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CEMP-E TI 809-07 30 November 1998 D-1 APPENDIX D SEISMIC DESIGN EXAMPLE (English I-P units only) CEMP-E
TI 809-07
30 November 1998
D-1
APPENDIX D
SEISMIC DESIGN EXAMPLE
(English I-P units only)
D1. EXAMPLE DESIGN PROBLEM. An example problem is presented here to demonstrate the
design process presented in Chapter 3 and Appendix C. Shear panels will be designed in the short
direction of the building only to illustrate the design process. In an actual building the lateral load
resisting system must be designed in both directions. This example is a barracks-type building that
will be designed for construction at Fort Lewis, located between Tacoma and Olympia, Washington.
This building is similar to a Prototype 3 Story Steel Stud Framed Barracks Building for Seismic Zones
0 2
1
. The reader will be referred to tabular data and equations presented in Chapter 3 and
Appendix C. When needed, FEMA 302 guidance will be referenced.
The barracks building has a Seismic Use Group of I (FEMA 302, 1.3), which gives it an Occupancy
Importance Factor, I, of 1.0 (see Table C-1).
D2. GROUND MOTION DEFINITION. The maximum considered earthquake ground motions are
determined from spectral response acceleration Maps 9 and 10 (for the Pacific Northwest). The
spectral response acceleration for short periods, S
S
, is 1.2 g (Map 9). The spectral response
acceleration for 1 second, S
1
, is 0.39 g (Map 10). Table D-1 summarizes these values. These
values are determined by interpolating between the map contours for the Fort Lewis location. The
soil conditions are unknown, so a reasonable worst-case site classification of D is used. Values of
Site Coefficients, F
a
and F
v
, are calculated based on straight-line interpolation from the values in
Tables C-2a and C-2b, and are shown in Table D-1. Values for the maximum considered earthquake
spectral response acceleration for short periods, S
MS
and at 1 second, S
M1
adjusted for site class
effects, are calculated using Equations C-1 and C-2, and are shown in Table D-1. Design earthquake
spectral response acceleration at short periods, S
DS
and 1 second period, S
D1
are calculated using
Equations C-3 and C-4, and are shown in Table D-1.
Table D-1. Earthquake Ground Motion Definition
Summary for Fort Lewis.
Importance Factor, I
1.0
Short Period Spectral Response Acceleration, S
S
1.2 g
1 Second Spectral Response Acceleration, S
1
0.39 g
Site Classification
D
Site Coefficient, F
a
1.02
Site Coefficient, F
v
1.62
Adjusted Short Period Spectral Response Acceleration, S
MS
1.22 g
Adjusted 1 Second Spectral Response Acceleration, S
M1
0.63 g
Design Short Period Spectral Response Acceleration, S
DS
0.82 g
Design Short Period Spectral Response Acceleration, S
D1
0.42 g
T
0
0.103 seconds
T
S
0.516 seconds
Assumed Design Spectral Response Acceleration, S
a
0.82 g
Seismic Design Category
D
Response Modification Factor, R
4
Deflection Amplification Factor, C
d
3.5
A design response spectrum is developed from these terms, as described in Appendix C, Paragraph
C2, using Equations C-5 and C-6, and plotted in Figure D-1. For the natural period of the structure,
T, this spectrum defines values of effective acceleration. The natural period of the barracks building,
T, will almost certainly fall between T
0
and T
S
, defined in Appendix C, Paragraph C2, so that the

1
U.S. Army Corps of Engineers Barracks Prototype Department of the Army, for the National Association of Architectural Metal
Manufactures (NAAMM), by Matsen Ford Design, Drawings Dated 1/3/97. CEMP-E
TI 809-07
30 November 1998
D-2
design spectral acceleration S
a
will equal S
DS
. Values for T
0
and T
S
are shown in Table D-1. After
the building frame is designed, the building natural period will be calculated to ensure that it falls
between T
0
and T
S
, and corrections will be made if needed.
D3. SEISMIC DESIGN CATEGORY. The seismic design category for the barracks building is
determined from Tables C-3a or C-3b, based on the seismic use groups and values of S
DS
and S
D1
. If
the tables give different categories, the larger letter is chosen. For the barracks building, the seismic
design category is D (see Table D-1).
D4. STRUCTURAL DESIGN CRITERIA. The lateral-load-resisting system of the barracks building
will be designed with cold-formed steel shear panels with diagonal straps acting as the sole lateral-
load-resisting element. Values of the response modification factor, R and deflection amplification
factor, C
d
are taken from Table 3-1 and shown again in Table D-1.
The diaphragms of the barracks buildings are reinforced concrete and are considered rigid. The
reliability factor, x
, is calculated using Equation C-7, which for the barracks building for every floor
level gives:
8
.
1
.
ft
.
sq
8971
18
1
20
2
A
r
20
2
x
x
max
x = = = (Eq D-1)
The value of x
shall not be taken as less than 1.0. Therefore no correction is needed for lateral-load-
resisting system reliability.
D5. BARRACKS BUILDING LOAD CALCULATIONS. The effects of gravity load (dead, live, and
snow) and seismic forces shall be combined as defined by Equations C-12 and C-13. As explained in
Appendix C, Paragraph C5, the total lateral force that must be resisted by the shear panel diagonal
straps is simply defined by Q
E
in these equations. In the case of the barracks building this becomes
Q
E
, and the diagonal straps are first sized based on this force.
The barracks building will be designed to act independently in the two orthogonal directions. Figures
D-2 and D-3 show schematic drawings of the barracks building. Figure D-2 shows the plan view and
long-direction elevation. Figure D-3 shows the short-direction elevation of the building. Table D-2
summarizes the weight calculations for the entire building using spreadsheet calculations. These
weights include roof and floor dead load (20 and 40 psf, respectively); exterior wall weight (10 psf);
interior wall weight (10 psf); brick veneer weight (40 psf); and room and corridor live load (40 and 80
psf, respectively).
2
The brick veneer is self-supporting for gravity loads, and vertical and in-plane
lateral seismic forces. The building lateral-load-resisting system (shear panels) does resist out-of-
plane lateral seismic forces from the brick veneer weight. Therefore, the out-of-plane long-direction
brick veneer lateral seismic forces are resisted by the short-direction shear panels.
The short-direction shear panels will be placed at every bay (20 feet, 6-5/8 inches spacing) of the
building as shown in Figure D-2, for a total of nine short-direction frames. A trial shear panel
configuration will be assumed in which two shear panels are placed at every frame, as shown in
Figure D-3. Figure D-3 shows that two shear panels will be placed against the perpendicular outside
walls of the building. Shear panels will be located in the same bay at each floor level, with decreasing
capacity at the higher floor levels.

2
Barracks Prototype Drawings, Sheet C-1
. CEMP-E
TI 809-07
30 November 1998
D-3
Table D-2. Barracks Building Weight Calculations.
The ground snow load, p
g
, for Fort Lewis is 20 psf
3
. The flat-roof snow load, p
f
, is calculated as
follows (ASCE 7-95, Eq 7-1)
4
:
psf
6
.
12
)
psf
20
)(
0
.
1
)(
0
.
1
)(
9
.
0
(
7
.
0
Ip
C
C
7
.
0
p
g
t
e
f
=
=
=
(Eq D-2)
Where:
C
e
= the exposure factor (ASCE 7-95, Table 7-2), which for an exposure category C, fully
exposed roof is 0.9.
C
t
= the thermal factor (ASCE 7-95, Table 7-3), which is taken as 1.0.
I = the importance factor (ASCE 7-95, Table 7-4), which for Category II of the barracks
building is 1.0.
However, the flat-roof snow load shall not be less than the ground snow load multiplied by the
importance factor (p
g
I), so that the p
f
= 20 psf. The sloped-roof snow load, p
s
is calculated as follows
(ASCE 7-95, Eq 7-2):
psf
15
)
psf
20
)(
75
.
0
(
p
C
p
f
s
s
=
=
=
(Eq D-3)
Where:
C
s
= the roof slope factor (ASCE 7-95, Figure 7.2), which is 0.75 for the barracks building with
a 5/12 roof slope.
The snow load will not be used in this example because the flat roof snow load does not exceed 30
psf, and therefore is not included in load combinations that include seismic forces.
D6. EARTHQUAKE FORCE DEFINITION. Seismic forces are now defined based on the equivalent
lateral force procedure (see Appendix C, Paragraphs C6 through C9). The seismic base shear, V in
the direction of the shear walls is given by (Equation C-19):
W
C
V
s
=
(Eq D-4)
The seismic response coefficient, C
s
(Equation C-20) is calculated with the variables given in Table
D-1, which becomes:
g
g
I
R
S
C
DS
s
204
.
0
0
.
1
4
82
.
0
=
=
=
(Eq D-5)
The value of for C
s
need not exceed the following (Equation C-21), where T = T
a
(see Equation D-8):

3
ASCE 7-95, Chapter 7 and Chapter 7 Commentary.
4
NEHRP, Section 5.3.2, states that in areas where the design flat roof snow load does not exceed 30 psf, the effective snow
load is permitted to be taken as zero. The Commen