APPENDIX E
DESIGN EXAMPLE
This example demonstrates the design methods for analysis of the lateral force resisting system
of a one-story house (Figure E1). The design lateral load is distributed between the shear walls
according to two methods: flexible diaphragm method and rigid diaphragm method (see
Appendix C for description of the methods). Figures E2 and E3 show a graphical representation
of analytical models for both methods. Then, the shear resistance of Wall 4 (Figures E1 and E4)
is analyzed using three methods: segmented shear wall method, perforated shear wall method,
and Ni-Karacabeyli’s method (see Appendix D description of the methods).
Figure E1
Shear Wall Schedule for a One-Story House
D
ESIGN
I
NPUT
Design Format ASD
Load Direction North-South (NS)
Wind Load in NS direction 20,000 lb (assumed)
Design Basis Capacity
Reduction Factor 0.5 (Table 4.2)
Load Duration Factor 1.0 (Wind Load)
Shear Wall Parameters:
Structural Sheathing Panels Structural OSB panels
Sheathing Nails Common nails
Lumber Species SPF (SG = 0.42)
Stud Spacing 16 inches o.c.
E-1
Shear Wall Height 8.1 ft
Interior Sheathing none
Wall configurations See Table E1
TABLE E1
WALL CONFIGURATIONS
Parameter Wall 1 Wall 2 Wall 3 Wall 4
Total length 32 ft 9 ft 21 ft 20 ft
Number of openings 1 none 1 1
Opening type Window
Window Door
Opening length 3 ft
6 ft 4 ft
First segment 6 ft
9 ft 11 ft
Second segment 21 ft
6 ft 5 ft
L
ATERAL
L
OAD
D
ISTRIBUTION
Flexible Diaphragm Method
The total lateral load is distributed between the shear walls based on the tributary areas
associated with each wall on a purely geometric basis. Figure E2 is a graphical representation of
the mechanical model based on a simple beam approach. Table E2 summarizes individual shear
wall loads.
Figure E2
Flexible Diaphragm Method Model
TABLE E2
SHEAR WALL LOADS ACCORDING TO FLEXIBLE DIAPHRAGM METHOD
Shear Wall #
Tributary Area of
Associated Wall, ft
2
Fraction of Total
Tributary Wall Area
Shear Wall Load, lb
Wall 1 (6.0)(8.1) = 48.6 0.125 2,500
Wall 2 (19.5)(8.1) = 157.95 0.410 8,125
Wall 3 (18)(8.1) = 145.8 0.375 7,500
Wall 4 (4.5)(8.1) = 36.45 0.090 1,875
TOTAL 388.8 1.0 20,000
E-2
Rigid Diaphragm Method
The total lateral load is distributed between the shear walls based on the relative capacities.
Figure E3 is a graphical representation of the mechanical model based on a continuous rigid
beam approach. For the first iteration, the segmented shear wall method is used to determine the
wall capacities. Table E3 summarizes individual shear wall loads.
Figure E3
Rigid Diaphragm Method Model
TABLE E3
SHEAR WALL LOADS ACCORDING TO RIGID DIAPHRAGM METHOD
Shear Wall #
Segmented Shear Wall
Length, ft
Fraction of Total Wall
Length
Shear Wall Load, lb
Wall 1 29.0 0.42 8,400
Wall 2 9.0 0.13 2,600
Wall 3 15 0.22 4,400
Wall 4 16 0.23 4,600
TOTAL 69.0 1.0 20,000
Table E4 compares results of flexible vs. rigid diaphragm methods. The flexible diaphragm
method both underestimates and overestimates the shear wall loads as compared to the rigid
diaphragm method. While providing a more conservative design, the flexible diaphragm method
requires an impractical shear wall schedule for this building configuration (Figure E1). For
example, Wall 2 has to be excluded from the analysis, because it is impractical to design a short
wall segment that accounts for only 13 percent of the total shear wall length of the building in the
North-South direction to resist as much as 41 percent of the total story shear load. Although
Walls 3 and 4 have practically the same lengths, according to the flexible diaphragm method,
Wall 3 should have capacity four times greater than that of Wall 4. The differences between the
two methods diminish in significance for simple rectangular buildings that resist shear loads by
only two exterior walls. Appendix C discusses the methods of lateral load distribution and
examines aspects and limitations of various methods of analysis.
E-3
TABLE E4
COMPARISON OF FLEXIBLE AND RIGID DIAPHRAGM METHOD
Shear Wall Load, lb
Shear Wall #
Flexible
Diaphragm
Rigid
Diaphragm
Absolute
Difference, lb
Relative
1
Difference, %
Wall 1 2,500 8,400 5,900 70
Wall 2 8,125 2,600 -5,525 -213
Wall 3 7,500 4,400 -3,100 -70
Wall 4 1,875 4,600 2,725 59
Total 20,000 20,000
1
Rigid diaphragm method is used as a basis.
Shear Wall Analysis
Results of the rigid diaphragm analysis are used to design Wall 4 (Figure E4). The shear wall is
designed using three methods: segmented, perforated, and Ni-Karakabeyli’s (see Appendix D for
description of the methods).
Figure E4
Wall 4
LOAD
Load: P = 4,600 lb (Table E3)
Segmented Shear Wall Method
Minimum required unit shear wall capacity:
() ()
ft/lb575
5115.0
600,4
ll
P
v
21
=
+
=
+Ω
=
where:
P, lb = load;
Ω = 0.5 = reduction factor for ASD design format (Table 4.2);
(l
1
+ l
2
), ft = total length of wall segments.
E-4
Characteristic unit shear wall resistance adjusted for lumber species:
(650) [1- (0.5-0.42)] = 598 lb/ft (Table B1 of Appendix B)
Wall Characteristics:
Structural sheathing 5/16 wood structural panel
Nail size 6d common (D = 0.113 inch)
Nail spacing 6 inch o.c. on perimeter and 12 inch o.c. in field
Stud spacing 16 inches o.c.
Lumber species SPF lumber
Holddowns: at the end of each segment – four holddowns overall for
two segments
Perforated Shear Wall Method
Empirical perforation reduction factor, F:
62.0
)83.0()2(3
83.0
r23
r
F
=
−
=
−
=
83.0
)115)(1.8(
)5.6)(4(
1
1
lH
A
1
1
r
i
o
=
+
+
=
+
=
∑
where:
A
o
= total area of openings;
H = shear wall height;
Σl
i
= summation of lengths of all full height wall segments.
Minimum required unit shear wall capacity:
ft/lb742
)62.0()20()5.0(
600,4
FL
P
v ==
Ω
=
Characteristic unit shear wall resistance adjusted for lumber species:
(820) [1- (0.5-0.42)] = 754 lb/ft (Table B1 of Appendix B)
Wall Characteristics:
Structural sheathing 15/32 wood structural panel
Nail size 8d common (D = 0.131 inch)
Nail spacing 6 inch o.c. on perimeter and 12 inch o.c. in field
Stud spacing 16 inches o.c.
Lumber species SPF lumber
Holddowns: at the wall corners – two holddowns overall
E-5
Ni-Karacabeyli’s Method
The wall is analyzed in both directions:
Direction of Loading: Left-to-Right (Figure E4)
Segment 1:
Segment length l
1
= 11 feet
Uplift restraint effect: ϕ
1
= 1.0 – holddown bracket is installed
Capacity ratio: α
1
= 1.0 – segment is fully restrained
Segment 2:
Segment length l
2
= 5 feet
Uplift restraint effect: ϕ
2
= 0 – no overturning restraint at door opening
Segment aspect ratio: γ
2
= 8.1/5 = 1.62
Capacity ratio:
28.062.162.1)62.1()0(2121
22
=−++=γ−γ+ϕγ+=α
Minimum required unit shear wall capacity:
ft/lb740
)5.0()]5)(28.0()11)(0.1[(
600,4
]ll[
P
v
2211
=
+
=
Ωα+α
=
Direction of Loading: Right-to-Left (Figure E4)
Segment 2:
Segment length l
2
= 5 feet
Uplift restraint effect: ϕ
2
= 1.0 – holddown bracket is installed
Capacity ratio: α
2
= 1.0 – segment is fully restrained
Segment 1:
Segment length l
1
= 11 feet
Uplift restraint effect: ϕ
1
= 0 – no overturning restraint at door opening
Segment aspect ratio: γ
1
= 8.1/11 = 0.75
Capacity ratio:
50.075.075.0)75.0()0(2121
22
=−++=γ−γ+ϕγ+=α
Minimum required unit shear wall capacity:
ft/lb874
)5.0()]11)(50.0()5)(0.1[(
600,4
]ll[
P
v
1122
=
+
=
Ωα+α
=
The Right-to-Left direction governs the design.
E-6
Characteristic unit shear wall resistance adjusted for lumber species:
(1040) [1- (0.5-0.42)] = 956 lb/ft (Table B1 of Appendix B)
Wall Characteristics:
Structural sheathing 15/32 wood structural panel
Nail size 8d common
Nail spacing 4 inch o.c. on perimeter and 12 inch o.c. in field
Stud spacing 16 inches o.c.
Lumber species SPF lumber
Holddowns: at the wall corners – two holddowns overall
E-7
