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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


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.


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




8” 61.981 Global_ Panel


Wall sheathed

with OSB

panels


continuous 63.07 64.486 Local _ Stud



Wall sheathed

with GWB

panel


8





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


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).


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




Wall sheathed

with OSB

panels






continuous 63.07 51,218 Global Flex-Tors








Wall sheathed

with GWB

panel


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.


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


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


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


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.


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

GWB wall, respectively.

OSBwall96x12

0

20

40

60

80

100

120

140

160

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

scr

FEM-local FEM-GL-Flex-tors FEM-Gl-Flex FEM-Dist2FEM-dist1 CUFSM-local CUFSM-Gl.-Flex-Tors CUFSM-Dist2CUFSM-dist1 CUFSM-GL-Flex CUFSM-C-Loc CUFSM-C-FlexCUFSM-C-Flex-Tors CUFSM-C-Dist CUFSM-C-Dist2

Figure 31: Trend of the buckling modes for an OSB 96”x12”wall studs.

GWB-96x112 constr 1-2-4

0

20

40

60

80

100

120

140

160

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

scr

FEM-local FEM-Flex-Tors FEM -Flex FEM-dist1 FEM-dist2CUFSM-local CUFSM-Flex-Tors CUFSM-Flex CUFSM-Dist1 CUFSM-Dist2CUFSM-C-Loc CUFSM-C-Flex-Tors CUFSM-C-flex CUFSM-C-Dist CUFSM-C-Dist2

Figure 32: Trend of the buckling modes for an GWB 96”x12”wall studs.

OSB 96x24”: Model with general constraints direction 1-2-4


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 Screw spacing CUFSM (Load

factor)

Abaqus (Load

factor) Buckling mode

Without

connection - 11.125 11.325

Global

Flex-Tors

continuous 60.57 60.671 Global

Flex-Tors

2” 60.669 Global

Flex-Tors

3” 59.637 Local

4” 59.665 Local

6” 59.59 Local

8” 59.591 Local

12” 59.569 Local

Wall sheathed

with OSB

panels

24” 59.526 Local

20

48” 51.785

Global

Flex-Tors

continuous 60.44 60.23 Global

Flex-Tors

2” 60.23 Global

Flex-Tors

3” 59.65 Local

4” 59.71 Local

6” 59.59 Local

8” 59.59 Local

12” 59.57 Local

24” 59.53 Local

Wall sheathed

with GWB

panel

48” 51.459

Global

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.


Figure 34: OSB 96x24in – Deformed shapes corresponding to Local, Global Flexural-

Torsional and Global Flexural from the top to the bottom.

Model Screw

spacing

Local

buckling

Dist

buckl1

Dist

buckl2

Global

flex-

tors

Global

dist+flex


mode1

235.93

mode3

60.57

mode1

length

96”

534.71

mode3

length

96”

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

Wall

sheathed

with OSB

panel

Abaqus

48” 59.50 77.20 155.20 51.79 600.58

Table 7: OSB 96x24-constr1-2-4

Model Screw

spacing

Local

buckling

Dist

buckl1

Dist

buckl2

Global

flex-

tors

Global

dist+flex

Wall

sheathed CUFSM contin 63.06 114.05 263.7 60.44 453.31

mode3

22

mode1 mode3 mode1

length

96”

length

96”

contin 61.861 101.43 220.49 60.23 474.76

2” 61.176 100.69 196.66 60.23 474.35

3” 59.651 99.71 192.15 60.227 474.18

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

with GWB

panel

Abaqus

48” 59.499 76.323 155.25 51.459 452.88

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.


OSB 96x24- constr124

0

100

200

300

400

500

600

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

eige

nval

ue

FEM-local FEM-Dist1 FEM-Dist2 FEM-Flex.Tors FEM-FlexCUFSM-Local CUFSM-Dist1 CUFSM-Dist2 CUFSM-Flex Tors CUFSM-FlexCUFSM-C-Local CUFSM-C-Dist1 CUFSM-C-Dist2 CUFSM-C-Flex Tors CUFSM-C-Flex

Figure 35: Comparative study of the buckling behaviors of GWB sheathed wall stud

GWB wall 96x24 constr1-24

0

50

100

150

200

250

300

350

400

450

500

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

eige

nval

ue

FEM-local FEM-Dist1 FEM-Dist2 FEM-Flex-Tors FEM-FlexCUFSM-local CUFSM-Dist1 CUFSM-Dist2 CUFSM-Flex-Tors CUFSM-FlexCUFSM-C-local CUFSM-C-Dist1 CUFSM-C-Dist2 CUFSM-C-Flex-Tors CUFSM-C-Flex

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 Screw

spacing

Local

buckling

Dist

buckl1

Dist

buckl2

Global

flex-tors

Global

flex


mode1

263.7

mode3

60.44

mode1

length

96”

453.31

mode3

length

96”

contin 60.672 86.196 173 59.069 291.98

2” 60.442 85.929 175.5 56.538 211.97

3” 60.289 84.956 167.31 54.724 178.25

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

Wall

sheathed

with

GWB

panel Abaqus

48” 59.872 77.407 75.447 37.728 61.881

Table14: Comparison between load factors obtained in CUFSM and Abaqus in case of

Spring model.

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748screw spacing

scr

FEM-local FEM-Dist1 FEM-Dist2 FEM-GL-Flex-torsFEM-Gl-Flex CUFSM-local CUFSM-Dist1 CUFSM-Dist2CUFSM-Gl.-Flex-Tors CUFSM-GL-Flex CUFSM-C-Loc CUFSM-C-Dist1CUFSM-C-Dist2 CUFSM-C-Flex-Tors CUFSM-C-Flex FEM-Panel

Figure 37:Buckling behaviors of OSB sheathed wall stud with screw modeled by spring

with fixed stiffness

26

OSBwall96x12

0

20

40

60

80

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748screw spacing

scr

FEM-local CUFSM-local CUFSM-C-Loc

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).


OSBwall96x12

0

20

40

60

80

100

120

140

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748screw spacing

scr

FEM-Dist1 CUFSM-Dist1 CUFSM-C-Dist

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

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233343536373839404142434445464748screw spacing

scr

FEM-Dist2 CUFSM-Dist2 CUFSM-C-Dist2


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


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

0

50

100

150

200

250

300

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FEM-Dist2 CUFSM-Dist2 CUFSM-C-Dist2 FEM-Flex CUFSM-C-Flex

Figure 41: OSB– Distortional Buckling 2- screw spacing equal to 24”

30

OSBwall96x12

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FEM-GL-Flex-tors CUFSM-Gl.-Flex-Tors CUFSM-C-Flex-Tors

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%.


OSBwall96x12

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FEM-Gl-Flex CUFSM-GL-Flex CUFSM-C-Flex

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

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FEM-Panel-spring FEM-Panel-general constraint

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.


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

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Figure 50: Buckling behavior of a wall stud sheathed on one side_contsr 124.


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FEM-local CUFSM-local CUFSM-C-Loc

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.


0

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Figure 47: Distortional 1of a wall stud sheathed on one side_contsr 124.


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Figure 48: Distortional2 of a wall stud sheathed on one side_contsr 124.


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.


0

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ueFEM-GL-Flex-tors CUFSM-Gl.-Flex-Tors CUFSM-C-Flex-Tors

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

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36

Wall stud sheathed on one side with screw modelled with spring

with fixed stiffness.

OSBwall96x12_spring

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ueFEM-local CUFSM-local CUFSM-C-Loc

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.


OSBwall96x12_spring

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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

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Distortional buckling2

The distortional buckling is sensitive to the presence of


OSBwall96x12_spring

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FEM-GL-Flex-tors CUFSM-Gl.-Flex-Tors CUFSM-C-Flex-Tors

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..) .

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OSBwall96x12_spring

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FEM-Panel-spring FEM-Panel-general constraint

Figure 55: Panel buckling of a wall stud sheathed on one side_contsr 124.

OSB+GWBwall96x12_constr124

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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.

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