Effect of overturning restraint on performance of shear walls

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Jul 18, 2012 (5 years and 2 months ago)

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Effect of overturning restraint on performance of shear walls
Ni, Chun
1
and Karacabeyli, Erol
2
ABSTRACT
Nailed shear walls are the primary lateral load-resisting components in wood-frame construction. They possess excellent
energy dissipating characteristics, which make them a suitable choice in resisting seismic loads. In designing wood-frame
nailed shear walls, hold-down (or tie-down) connections are often required at both ends of the shear walls to provide restraint
against overturning moment. Dead loads, sheathings above and below openings, and perpendicular walls connected at the end
of shear walls may help to reduce the forces to be resisted by hold-down connectors. In this paper, results from full-scale shear
wall specimens tested under lateral loads with and without hold-down connections, and with and without dead loads, are
presented. Two methods, one empirical and one mechanics-based, are developed to account for the effects of vertical loads
and perpendicular walls on the performance of shear walls. Predicted capacities from both methods are found to be in
reasonable agreement with the test results.
INTRODUCTION
In most wood design codes, lateral load capacities for shear walls are given for walls which are fully restrained against
overturning by means of hold-down (or tie-down) connections. The hold-down connections, on the other hand, are not always
used in conventional wood-frame construction, particularly at the end of wall segments near openings (e.g. next to a door
opening). Dead loads, adjacent sheathings above and below openings, and perpendicular walls (e.g. corner framing) at the end
of shear wall segments may help reduce the uplift forces to be resisted by the hold-down connectors. Lateral load tests
conducted by Dolan and Heine (1997c) showed that partial overturning restraints (such as corner framing on each end)
provided a hold-down effect that increased the wall capacity and ductility when compared to walls without overturning
restraint.
Sugiyama (1981) proposed an empirical equation to calculate the lateral load carrying capacity and the stiffness of shear walls
without hold-downs around openings. His empirical equation forms the basis of the “perforated” shear wall (shear walls with
openings) design method which appears in the Standard Building Code 1994 Revised Edition (SBC 1994) and the Wood
Frame Construction Manual for One- and Two- Family Dwellings - 1995 High Wind Edition (WECM 1996). Although
Sugiyama method results in conservative capacities for shear walls with openings, it does not give capacities for individual
wall segments. Neither it accounts for the effect of dead loads. Since the current design practice is based on assigning
capacities to individual segments, an attempt is made here to assign capacities to shear wall segments without hold-downs.
In order to quantify the effects of overturning restraints on the performance of wood-frame shear walls, full-scale shear wall
specimens were tested under lateral loads with and without hold-down connections, and with and without dead loads. Two
methods, one empirical and one mechanics-based, are developed to account for the effects of uplift restraint on the
performance of shear walls. Results from shear walls subjected to monotonic and reversed cyclic loads were used to verify
the proposed methods. The findings of the study are anticipated to be instrumental in refining current design methodologies
for shear walls.
PROPOSED METHODS
Mechanics-Based Approach
Figure 1 shows a shear wall with partial uplift restraints (force P). For studs where two panels meet, with the assumption that

1 Wood Engineering Scientist, Forintek Canada Corp., 2665 East Mall, Vancouver, British Columbia, Canada.
2 Group Leader, Wood Engineering Department, Forintek Canada Corp., 2665 East Mall, Vancouver, British Columbia,
Canada.
the forces from nails on either side of the gap act vertically and opposed to each other, the studs work as only a splice plate
that transfers the shear from one panel to another through the nail joints. Because the nail forces from adjacent panels “cancel
each other out”, no appreciable axial force would be generated in the studs. However, the nail forces at the end studs do not
“cancel out”; consequently, the end studs must carry the resulting axial force and that force must be transferred to the
foundation. For an end stud under compression, the force is directly supported by foundation. For an end stud under tension,
in the absence of a hold-down connection, the force is resisted by nail joints attaching the edge of the panel to the bottom plate.
Assuming that the shear wall reaches its lateral load capacity when all nails along the bottom plate reach their load capacity,
C
N
, based on force equilibrium, the following equations can be obtained
L
4
V
1
N
N
C
2
V
1
V
H
V
3
2
N
N
C
P
V
a) Forces on wood frame members
4
V
2
V
A
L
H
V
L
V
3
P
V
b) External forces on wall segment
Figure 1 A simplified model for shear walls without overturning restraints.
N
CNV
12
=
(1)
N
CNV
23
=
(2)
PL
L
LVHV
v
+−= )
2
(
32
(3)
where
H – height of the wall
L – length of the wall
L
v
– length of bottom plate where the nails are required to resist the vertical tension force
N
1
– number of nails resisting lateral load along bottom plate
N
2
– number of nails resisting vertical tension force along bottom plate over length L
v
C
N
– lateral load capacity of a single nailed joint
P – uplift restraint force on the end stud of a shear wall segment
For a shear wall segment in a given storey, the uplift restraint force, P is the resultant of the following forces: a) resultant force
from upper storeys (negative if it is a net uplift force), b) forces due to dead weight, corner framing or sheathings above and
below openings in that storey, c) the capacity of hold-down connection in that storey. If P is less than zero, a hold-down
connection would be required.
Assuming N is the total number of nails along the bottom plate, then the N
1
, N
2
, and L
v
have the following relations
NNN =+
21
(4)
N
L
N
L
N
LL
vv
==

21
(5)
Based on Equations 1, 2, and 5, the Equation 3 can be rewritten as
N
C
PL
L
N
N
LNHN +−=
)
2
(
2
21
(6)
Assuming Μ is the total number of nails along the end stud of a particular shear wall segment, then MC
N
would be the
unbalanced uplift force at the wall's shear capacity, and parameter
N
MC
P
=
φ
, can be defined as uplift restraint effect.
Parameter φ will equal 1.0 if uplift restraint is large enough to prevent end stud uplift at the ultimate shear wall capacity.
Let
N
N
1

,
N
N
2

, and
L
H

, where parameter α is the ratio of the lateral load capacity of walls with partial uplift
restraint compared to the capacity of walls with full uplift restraint. Parameter γ is the aspect ratio of the shear wall segment.
Equation 6 can be rewritten as
φγββαγ +−=
)
2
1
1(
(7)
Since
1=+
β
α
(Equation 4), α is then obtained from Equation 7 as
γγφγα −++=
2
21
(8)
Figure 2 shows the effect of uplift
restraint on the lateral load capacity
of a wall, based on Equation 8. It is
clear that both the aspect ratio and
the uplift restraint influence the
lateral load capacity of shear wall.
The shorter the shear wall, the
greater the influence from uplift
restraint.
Empirical Approach
An empirical equation is obtained by
fitting the equation to test results of
shear wall segment tested with and
without hold-down connections at
both end studs. The details of the
shear wall tests will be discussed in
the following section. The ratio of
the lateral load capacity of a wall
with no uplift restraint to a wall with
full uplift restraint can be closely
represented by the following
equation
L
H
+
=
1
1
α
(9)
As previously mentioned, the uplift restraints due to dead weight, corner framing or sheathings above and below an opening
generally provide a hold-down effect that increase wall capacity and ductility when compared to walls without any uplift
0%
20%
40%
60%
80%
100%
0% 20% 40% 60% 80% 100%
φ
φφ
φ
, End stud uplift restraint
α
α
α
α
L=2'
L=4'
L=8'
L=16'
L=32'
Figure 2 Effect of uplift restraint on the lateral load capacity of a shear wall based
on mechanics-based approach.
restraints. To take those effects into account, Equation 9 is modified as follows:
n
L
H
)1(1
1
φ
α
−+
=
(10)
where the parameter φ is the uplift
restraint effect as previously
defined. Because
HvMC
dN
=
,
where v
d
is the ultimate unit lateral
load capacity of the shear wall, the
parameter φ can be rewritten as
Hv
P
d

, which is easier to use in
practice. Parameter φ equals 1.0 if
uplift restraint is sufficiently large
to prevent end stud uplift at the
ultimate shear wall capacity.
Parameter n can be obtained
through the non-linear least square
method based on test results. It was
found that n = 3 best fitted the test
data. Figure 3 shows the effect of
uplift restraint on the lateral load
capacity of a wall based on
Equation 10.
SHEAR WALL TESTS
Shear Wall Configuration
Two groups of full-scale shear walls were tested under monotonic and reversed cyclic tests. The details of the shear walls are
summarized in Tables 1 and 2. These two groups were designed to evaluate the effect of shear wall length and vertical load
on the performance of shear walls without hold-downs. All shear wall specimens were constructed using NLGA No. 2 and
better grades of Spruce-Pine-Fir 38mm × 89mm

lumber for the wall studs, and 1650f-1.5E MSR 38mm × 89mm

lumber for
the top and bottom plates. Stud members were spaced at 400mm on center. Canadian Softwood Plywood (CSP), 9.5mm thick,
was used to sheath the walls. The sheathing panels were connected to the framing members with 8d common nails at nail
spacing 150 mm around the panel perimeter, and 300 mm elsewhere. Conditioning and testing were performed at ambient
laboratory conditions where average oven-dry moisture content of both lumber and the plywood were approximately 9 percent.
The average oven-dry relative density of the lumber was approximately 0.44.
Table 1 Test matrix of shear walls with different wall lengths.
Wall
No.
Wall length
(m)
No. of
tests
Hold-down Panel Orientation Fastener Load protocol
1 1.22 4
1
Yes 9.5 mm CSP Vertical 8d common nail Monotonic & ISO97
2 2.44 4
1
Yes 9.5 mm CSP Vertical 8d common nail Monotonic & ISO97
3 4.88 4
1
Yes 9.5 mm CSP Vertical 8d common nail Monotonic & ISO97
4 4.88 2
2
Yes 9.5 mm CSP Horizontal 8d power nail Monotonic & ISO97
5 1.22 4
1
No 9.5 mm CSP Vertical 8d common nail Monotonic & ISO97
6 2.44 4
1
No 9.5 mm CSP Vertical 8d common nail Monotonic & ISO97
7 4.88 4
1
No 9.5 mm CSP Vertical 8d common nail Monotonic & ISO97
8 4.88 2
2
No 9.5 mm CSP Horizontal 8d power nail Monotonic & ISO97
Note: No vertical load applied.
1
Two walls were tested under monotonic, the other two were tested under reversed cyclic load ISO 97.
2
One walls was tested under monotonic, the other one was tested under reversed cyclic load ISO 97.
0%
20%
40%
60%
80%
100%
0% 20% 40% 60% 80% 100%
φ
φφ
φ
, End stud uplift restraint
α
α
α
α
L=2'
L=4'
L=8'
L=16'
L=32'
Figure 3 Effect of uplift restraint on the lateral load capacity of a shear wall based
on empirical approach.
Table 2 Test matrix of shear walls with different vertical loads
1
.
Wall
No.
Wall length
(m)
Vertical load
(kN/m)
No. of
tests
Hold-down Panel Orientation Fastener
Load
protocol
9 2.44 0 2 Yes 9.5 mm CSP Vertical 8d common nail Monotonic
10 2.44 18.2 2 Yes 9.5 mm CSP Vertical 8d common nail Monotonic
11 2.44 0 2 No 9.5 mm CSP Vertical 8d common nail Monotonic
12 2.44 4. 6 2 No 9.5 mm CSP Vertical 8d common nail Monotonic
13 2.44 9.1 2 No 9.5 mm CSP Vertical 8d common nail Monotonic
14 2.44 13.7 2 No 9.5 mm CSP Vertical 8d common nail Monotonic
15 2.44 18.2 2 No 9.5 mm CSP Vertical 8d common nail Monotonic
1
Constant vertical loads were applied by two hydraulic actuators, at a distance of 609 mm from the edge of the wall, as point
loads on the load spreader which was attached to the double top plates.
The bottom plates of the walls were attached to the foundation through 12.7 mm (1/2 inch) diameter anchor bolts spaced at
406 mm on center. The distance between the center of the first anchor bolt and the outer edge of the wall was 203 mm. The
same anchorage was used between the double top plates and the load spreader. The walls with hold-down connections used
commercially available hold-downs attached to the double end studs through two 15.9 mm (5/8 inch) diameter bolts, and to
the foundation by one 15.9 mm (5/8 inch) diameter bolt. A more detailed description of the test apparatus is given by
Karacabeyli and Ceccotti (1996).
Load Protocols
Two loading protocols were used: 1) a
monotonic loading, and 2) a reversed cyclic
loading – ISO 97. The ISO 97 protocol
(Figure 4) has been proposed for the working
draft of the ISO Standard "Timber structures
– Joints made with mechanical fasteners –
Quasi-static reversed-cyclic test method". The
rates of displacement were 7.5 mm/min for the
monotonic test and 20 mm/sec for the reversed
cyclic test.
TEST RESULTS
Test results are summarized in Tables 3 and 4.
As expected, the ultimate unit lateral load
capacities were similar for shear walls with
different wall lengths when hold-downs were
installed. A combination of nail withdrawal,
nail pull-through, and nail chip-out was
observed at the perimeter of the panels.
The ultimate unit lateral load capacities from walls tested at different lengths were quite different when the shear walls were
built without hold-downs and tested without vertical loads. The unit lateral load capacity was strongly influenced by the wall
aspect ratio (height/length). The unit lateral capacity varies inversely with the wall aspect ratio. The end studs of the walls with
no hold-downs and vertical loads separated almost completely from the bottom plate at large displacements. Without hold-
downs, the lifting force strove to draw the panel apart from the bottom plate and force the nails to act almost perpendicular
to the edge of the panel. This redistribution of the nail forces resulted in a lower load capacity for the shear wall: the shorter
the wall length, the greater the effect on the lateral load capacity.
For shear walls with or without hold-downs, the secant stiffness, obtained from a line drawn through points at 10% and 40%
of the maximum load, were found to be similar. This suggests that at relatively low load levels, the shear wall stiffness is not
significantly influenced by the use of hold-downs. However, the ultimate displacements of shear walls were greatly influenced
-150
-100
-50
0
50
100
150
0 50 100 150 200 250 300
Time (sec)
Displacement (mm)
ISO 97
Figure 4 ISO 97 loading protocol.
by hold-downs. Without hold-downs, the ultimate displacement of a 2.44 m shear wall had less than 50% of the ultimate
displacement of the shear wall with hold-downs.
Table 3 Summary of test results of shear walls with different wall lengths.
With hold-down Without hold-down
Wall length
(m)
No. of
Tests
P
max

1
(kN/m)

u

2
(mm)
K
3
(kN/m/mm)
No. of
Tests
P
max

1
(kN/m)

u

2
(mm)
K
3
(kN/m/mm)
Ramp 2 8.5 114 0.428 2 2.9 46 0.491
1
st

4
2 8.7 99 0.425 2 3.0 39 0.5241.22
3
rd

5
7.2 87 0.546 2.5 43 0.615
Ramp 2 8.9 85 0.899 2 5.0 31 0.773
1
st

4
2 8.7 71 0.878 2 5.1 28 0.8182.44
3
rd

5
6.9 57 0.993 4.2 28 0.944
Ramp 2 7.4 106 0.861 2 6.9 46 0.925
1
st

4
2 8.3 73 1.0584.88
3
rd

5
6.6 59 1.206
Ramp 1 9.1 77 0.598 1 5.8 44 0.544
1
st

4
1 8.0 50 0.913 1 5.3 38 0.6384.88
3
rd

5
6.6 40 0.882 4.6 31 0.721
Note: No vertical load applied.
1
P
max
is the average value of maximum unit lateral load.
2

u
is the average value of ultimate displacement, which is defined as the displacement at 80% of maximum load on the
descending portion of the load-displacement curve.
3
K is the average value of the secant stiffness between 10% and 40% of the maximum load.
4
Values in row 1
st
is the average (+/-) first envelope in the reversed cyclic test.
5
Values in row 3
rd
is the average (+/-) third envelope in the reversed cyclic test.
Table 4 Summary of test results of 2.44 m shear walls with different vertical loads.
With hold-down Without hold-down
Vertical load
(kN/m)
No. of
Tests
P
max

1
(kN/m)

u

2
(mm)
K
3
(kN/m/mm)
No. of
Tests
P
max

1
(kN/m)

u

2
(mm)
K
3
(kN/m/mm)
0.0 2 8.7 88 0.560 2 4.6 43 0.628
4.6 2 7.0 85 0.507
9.1 2 7.4 103 0.521
13.7 2 8.5 109 0.511
18.2 2 9.0 107 0.640 2 8.7 111 0.568
1
P
max
is the average value of maximum unit lateral load.
2

u
is the average value of ultimate displacement, which is defined as the displacement at 80% of maximum load on the
descending portion of the load-displacement curve.
3
K is the average value of secant stiffness between 10% and 40% maximum load.
This negative impact on ductility characteristics was offset by the vertical loads which had a large influence on the unit lateral
load capacity of shear walls without hold-downs. By applying a vertical load of 18.2 kN/m which was sufficient to resist
overturning moment, the shear wall was able to reach its full lateral load capacity. Without the vertical load, the unit lateral
load capacity of the 2.44 m shear wall was only about 50% of the capacity of shear wall with hold-downs. With a vertical load
of 4.6 kN/m, the unit lateral load capacity of a 2.44 m shear wall reached to 80% of its full capacity. The rate of increase in
lateral load capacity decreased as the applied vertical loads increased. The ultimate displacement follows almost the same trend
as lateral load capacity.
COMPARISON
The test and predicted lateral load capacities are summarized in Tables 5 and 6. The comparison is also presented in Figure
5. The test data reported by Dolan and Heine (1997a, 1997b) are also included. The walls tested by Dolan and Heine were
constructed with 38 mm × 89 mm Spruce-Pine-Fir lumber as framing members. The studs were spaced at 406 mm on center.
The exterior and interior sheathings were 11 mm (7/16") OSB and 12.5 mm (1/2") gypsum wallboard, respectively. The OSB
sheathing was connected to the framing members with 8d common nails at nail spacing 150 mm around panel perimeter, and
300 mm elsewhere. The gypsum wallboard were connected to the framing members with 13 gauge drywall nails spaced at 180
mm around the panel perimeter, and 250 mm elsewhere.
Predictions based on mechanics-based and empirical approach are in good agreement with the test data (Figures 5a and 5b).
The mechanics-based approach is more conservative compared to empirical approach. For walls tested under reversed cyclic
loads, the prediction applies to both first and third (stabilized) envelope curves.
Table 5 Comparison of test and predicted lateral load capacities for shear walls with different wall lengths.
With hold-down Without hold-down
Wall length
(m)
No. of
Tests
Min.
(kN/m)
Max.
(kN/m)
Avg.
(kN/m)
No. of
Tests
Min.
(kN/m)
Max.
(kN/m)
Avg.
(kN/m)
P
NHD
/P
HD

1
α
1

2
α
2

3
Ramp 2 8.3 8.7 8.5 2 2.8 3.0 2.9 0.34 0.24 0.33
1
st

4
2 8.6 8.9 8.7 2 2.6 3.4 3.0 0.34 0.24 0.331.22
3
rd

5
7.0 7.4 7.2 2.2 2.8 2.5 0.35 0.24 0.33
Ramp 2 8.7 9.2 8.9 2 4.6 5.4 5.0 0.56 0.41 0.50
1
st

4
2 8.5 8.8 8.7 2 4.9 5.3 5.1 0.59 0.41 0.502.44
3
rd

5
6.8 7.0 6.9 4.0 4.4 4.2 0.61 0.41 0.50
Ramp 2 7.1 7.7 7.4 2 6.7 7.0 6.9 0.92 0.62 0.67
1
st

4
2 8.1 8.6 8.34.88
3
rd

5
6.6 6.7 6.6
Ramp 1 9.1 1 5.8 0.64 0.62 0.67
1
st

4
1 8.0 1 5.3 0.66 0.62 0.674.88
3
rd

5
6.6 4.6 0.71 0.62 0.67
Ramp 1 12.6 1 9.2 0.73 0.82 0.83
1
st

4
1 10.1 1 9.7 0.96 0.82 0.8312.2
6
3
rd

5
8.6 8.2 0.95 0.82 0.83
Note: No vertical load applied.
1
P
NHD
– the capacity of shear wall without hold-down; P
HD
- the capacity of shear wall with hold-down.
2
Prediction based on mechanics-based approach.
3
Prediction based on empirical approach.
4
Values in row 1
st
is the average (+/-) first envelope in the reversed cyclic test.
5
Values in row 3
rd
is the average (+/-) third envelope in the reversed cyclic test.
6
Test data from Dolan and Heine (1997a, 1997b).
Table 6 Comparison of test and predicted lateral load capacities for 2.44 m shear walls with different vertical loads.
With hold-down Without hold-down
Vertical load
(kN/m)
No. of
Tests
Min.
(kN/m)
Max.
(kN/m)
Avg.
(kN/m)
No. of
Tests
Min.
(kN/m)
Max.
(kN/m)
Avg.
(kN/m)
P
NHD
/P
HD

1
α
1

2
α
2

3
0.0 2 8.6 8.9 8.7 2 4.5 4.7 4.6 0.53 0.41 0.50
4.6 2 6.9 7.1 7.0 0.80 0.58 0.70
9.1 2 7.2 7.6 7.4 0.85 0.73 0.89
13.7 2 8.3 8.6 8.5 0.97 0.87 0.98
18.2 2 8.9 9.2 9.0 2 8.7 8. 8 8.7 1.00 1.00 1.00
1
P
NHD
– the capacity of shear wall without hold-down; P
HD
- the capacity of shear wall with hold-down.
2
Prediction based on mechanics-based approach.
3
Prediction based on empirical approach.
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12 14
Wall Length (m)
PNHD / PHD
Test
Mechanics-based approach
Empirical approach
a) shear walls with different wall lengths
0
0.2
0.4
0.6
0.8
1
0 4 8 12 16 20
Vertical Load (kN/m)
PNHD/PHD
Test
Mechanics-based approach
Empirical approach
b) shear walls with different vertical loads
Figure 5 Comparison of test and predicted shear wall lateral load capacities.
CONCLUSION
Both the aspect ratio and the amount of uplift restraint influences the lateral load capacity of a shear wall without hold-downs.
The unit lateral capacity and ultimate displacement are reduced as the aspect ratio increases, especially when no vertical loads
are applied. Shear walls without hold-downs reached their full capacity when sufficient amount of vertical loads were applied
to resist the overturning moment. Without vertical loads, the unit lateral load capacity of a 2.44 m shear wall was about 50%
of its full capacity and ultimate displacement. With a vertical load of 4.6 kN/m which was only sufficient to resist 25% of the
overturning moment, the unit lateral load capacity of a 2.44 m shear wall was able to reach to 80% of its fully restrained
capacity and ultimate displacement. The rate of increase in lateral load capacity decreased as the applied vertical loads
increased.
A mechanics-based method and an empirical method were developed to account for the partial uplift resistance provided by
dead loads, corner framing, and sheathings above and below the openings. Predictions based on mechanics-based and
empirical methods are in reasonable agreement with test data. The mechanics-based method is more conservative compared
to empirical method. The findings of the study are anticipated to be instrumental in refining current design methodologies for
shear walls.
REFERENCES
Dolan, J.D., Heine, C.P., 1997a. Monotonic tests of wood-frame shear walls with various openings and base restraint
configurations. VPI&SU Report No. TE-1997-001, Department of Wood Science and Forests Products, Virginia Polytechnic
Institute and State University, Blacksburg, Virginia.
Dolan, J.D., Heine, C.P., 1997b. Sequential phased displacement cyclic tests of wood-frame shear walls with various openings
and base restraint configurations. VPI&SU Report No. TE-1997-002, Department of Wood Science and Forests Products,
Virginia Polytechnic Institute and State University, Blacksburg, Virginia.
Dolan, J.D., Heine, C.P., 1997c. Sequential phased displacement tests of wood-framed shear walls with corners. VPI&SU
Report No. TE-1997-003, Department of Wood Science and Forests Products, Virginia Polytechnic Institute and State
University, Blacksburg, Virginia.
Karacabeyli, E., Ceccotti, A., 1996. Test results on the lateral resistance of nailed shear walls. Proceedings of the International
Wood Engineering Conference, New Orleans, USA. Vol.2, p.179-187.
SBC, 1994. Standard Building Code - Revised Edition, Southern Building Code Congress International, Birmingham, AL.
Sugiyama, H., 1981. The evaluation of shear strength of plywood-sheathed walls with openings, Mokuzai Kogyo (Wood
Industry), Vol.36, No.7.
WECM, 1996. Wood Frame Construction Manual for One- and Two- Family Dwellings – SBC High Wind Edition, American
Forest and Paper Association, Washington, D.C.