
Dist
Global
Global
spacing
buckling
buckl
buckl
flex-tors
flex
54.03
100.84
contin
114.40
235.62
mode1
mode3
mode1
mode3
length
length
96”
96”
62.19
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
48”
59.50
77.27
155.24
41.64
70.21*
with GWB
panel
Abaqus
16
Table 8: OSB 96x12-constr1-2-4
Model
Screw
Local
Dist
Dist
spacing
buckling
buckl
buckl
Global
flextors
56.32
115.34
CUFSM
contin
301
mode1
64.08
mode1
Global
flex
139.25
mode3
length
mode3
l.th96”
96”
contin
62.6
118.9
209.73
51.22
141.24
Wall
2”
61.59
116.49
204.54
51.21
141.22
sheathed
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
48”
59.50
77.81
155.31
45.26
75.76*
with GWB
panel
Abaqus
Table 9: GWB 96x12-constr1-2-4
* In this case the wall is subjected to global flexural buckling + some
distortional.
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 FlexuralTorsional 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
GWB wall, respectively.
OSBwall96x12
FEM-local
FEM-dist1
CUFSM-dist1
CUFSM-C-Flex-Tors
FEM-GL-Flex-tors
CUFSM-local
CUFSM-GL-Flex
CUFSM-C-Dist
FEM-Gl-Flex
CUFSM-Gl.-Flex-Tors
CUFSM-C-Loc
CUFSM-C-Dist2
FEM-Dist2
CUFSM-Dist2
CUFSM-C-Flex
160
140
120
scr
100
80
60
40
20
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
screw spacing
Figure 31: Trend of the buckling modes for an OSB 96”x12”wall studs.
GWB-96x112 constr 1-2-4
FEM-local
FEM-Flex-Tors
FEM -Flex
FEM-dist1
FEM-dist2
CUFSM-local
CUFSM-Flex-Tors
CUFSM-Flex
CUFSM-Dist1
CUFSM-Dist2
CUFSM-C-Loc
CUFSM-C-Flex-Tors
CUFSM-C-flex
CUFSM-C-Dist
CUFSM-C-Dist2
160
140
120
scr
100
80
60
40
20
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
screw spacing
Figure 32: Trend of the buckling modes for an GWB 96”x12”wall studs.
OSB 96x24”: Model with general constraints direction 1-2-4
19
All the study has also been developed for 96”x24” wall studs and Figure
24 shows the buckling curves obtained in CUFSM.
Figure 33: OSB 96x24in – Buckling curves for higher modes
In case of 96x24” walls, as summarized in Table 10, the Global Flexural
– Torsional buckling governs the behavior for screw spacing equal to 1 and
2” , whilst for larger screw spacing the local buckling occurs as first mode.
An unusual behavior is verified for screw spacing equal to 48”, when the
Global flexural buckling governs the behavior.
Model
Without
connection
Wall sheathed
with OSB
Screw spacing
CUFSM (Load
Abaqus (Load
factor)
factor)
11.125
11.325
Buckling mode
Global
-
Flex-Tors
continuous
60.57
60.671
Global
Flex-Tors
panels
2”
60.669
Global
Flex-Tors
3”
59.637
Local
4”
59.665
Local
6”
59.59
8”
59.591
Local
12”
59.569
Local
24”
59.526
Local
Local
20
51.785
Global
48”
Flex-Tors
Global
continuous
60.44
60.23
Flex-Tors
2”
60.23
Global
Flex-Tors
Wall sheathed
with GWB
panel
3”
59.65
Local
4”
59.71
Local
6”
59.59
8”
59.59
Local
12”
59.57
Local
24”
59.53
Local
51.459
Local
Global
48”
Flex-Tors
Table10. Wall 96”x24”: comparison between CUFSM and Abaqus results (1st mode) for
the three models varying the screw spacing.
Following, the deformed shapes corresponding to the different buckling
modes is shown in Figure 25 and the comparisons among all the results
varying the screw spacing are summarized in Table 11 and 12.
21
Figure 34: OSB 96x24in – Deformed shapes corresponding to Local, Global FlexuralTorsional and Global Flexural from the top to the bottom.
Model
CUFSM
Wall
sheathed
Screw
Local
Dist
Dist
spacing
buckling
buckl1
buckl2
contin
Global
flextors
Global
dist+flex
60.57
534.71
118.77
235.93
mode1
mode3
mode1
mode3
length
length
96”
96”
62.19
contin
61.21
105.92
192.71
60.67
546.70
2”
60.78
106.63
189.73
60.67
546.45
3”
59.64
104.6
186.04
60.67
546.05
4”
59.67
102.28
182.88
60.66
545.52
6”
59.59
97.78
176.47
60.65
544.09
8”
59.59
95.82
160.91
60.64
542.63
12”
59.57
83.63
159.47
60.60
538.29
24”
59.33
80.42
140.72
60.35
538.09
48”
59.50
77.20
155.20
51.79
600.58
with OSB
panel
Abaqus
Table 7: OSB 96x24-constr1-2-4
Model
Screw
Local
Dist
Dist
spacing
buckling
buckl1
buckl2
contin
63.06
114.05
263.7
Global
flextors
Global
dist+flex
Wall
sheathed
CUFSM
60.44
453.31
mode3
22
mode1
mode3
mode1
length
length
96”
96”
contin
61.861
101.43
220.49
60.23
474.76
2”
61.176
100.69
196.66
60.23
474.35
with GWB
3”
59.651
99.71
192.15
60.227
474.18
panel
4”
59.707
98.58
188.56
60.222
473.7
6”
59.59
99.38
179.3
60.21
472.52
8”
59.592
96.6
161.14
60.195
471.41
12”
59.568
89.498
160.28
60.157
467.84
24”
59.526
78.263
155.79
59.895
422.11
48”
59.499
76.323
155.25
51.459
452.88
Abaqus
Table12: GWB 96x24-constr1-2-4
The results obtained for 96x24” wall studs seem to confirm the result
obtained for the stud spacing equal to 12”. In fact, even in this case, the
local buckling is independent on the screw spacing and it is verified for a
load factor pretty closed (LF=62.19).
The distortional buckling seems to be strongly dependent on the screw
spacing.
The global buckling corresponding to mode 1 length 96” keeps being
Flexural Torsional, with an higher load factor (60.57 vs 54.03), while, the
Global buckling corresponding to mode 3 length 96” seems to be
distortional + flexural instead of only flexural.
The diagrams in Figure 35 and 36 show the trend of buckling modes
varying the screw spacing for OSB and GWB wall, respectively.
23
OSB 96x24- constr124
FEM-local
CUFSM-Local
CUFSM-C-Local
FEM-Dist1
CUFSM-Dist1
CUFSM-C-Dist1
FEM-Dist2
CUFSM-Dist2
CUFSM-C-Dist2
FEM-Flex.Tors
CUFSM-Flex Tors
CUFSM-C-Flex Tors
FEM-Flex
CUFSM-Flex
CUFSM-C-Flex
600
500
eigenvalue
400
300
200
100
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
screw spacing
Figure 35: Comparative study of the buckling behaviors of GWB sheathed wall stud
GWB wall 96x24 constr1-24
FEM-local
CUFSM-local
CUFSM-C-local
FEM-Dist1
CUFSM-Dist1
CUFSM-C-Dist1
FEM-Dist2
CUFSM-Dist2
CUFSM-C-Dist2
FEM-Flex-Tors
CUFSM-Flex-Tors
CUFSM-C-Flex-Tors
FEM-Flex
CUFSM-Flex
CUFSM-C-Flex
500
450
400
eigenvalue
350
300
250
200
150
100
50
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
screw spacing
Figure 36: Comparative study of the buckling behaviors of GWB sheathed wall stud
24
3) Connections characterized by stiffness obtained by experimental
tests.
In order to study the behaviour of a cold formed steel wall under vertical
load, the connections between stud and sheathing have been modelled by
springs. The stiffness has been evaluated as follow:
s
k1
k2
k3
k4
k5
in
kip/in
kip/in
kip/in
kip*in/in*rad
kip*in/in*rad
1
2.248
2.248
0.18
0.12
0.12
2
2.248
2.248
0.36
0.24
0.24
3
2.248
2.248
0.54
0.357
0.357
4
2.248
2.248
0.72
0.47
0.47
6
2.248
2.248
1.08
0.71
0.71
8
2.248
2.248
1.44
0.95
0.95
12
2.248
2.248
2.16
1.42
1.42
24
2.248
2.248
2.16
1.42
1.42
48
2.248
2.248
2.16
1.42
1.42
Table13: Spring stiffness values.
The simulation demonstrate that the for screw spacing between 1 and 24
inches, the wall reaches the collapse for Flexural torsional buckling. Only
in case of spacing equal to 48 inches, the wall is subjected to panel
buckling.
Moreover, in order to investigate the full behaviour, all the buckling
behaviours have been studied.
Model
25
Screw
Local
Dist
Dist
Global
Global
spacing
buckling
buckl1
buckl2
flex-tors
flex
60.44
453.31
CUFSM
contin
114.05
263.7
mode1
mode3
mode1
mode3
length
length
96”
96”
63.06
contin
60.672
86.196
173
59.069
291.98
2”
60.442
85.929
175.5
56.538
211.97
with
3”
60.289
84.956
167.31
54.724
178.25
GWB
4”
60.212
84.254
167.2
53.358
159.33
6”
60.07
83.134
145.7
51.41
138.3
8”
60.04
82.185
132.47
50.059
126.42
12”
59.975
84.993
116.32
48.205
112.62
24”
59.918
77.415
96.944
44.717
93.541
48”
59.872
77.407
75.447
37.728
61.881
Wall
sheathed
panel
Abaqus
Table14: Comparison between load factors obtained in CUFSM and Abaqus in case of
Spring model.
FEM-local
FEM-Dist1
FEM-Dist2
FEM-GL-Flex-tors
FEM-Gl-Flex
CUFSM-local
CUFSM-Dist1
CUFSM-Dist2
CUFSM-Gl.-Flex-Tors
CUFSM-GL-Flex
CUFSM-C-Loc
CUFSM-C-Dist1
CUFSM-C-Dist2
CUFSM-C-Flex-Tors
CUFSM-C-Flex
FEM-Panel
300
250
scr
200
150
100
50
0
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748
screw spacing
Figure 37:Buckling behaviors of OSB sheathed wall stud with screw modeled by spring
with fixed stiffness
26
OSBwall96x12
FEM-local
CUFSM-local
CUFSM-C-Loc
80
scr
60
40
20
0
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748
screw spacing
Figure 38: OSB– Local Buckling
Local Buckling
Figure 38 shows that the local buckling of the stud is always
concentrated on the web. Hence, the sheathing does not influence this
behavior. The buckling mode is not sensitive to screw spacing and the
results are very close to that obtained considering spring with stiffness
equal to 0 (i.e. single compressed stud).
27
OSBwall96x12
FEM-Dist1
CUFSM-Dist1
CUFSM-C-Dist
140
120
100
scr
80
60
40
20
0
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748
screw spacing
Figure 39: OSB– Distortional Buckling 1
Distortional buckling 1
The behavior of the wall modeled with spring of fixed stiffness is in the
range between the model with spring with stiffness equal to 0 and spring
with infinite stiffness. This means that the interaction between panel and
studs improve the wall behavior of the wall stud, and this improvement is
more significant for little screw spacing. In fact, the graph in Figure 25
shows the load factor increments of 13% can be obtained for screw spacing
equal to1” whilst an increment of 0.4% .
28
OSBwall96x12
FEM-Dist2
CUFSM-Dist2
CUFSM-C-Dist2
300
250
scr
200
150
100
50
0
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748
screw spacing
Distortional Buckling 2
In the distortional buckling 2 the section is subjected to distortional
buckles in direction of the strong axis. Since the screw are located in
correspondence of the strong axis as well, them contribution influences the
wall behavior strongly. In fact, as Figure 40 shows this distortional
behavior is strongly sensitive to screw spacing. Moreover, for screw
spacing between up to 4’, the interaction sheathing-connections-stud
improves the behavior of wall stud without sheathing, and this
improvement is equal to 23% for screw spacing equal to 1” while it is
almost zero for screw spacing equal to 6”.
Instead, in case of larger screw spacing (6” to 48”) the load factor start
to be less than that required in case of a single compressed stud, because
29
the buckling starts to move from a local to a global buckling. In fact as can
be seen in Figure40 the distortional buckling start to follow the Global
Flexural buckling.
OSBwall96x12
FEM-Dist2
CUFSM-Dist2
CUFSM-C-Dist2
FEM-Flex
CUFSM-C-Flex
300
250
scr
200
150
100
50
0
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748
screw spacing
Figure 41: OSB– Distortional Buckling 2- screw spacing equal to 24”
30
OSBwall96x12
FEM-GL-Flex-tors
CUFSM-Gl.-Flex-Tors
CUFSM-C-Flex-Tors
100
80
scr
60
40
20
0
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748
screw spacing
Figure 42: OSB– Flexural torsional buckling
Global Flexural-Torsional Buckling
The global flexural-Torsional buckling occurs as first mode for screw
spacing up to 24”. This means that the sheathing improve the resistance of
non sheathed wall stud. Mainly, it’s worth to be noted that while the single
stud is subject to flexural buckling in direction of the weak axis, with a load
factor equal to 11.13, the sheathed wall is subjected to flexural torsional
buckling in direction of the strong axis, with a load factor 60.44 (CUFM
result). Hence, this buckling mode is very sensitive of the sheathing-to-stud
interaction (i.e. screw spacing). In fact, screw spacing equal to 1” can
improve the behavior respect to a single stud of about 47%.
31
OSBwall96x12
FEM-Gl-Flex
CUFSM-GL-Flex
CUFSM-C-Flex
300
250
scr
200
150
100
50
0
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748
screw spacing
Figure 31: OSB– Flexural buckling
Global Flexural Buckling
The flexural buckling (weak axis buckling) is strongly influenced by the
sheathing-to-stud interaction, In fact, the flexural buckling moves from the
buckling of a single section to the buckling of a composed section.
Moreover, this composed section is strong for few screw spacing and it
becomes closed to the stud behavior for larger screw spacing.
32
OSBwall96x12
FEM-Panel-spring
FEM-Panel-general constraint
300
250
scr
200
150
100
50
0
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748
screw spacing
Figure 32: Panel.
Panel
The global panel buckling cannot be predicted with CUFSM, because in
this case the stud is not influenced by the panel behavior, but the wall
seems to be sensitive to this buckling mode.
The only consideration that can be done is that the panel buckling is
sensitive to the crew spacing and that lower load factor are obtained for
larger screw spacing, because in that case the sheathing section is more
stiff.
33
Wall stud sheathed on one flange
All the studies described before have been extended to the case of a wall
sheathed on one side. In fact, it can be possible to fasten a structural panel
only on one flange and using a non-structural panel on the other flange of a
section. Therefore, the three models: a) constraints with stiffness equal to =,
b) constraints with infinite stiffness and , c) constraints with fixed stiffness
have been analyzed. Figure45 summarize the results for the first model.
OSBwall96x12_constr124
FEM-local
FEM-Dist1
FEM-Dist2
FEM-GL-Flex-tors
FEM-Gl-Flex
CUFSM-local
CUFSM-Dist1
CUFSM-Dist2
CUFSM-Gl.-Flex-Tors
CUFSM-GL-Flex
CUFSM-C-Loc
CUFSM-C-Dist1
CUFSM-C-Dist2
CUFSM-C-Flex-Tors
CUFSM-C-Flex
FEM-Panel
300
250
eigenvalue
200
150
100
50
0
0
6
12
18
24
30
36
42
48
screw spacing
Figure 50: Buckling behavior of a wall stud sheathed on one side_contsr 124.
FEM-local
CUFSM-local
CUFSM-C-Loc
80
scr
60
40
20
0
0
6
12
18
24
30
36
42
48
screw spacing
Figure 46: Local Buckling behavior of a wall stud sheathed on one side_contsr 124.
34
The local buckling of a one-side sheathed wall stud is not influenced by
the presence of sheathing panel. In fact, as it can be noticed, in case of
sheathed wall attached with screw spaced from 0 to 24inches the local
behavior follows that of a no-sheathed wall.
FEM-Dist1
CUFSM-Dist1
CUFSM-C-Dist
120
100
eigenvalue
80
60
40
20
0
0
6
12
18
24
30
36
42
48
screw spacing
Figure 47: Distortional 1of a wall stud sheathed on one side_contsr 124.
FEM-Dist2
CUFSM-Dist2
CUFSM-C-Dist2
250
200
eigenvalue
150
100
50
0
0
6
12
18
24
30
36
42
screw spacing
Figure 48: Distortional2 of a wall stud sheathed on one side_contsr 124.
48
35
The distortional buckling 1 and 2 seem to be is influenced by the
presence of the sheathing panelwhen the screw spacing is between 1” and
12”. For larger screw spacing the strength increment is very low.
FEM-GL-Flex-tors
CUFSM-Gl.-Flex-Tors
CUFSM-C-Flex-Tors
50
eigenvalue
40
30
20
10
0
0
6
12
18
24
30
36
42
48
screw spacing
Figure 49: Global Flexural torsional of a wall stud sheathed on one side_contsr 124.
This model shows that the presence of the sheathing panel would not
effect the Flexural Torsional Buckling, since the FEM results are very close
to the results for a single stud.
Therefore, the diea is that there is something wrong in the model. Figure
50 summarizes the results.
OSBwall96x12_spring
FEM-local
FEM-Dist1
FEM-Dist2
FEM-GL-Flex-tors
FEM-Gl-Flex
CUFSM-local
CUFSM-Dist1
CUFSM-Dist2
CUFSM-Gl.-Flex-Tors
CUFSM-GL-Flex
CUFSM-C-Loc
CUFSM-C-Dist1
CUFSM-C-Dist2
CUFSM-C-Flex-Tors
CUFSM-C-Flex
FEM-Panel
300
250
eigenvalue
200
150
100
50
0
0
6
12
18
24
30
36
42
48
screw spacing
36
Wall stud sheathed on one side with screw modelled with spring
with fixed stiffness.
OSBwall96x12_spring
FEM-local
CUFSM-local
CUFSM-C-Loc
80
eigenvalue
60
40
20
0
0
6
12
18
24
30
36
42
48
screw spacing
Figure 51: OSB– Local Buckling
Local buckling
The local buckling is not influenced by the presence of the sheathing
panel. In fact, the behavior of the wall either sheathed on one side or on two
sides is the same as a non-sheathed wall.
37
OSBwall96x12_spring
FEM-Dist1
CUFSM-Dist1
CUFSM-C-Dist
140
120
eigenvalue
100
80
60
40
20
0
0
6
12
18
24
30
36
42
48
screw spacing
Distortional buckling
The distortional buckling is sensitive to the presence of sheathing
panels. In fact as can be seen in the following figure, the presence of one
panel increment the strength of the load factor
38
OSBwall96x12_spring
FEM-Dist2
CUFSM-Dist2
CUFSM-C-Dist2
300
250
eigenvalue
200
150
100
50
0
0
6
12
18
24
30
36
screw spacing
Distortional buckling2
The distortional buckling is sensitive to the presence of
42
48
39
OSBwall96x12_spring
FEM-GL-Flex-tors
CUFSM-Gl.-Flex-Tors
CUFSM-C-Flex-Tors
100
eigenvalue
80
60
40
20
0
0
6
12
18
24
30
36
42
48
screw spacing
Figure 54: Global Flexural torsional of a wall stud sheathed on one side_contsr 124.
Flexural torsional
In spring model, the global flexural torsional buckling occurs as first
mode, for all the considered screw spacing.
As shown in the graph, it seems to be not sensitive to the presence of 1
sheathing panel, and therefore it is not sensitive to the screw spacing.
Instead, as shown in the previous section, the presence of two sheathing
panels improve the wall beahviour as long as te screw spacing is less than
24 inches (Figure..) .
40
OSBwall96x12_spring
FEM-Panel-spring
FEM-Panel-general constraint
300
250
eigenvalue
200
150
100
50
0
0
6
12
18
24
30
36
42
48
screw spacing (in.)
Figure 55: Panel buckling of a wall stud sheathed on one side_contsr 124.
OSB+GWBwall96x12_constr124
FEM-local
FEM-Dist1
FEM-Dist2
FEM-GL-Flex-tors
FEM-Gl-Flex
CUFSM-local
CUFSM-Dist1
CUFSM-Dist2
CUFSM-Gl.-Flex-Tors
CUFSM-GL-Flex
CUFSM-C-Loc
CUFSM-C-Dist1
CUFSM-C-Dist2
CUFSM-C-Flex-Tors
CUFSM-C-Flex
FEM-Panel
300
250
eigenvalue
200
150
100
50
0
0
6
12
18
24
30
36
42
48
screw spacing
REFERENCES
[1] Boudreault F.A., Seismic Analysis of Steel Frame/Wood Panel Shear
Walls, Thesis, Dept. of Civil Engineering and Applied Mechanics, McGill
Univ., Montreal, 2005.
[2] Fiorino et al. (ref.)
[3] Richard J. Schmidt and Russell C. Moody (1989) Modelling laterally
loaded
light-frame building, Journal of structural engineering, Vol. 115, No. 1,
pp. 201-217.(mail12febr)
[4] Ajaya K. Gupta and George P. Kuo (1987) Modelling of a wood-framed
house, Journal of structural engineering, Vol. 113, No. 2, pp. 260-278.
[5] Gypsum Association, Gypsum Board Typical Mechanical and Physical
Properties (GA-255-05), 2005
[6] Schafer, B.W., Sangree, R.H., Guan, Y., Experiments on Rotational
Restraint of Sheathing, Final Report for American Iron and Steel Institute
– Committee on Framing Standards, 2007.
41

elastic buckling of stud walls xjhu

Transcription

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