CEE 285 BEHAVIOR OF STRUCTURAL SYSTEMS
FOR BUILDINGS
DESIGN PROJECT
Professor H. Krawinkler
Stanford University
Submitted: March 22, 2006
Team Members:
Jimmy Chan
Asphica Chhabra
Jennifer Moore
Jana Tetikova
Nick Wann
CEE 285 BEHAVIOR OF STRUCTURAL SYSTEMS
FOR BUILDINGS
DESIGN PROJECT
Professor H. Krawinkler
Stanford University
Team Members:
Jimmy Chan
Asphica Chhabra
Jennifer Moore
Jana Tetikova
Nick Wann
BD Inc.
Project: Palo Alto Office Tower
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Table of Contents
PART ONE: SYSTEM ASSESSMENT............................................................................. 4
1.0 Introduction ............................................................................................................... 4
1.1 Project Proposal .................................................................................................... 4
1.2 Individual Roles .................................................................................................... 4
2.0 Load Determination .................................................................................................. 8
2.1 Gravity .................................................................................................................. 8
2.2 Lateral ................................................................................................................. 20
3.0 Structural Design .................................................................................................... 24
3.1 Gravity System.................................................................................................... 24
3.2 Perimeter Moment Frames .................................................................................. 30
3.3 Shear Wall Design .............................................................................................. 35
3.4 Connections......................................................................................................... 41
3.5 Foundation .......................................................................................................... 49
4.0 ETABS Modeling - Analysis and Discussion ......................................................... 51
4.1 Model Discussion................................................................................................ 51
4.2. Shear Wall-Frame Interaction ............................................................................ 52
4.3 ETABS Model and Frame- Shear Wall Interaction Comparison ....................... 53
5.0 Conclusions ............................................................................................................. 55
PART TWO: APPENDIX - DESIGN CALCULATIONS ............................................... 56
Appendix A – Load Determination...................................................................................
Appendix B – Gravity System Design ..............................................................................
Appendix C – SMRF Design ............................................................................................
Appendix D – Shear Wall Design .....................................................................................
Appendix E – Connection Details and Calculations .........................................................
Appendix F – Analysis Results (ETABS and Interaction) ...............................................
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PART ONE: SYSTEM ASSESSMENT
1.0 Introduction
1.1 Project Proposal
To build a 10 story office building in Palo Alto according to 1997 UBC specifications
keeping the following constraints in mind:
Site Constraints:

Seismic Loads: the building is located at 7 km from the San Andreas fault.

Soil profile SD
Architectural Constraints:

Clear Story height should be at least 8.5 ft.

80 ft x 140 ft floor plan
Other Considerations:

Insure elastic behavior of structure under strong motion earthquake

Consider foundation system
1.2 Individual Roles
Individual roles were given to each team member:

Owner: Jennifer Moore

Architect: Nick Wann

Structural: Jimmy Chan

Mechanical: Jana Tetikova

Contractor: Ashpica Chhabra
The responsibilities of each are outlined below. Each person performed research in
his/her own area in order to guide the building system design.
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1.2.1 Owner
The owner wanted to have flexibility in the use of functional spaces that can support the
unknown future demands on the structure as wells as to entice sales of spaces. Specific
areas were chosen and designed for heavier loads in order to meet this flexibility
requirement. To increase demand, the owner also requested specific physical
characteristics such as an atrium on the first floor and a restaurant. Commercial space on
the first floor was also set as a hard constraint in order to rent to retailers. Minimizations
of costs were also important to the owner, who desired to have a cost efficient building
system.
1.2.2 Architect
The architect responded to the owner’s vision of the building through an innovative and
practical extension of the atrium to improve the overall space. Instead of having the
atrium at the first floor level, he reversed the sequence and added a large opening running
through the building from the 6th to 10th floor. This large open space leads to a reduction
in the functional space of the building, however it allows ample natural light to enter the
building, creating a livelier atmosphere and increasing the productivity of its occupants.
The ceilings at the first floor were increased to 15 ft in order to increase the grandeur and
aesthetic appeal of the commercial area. The architect opted against a basement. The lack
of basement and commercial use of the first floor required that mechanical systems be
placed on the second floor, increasing the 2nd floor story height to 15 ft.
The architect designed two continuous shear wall cores, one on each side of the opening.
He has also provided for a restaurant on the fifth floor level, which provides for more
retail space in the building. This floor was chosen because its central location would be
more accessible to the building occupants, which would hopefully increase use. Also, the
restaurant’s location on the 5th floor would allow diners to look up through the opening,
improving the quality of the lunchtime experience. Additionally, people at the top floors
would be able to look down at the decorated restaurant.
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1.2.3 Structural Engineer
The mechanical and architectural requirements posed as the primary structural challenges
for the structural engineer. Owners concerns were addressed through the architect and not
the owner herself.
One of the most important decisions that the structural engineers made was the type of
lateral load resisting system.
The structural engineers decided on a dual system
consisting of concrete shears walls and steel special moment resisting frames (SMRF) in
both the EW and NS directions. Ductile shear walls provide excellent resistance to high
lateral loads that are probable in highly seismic regions. To achieve this ductility,
however, special attention had to be paid to the detailing of the walls’ reinforcement.
Additionally, the special moment resisting frames (SMRF) act as a “backup” system
providing necessary redundancy to the system.
Special attention also had to be paid to key areas for the heavy loads imposed by the
mechanical system components.
These areas were strategically placed in locations
approved by the architect, so as not to interfere with the flow of the building, yet provide
efficient service throughout. One of the most notable structural challenges in the building
has to do with the large open core running down the center of the building. This
architectural detail provided many structural challenges, beginning with the diaphragm
that was assumed to be rigid in this building design. With a plan discontinuity such as
this, the engineers would have to analyze the diaphragm further to validate the rigid
diaphragm assumption. Many other structural decisions had to be made throughout the
design process including the use of composite beams, shored construction, and
fireproofing around the stairways.
1.2.4 MEP
The structural engineers collaborated with the mechanical engineers to come up with a
scheme for the ductwork, which will primarily run along the interior corridor deck that
surrounds the opening. On the 1st through 5th floor, ductwork will run under the floor
beams which are not very deep. The mechanical engineer specified that two chillers and
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cooling towers are required for the building. Chillers and other Origination systems will
be housed in the two mechanical rooms on the second floor next to the cores. Coolers at
the roof are also located next to the cores. Four elevators are located in the building. The
shear core is housed around the stairway, allowing for most of the vertical pipes to also
run along the core. The transformer and generator which account for heavy concentrated
loads will be housed outside the building and hence do not affect the structural decisions.
Typical MEP features and loads can be found in Table 2-2.
1.2.5 Contractor
The primary role of the contractor was to promote efficiency of the structural design.
This affected decisions on member sizing, steel member and shear wall connections, and
concrete work. The more similar the connections and member sizes, the more cost
efficient the design. Also, connections and members that are readily available in the
market are more desirable. Labor was also a concern especially related to the installation
of the doubler plates which was avoided by increasing the interior column sizes. The
contractor participated in the design process.
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2.0 Load Determination
Gravity loads were computed based on MEP load requirements, typical dead loads, and
live loads based on varying functional uses. Wind and seismic loads were determined to
compute total lateral load effects.
2.1 Gravity
Table 2-1. Dead Load & Live Loads
Loads
Concret+deck+misc.
Partitions
DL
ksf
0.065
0.02
0.085
Exterior Cladding
Roofing system
0.02
0.05
Self Weights
Floor Beams
Girders
Columns
klf
0.05
0.1
0.2
Live Loads
Offices
Corridors, exits
File Rooms
Roof
ksf
0.05
0.1
0.15
0.02
The chillers, which may weigh up to 10,000 lbs, were placed on the second floor. The
cooling towers are in general placed on the roof for they require a continuous flow of air
and are quite noisy. Since at the time of conceptual design no decision was made as to
where exactly on the roof cooling towers would be placed, four areas of about 150 square
feet where designed to support loads up to 300 psf (Ref. Roof Load Key Sheet).
In addition to chillers and cooling towers, another important consideration is the chilled
water loop and condenser loop which will produce a reaction of about 80,000 lb. at the
base of the building.
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Other geometric constraints arise from providing the building with plumbing, storm, and
electrical system. Table 2-2 summarizes the MEP loads and considerations.
Table 2-2. MEP Loads and Considerations
Category
Related Constraints
Vertical Load
accessibility and fireproofing
2 x10000 lb
-
-
1. Elevator system
Elevators and dumbwaiters (DL and LL)
2. HVAC System
i) Origination System
area of 10 ft. x 20 ft.
Chillers
4(+) thick raised concrete pad
300 psf
12 - 15 ft. ceiling height
area of 15 ft. x 20
Cooling towers
ft. height of 15 ft. - 20 ft.
300 psf
raised above deck
Condenser loop (2 loops needed)
-
80000 lb
Chilled water loop (2 loops needed)
-
80000 lb
-
100 psf - 130 psf
-
5 psf
concrete encasing 2 ft. x 6 ft.
300 psf
Masonry wall enclosures and
increased slab thickness for pumps and
compressors
ii) Distribution System
Ductwork
3. Electrical System
Transformers
Emergency Generator
80000 lb
4. Plumbing System
Tanks and boilers
-
-
-
-
5. Fire Protection System
Distribution lines and sprinkler heads
A summary of the gravity loads along with the architectural renderings of the typical
floor plans are included herein.
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2.2 Lateral
Once the gravity loads are computed and finalized the lateral loads can be determined.
The lateral loads are applied in addition to the gravity loads and typically control the size
of the members. In our case, the lateral loads are resisted by a shear wall and moment
resisting frame system. Wind loads can be very high in some regions such as near the
shoreline of a major body of water, such as the Pacific Ocean or the Gulf of Mexico.
However, the seismic forces imposed on our building were much greater than the wind
forces, and therefore controlled the design. Other forms of lateral load, such as blast
loading or impact loading are not relevant for the design of an office building and
therefore were not considered in this preliminary design.
2.2.1 Wind Loads
The loads imposed on the building were calculated using the UBC formula 20-1. A
design wind speed of 90 mph and an exposure category B were used in the formulation of
the lateral wind loads. Using the following equation as well as Table 16-G of the UBC,
containing values for Ce, the wind pressure at each story and at each mid-story was
interpolated:
p = CeΣCqqsI where ΣCq = 0.8 + 0.5 = 1.3
Then, as shown in Figure 2-1, the values of the wind pressure, p, are averaged at each
interval and this value is then used as the design wind pressure over the entire half-story.
The design wind load was then represented as a line load over the width of the floor by
multiplying the wind pressure of the half-story above and below each floor by their
respective half-story heights and summing.
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Figure 2-1: Distribution of the Wind Pressures over the Height of the Building.
This line load, W in k/ft, was then multiplied by the width of the building to calculate the
total force imposed on each floor by the wind. These story forces were then summed
cumulatively down the building to arrive at the story shear force. Each story shear force
was then multiplied by the story height and again summed cumulatively down the
building to determine the overturning moment imposed by the wind loading.
The
calculations are summarized in Appendix A. As expected, the NS wind produces higher
base shear forces and overturning moments of 428 kips and 31,142 kip-ft, respectively.
This is nearly twice the loads imposed by an EW wind producing a base shear of 245 kips
and an overturning moment 17,950 kip-ft. However, while these lateral load effects are
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notably large due to the close proximity to the Pacific Coast, they were ultimately
neglected in place of the even larger seismic loads.
2.2.2 Seismic Loads
The seismic loads imposed on structures in the Palo Alto area are expected to be
significant.
The seismic loads were calculated according to the UBC (1997).
As
prescribed by the code, the total base shear is calculated according to design parameters,
such as proximity to an active fault, seismic zone, soil profile, type of lateral system,
period and the effective seismic weight of the building.
The seismic weight was
determined in Appendix A using many preliminary assumptions for material and
mechanical weights. These assumptions were later verified as conservative averages.
The elastic fundamental period of vibration of the structure was determined using code
Method A (equation 30-8):
T = Ct(hn)3/4,
where Ct = 0.035 for steel moment-resisting frame was used. Then, the base shear was
calculated using equations UBC (1997) 30-4 through 30-7:
V

CvI
W
RT
2.5CaI
W
R
 0.11CaW

0.8ZNvI
W
R
Once the total base shear was determined, the forces were distributed to each floor. Since
the natural fundamental period was determined to be 1.3 sec > 0.7 sec, the whiplash
force, Ft was determined according to:
Ft = 0.07TV< 0.25V,
This force was applied to the roof of the building to account for the wave reflection
which causes a higher inertia force on the top floor. The rest of the base shear was then
distributed to the individual floors based on their seismic weight and height. As was the
case with the wind loading, the seismic shear story forces were summed cumulatively
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down the building to determine the individual story shears and the base shear at the
ground level. The story shear was then multiplied by the story height and cumulatively
summed once more to determine the overturning moment.
The results of these
calculations can be observed in Figure 2-2.
Figure 2-2: Distribution of the Seismic Forces over the Height of the Building.
As can be easily seen from the results in the Appendix A, the base shear for the building
is 1,038 kips and the overturning moment at the ground floor is 96,698 kip-ft. These
results are nearly 3 times the largest values obtained from the wind loading, thus the wind
loads were ignored and the seismic loads were used as the controlling design lateral
loads. Additionally, unlike the wind loading, the lateral systems in both directions
experience the same loading and thus must both be designed for the same load effects.
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3.0 Structural Design
3.1 Gravity System
3.1.1 Gravity Columns
The gravity columns which make up all of the interior columns were designed for axial
load only.
These columns have beams framing into them and have simple shear
connections, which are modeled as pins so that virtually no moment is transferred into the
column. Thus, in order to design the columns we first had to determine the axial loads
due to dead and live loads only. These loads were based on the tributary area of the
column and gravity loads including the column self-weight. The resulting loads are
summarized in Appendix B.
The dead and live axial loads were summed cumulatively from the roof down to
determine the total axial load at each floor. These loads were then factored according to
the load combinations provided in the UBC (1997) to obtain a design load, Pu. However,
before we could continue with the design, two engineering decisions were made. First,
due to the column layout and symmetry of the building we determined that we could
reduce all of the interior gravity columns down to two typical columns; one on the corner
next to the elevators, and the other towards the middle of the building closer to the shear
wall.
This consistency provides a simplification during construction.
The second
engineering decision is that the columns would be spliced at 4 feet above every second
level. This decision is based on the transportation constraints of the columns as well as
the constructability of the building.
With these decisions in mind, the columns were then designed using a K= 1, F y = 50 ksi
and c = 0.85 for compression. Column sizes at each story were chosen so that the ratio
of axial compression from the loads to the axial compression capacity of the size,
Pu
c Pn , was less than or at most equal to 1.00. We used W14 sections for the gravity
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columns. The final preliminary design of the gravity columns were taken as the sizes
designed at the 1st, 3rd, 5th, 7th, and 9th floors. These are summarized in Table 3-1.
Table 3-1. Gravity Column Design
GRAVITY COLUMNS
Floor
Roof
Column 5
Column 6
W14X53
W14X53
W14X90
W14X90
W14X120
W14X109
W14X159
W14X145
W14x211
W14X176
10
9
8
7
6
5
4
3
2
1
3.1.2 Interior Girders
The interior girders are designed for 1.2 D + 1.6 L. Refer to the previous load key sheets
for the various load areas. For interior girders only, we analyzed the girders with
distributed loads and tributary areas. We looked at both the strength and deflection,
calculating the minimum section modulus as well as the minimum Ix before deciding the
girder sections. The deflection limits for live loads and dead loads are L/240 and L/360
respectively. Sample calculations can be found in Appendix B.
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3.1.3 Floor Beams
Floor beams and slab were designed as a fully composite system to reduce beam sizes
and to take advantage of the concrete floor strength. Floor beams were designed with the
following properties:
Total floor depth
- 6.25 inches
Concrete fill
- Lightweight concrete (fc’= 3ksi, 110pcf density)
Steel strength
- fy = 50ksi
Shear studs
- ¾ inch diameter 3 inches long
Shored and unshored construction was evaluated with the following assumed
construction loads:
Wet concrete
- 60 psf live load
Additional const. load - 20 psf live load
Finally, the choice of using composite beams was verified by performing a cost
comparison between composite and non-composite beams, detailed in Appendix B.
Loads:
Loads were obtained from the load key sheets. Three typical loadings and three floor
beam lengths/spacings were used in calculations.
Dead Load
- 85psf
Live Load
- Heavy =(150psf), Medium = (100psf) and Light = (50psf)
Floor beams
- 30'Long @10' spacing, 25'@10' and 25' @8'-4"
Required Flexural Strength:
The flexural resistance required was obtained from:
wL2
Mu 
8
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where w is the load per linear foot of beam obtained from tributary widths (half the
distance to adjacent beams) and L is the span of the beam.
Select Section and Properties:
Assuming the depth is the concrete stress block, a, is less than the thickness of the
concrete slab, the design flexural strength,  Mn is:
M n  As Fy (d 2  yconc  a 2)
where As is the area of the steel beam required, d is the depth of the steel beam (assumed
to be 10” for the first iteration), yconc is 6.25 inches, a is the depth of the concrete block
(assumed to be 2” for the first iteration).
A value of Y2 , distance from top of the steel flange to the center of the concrete stress
block, is also required. Assuming the depth of the concrete stress block is less then the
thickness of the slab, Y2 was obtained from:
Y2  y conc  a
2
Using these two values sections were chosen from the AISC LRFD Steel Design Manual
3rd edition Table 5-14 Composite W-Shapes.
Flexural capacity was check using:
M n  As f y (d 2  yconc  a 2) where
 1 * beamspan

8

 and
b  2 * min
 1 * centerline _ dis tan ce
 2

a
f y As
0.85 f c' b
Compute number of Shear Studs Required:
The nominal strength of 1 stud was obtained from:
Qn  0.5 Asc f c' Ec  Asc Fu
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where Asc is the cross-section of the shear stud (0.44in2) , Ec is the modulus of elasticity
of concrete given below (2085.3 ksi) and w is the unit weight of concrete (110pcf).
Ec  33w1.5 f c'
For a ¾ in diameter stud the strength is 17.47 kips. The number of studs required from
the point of max moment to its connected ends for full composite action was obtained
from:
# stud 
As f y
Qn
Since the beams are simply supported this number is for half the beam length. Total
number of studs required is then twice #stud.
Construction Phase Strength Check:
A flexural demand for an unshored beam was checked using the construction loads
assumed. For floor beams where the flexural capacity of the steel is exceeded, a larger
section was chosen and the number of shear studs recalculated.
Deflection Calculations:
Beams that are unshored were checked for deflection under dead loads using:
5wL4

384 EI
where unfactored load per linear foot of beam and E and I are the modulus of elasticity
and moment of inertia for the unshored beam. Where deflection are large (δ>L/360)
adequate cambering is required.
Beams that are composite were checked for deflections under live loads using:

5wL4
L

384 EI 360
where I is the lower bond elastic moment of inertia given Table 5-15 of the AISC LRFD
Steel Design Manual 3rd edition.
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Comparison to a Non-Composite Section:
Beam sections were chosen by comparing flexural capacity of the steel section to the
calculated flexural strength required. Sections chosen were also checked for live load
deflections as (Δ<L/360). Assuming 7lbs per stud (in cost) the amount of steel increase
due to the beam size increase was compared.
Sizes for each of the 3 loadings (heavy, medium and light) and for each of the 3
spans/spacings as described in A, are tabulated below. A sample calculation can be
found in Appendix B.
Table 3-2: Section Design
Heavy (LL = 150psf)
Type of Const
30'@10'
Section
Shored
Unshored
Non-Composite
W12x35
W12x35
W16x57
Heavy
Type of Const
25'@10'
Section
Shored
Unshored
Non-Composite
W14x22
W14x22
W16x40
Heavy
Type of Const
25'@8.333'
Section
Shored
Unshored
Non-Composite
W10x22
W10x22
W16x36
Medium(LL = 100psf)
Type of Const
30'@10'
Section
Shored
Unshored
Non-Composite
W10x26
W12x30
W16x45
Medium
Type of Const
25'@10'
Section
Shored
Unshored
Non-Composite
W10x19
W10x26
W14x34
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Stud
Stud Spacing
3/4"
3/4"
every 6"
every 6"
Stud
Stud Spacing
3/4"
3/4"
every 8"
every 8"
Stud
Stud Spacing
3/4"
3/4"
every 8"
every 8"
Stud
Stud Spacing
3/4"
3/4"
every 8"
every 7"
Stud
Stud Spacing
3/4"
3/4"
every 9"
every 6"
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Mu [kft]
384.75
144
384.75
Mu [kft]
267.2
100
267.2
Mu [kft]
φMn [kft]
439.5
192
394
φMn [kft]
280
124.5
274
φMn [kft]
222.57
83.3
222.57
Mu [kft]
294.75
144
294.75
Mu [kft]
204.7
100
204.7
255
97.5
240
φMn [kft]
302.1
161.6
308.6
φMn [kft]
224
117.4
204.75
29
Medium
Type of Const
25'@8.333'
Section
Shored
Unshored
Non-Composite
W10x15
W10x22
W14x34
Light (LL = 50psf)
Type of Const
30'@10'
Section
Shored
Unshored
Non-Composite
W10x19
W12x30
W14x34
Light
Type of Const
25'@10'
Section
Shored
Unshored
Non-Composite
W10x12
W10x26
W14x26
Light
Type of Const
25'@8.333'
Section
Shored
Unshored
Non-Composite
W10x12
W10x22
W12x26
Stud
Stud Spacing
3/4"
3/4"
every 11"
every 8"
Stud
Stud Spacing
3/4"
3/4"
every 11"
every 7"
Stud
Stud Spacing
3/4"
3/4"
every 14"
every 6"
Stud
Stud Spacing
3/4"
3/4"
every 14"
every 8"
Mu [kft]
170.5
83.3
170.5
Mu [kft]
204.75
144
204.75
Mu [kft]
142.2
100
142.2
Mu [kft]
118.4
83.3
118.4
φMn [kft]
176.4
97.5
204.75
φMn [kft]
226.72
161.6
204.75
φMn [kft]
142.34
117.4
139.5
φMn [kft]
142.34
97.5
139.5
3.1.4 Elevator Beams
Specials beams were designed above the roof to support the weight of the elevator and its
components. These beams, called sheave beams, were designed to carry 10,000 lbs each
as a centered point load. Additional beams were designed to support the sheave beams.
Limitations on deflection called for a W12x16 for the sheave beams, and W24x55 for the
support beams. Refer to Appendix B for calculations.
3.2 Perimeter Moment Frames
3.2.1 Fixed End Moments
The Perimeter Moment Resisting Frame of the building undergoes large moments
imposed both by lateral and gravity loading. These moments are transferred through the
beams to the columns and eventually to the foundation, where they are dispersed into the
earth.
Therefore, each member of this chain must be strong enough to resist the
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maximum moments imposed on it if the system is to carry the loads safely. However,
before we can design the members we must know the maximum loads that each would be
likely to experience. Thus, we can start with the perimeter girders to determine the
maximum moments imposed on them from the gravity loads. These can be calculated by
assuming the ends of the perimeter girders are fixed and calculating the fixed end
moments.
In our system, none of the perimeter girders carry distributed loads other than their own
self-weight or the exterior cladding which was assumed to be 0.34 k/ft along the length of
the beam. Additionally, there are two point loads caused by two beams framing into the
girders. Thus, before the fixed end moments can be calculated, the reactions from the
framing beams must be determined according to the load key sheet and beam layout
geometry. These calculations are shown in Appendix C.
3.2.2 Girder Design
The perimeter girders provide majority of the stiffness in the Perimeter Moment Resisting
Frames. However, we did not need to design the girders for stiffness since the moment
frame is the secondary or “backup” system. The primary shear wall system instead
provides the required stiffness. The moment frame hence only needs to be designed for
strength. The design load was taken as the maximum fixed end moments (gravity loads)
and moments due to earthquake loading, which were determined using the Portal Method.
The fixed end moments were factored by 1.1 and used for a preliminary estimate of the
gravity moments. These assumptions would later be checked by computer analysis.
Also, the ρ factor used in UBC ’97 for redundancy was ignored in this design, but the
load combinations provided in the code were utilized. The maximum moment obtained
from the load combinations and the determined moments was used for the preliminary
design.
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Using the design moment, we were able to calculate the minimum plastic section
modulus, Zx that was required. The appropriate  factor of 0.9 was used for bending.
The equation used to perform this calculation was:
Zx,min = Max Moment(from load combinations)*12/(0.9*50(ksi))
At this point, it was decided to use the same girder size for all three of the girders in each
moment frame. This consistency simplifies the construction process and thus reducing
the chance of beams placed in the wrong location. The results of the preliminary girder
design are shown in Appendix C.
3.2.3 SMRF Column Design
The columns in the SMRF undergo both axial compression and bending moments. It is
assumed that there’s no biaxial bending expected since the interior gravity beams framing
into the columns are shear connected. The perimeter columns were oriented such that
strong axis of the column would occur. We utilized symmetry and only two columns in
each direction of the moment resisting frame were designed. Also, we decided to use
W24 sections due to their large bending moment resistance.
Among the loads imposed on the perimeter columns are moments and axial loads from
dead, live, and seismic loads. To determine all of these components we began by
calculating the axial loads due to the dead and live loads. The procedure for this was
exactly the same as for the gravity columns, using the tributary area of the columns and
the gravity loads due to all possible sources including the self-weight of the column. A
moment distribution of the moment resisting frames was also completed to determine
how the fixed end moments determined earlier were actually distributed to the columns
of the frame. To compute the stiffness of each member in the moment distribution of the
frame, the moment of inertia of the columns was assumed to be 1.2 times the moment of
inertia of the beams. In performing the moment distribution, a concentrated moment of
100 kip-ft was used so that a simple percentage of the moments applied due to the fixed
end moment could be used to calculate the actual distribution of moment in columns due
to gravity loads. Also, an unbalanced loading was used in the moment distribution to
represent possible scenarios of live load.
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Another load effect obtained during the
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moment distribution was a continuity shear that resulted from the unbalanced moments in
the adjacent columns. This shear was computed by dividing the difference in moments in
the adjacent columns by the length of the beam. This shear in the beam is converted to
an axial load in the interior column and is added to the axial load due to dead loads. The
axial loads due to dead and live loads were cumulatively summed as before to determine
the total axial load at each floor due to the dead and live loads. Finally, the axial loads
and moments determined in the Portal Method are used to determine the ultimate loading
on the columns. These loads are summarized in Appendix C.
All of the load cases used in this design were considered. However, since rx/ry is large in
our case, we can ignore the first case (1.2D + 1.6L) and use the second case (1.2D + 0.5L
+ 1.0E) assuming Kx = Ky = 1.0, which is permitted by the seismic code, to determine the
ultimate axial load and bending moment on each column.
The results of this factoring
are shown in Appendix C.
Using the following interaction equations sizes were determined from the factored loads:
 M ux
M uy
Pu
P
 0.2  u  

Pn
 c Pn   b M nx  b M ny

  1.0


M uy
Pu
P
8  M ux
 0.2  u  

Pn
 c Pn 9   b M nx  b M ny

  1.0


Mu = B1Mnt + B2Mlt
Mnt= come from factored gravity loads
Mlt = come from factored lateral loads
Once again the columns were spliced at every 2nd level, so that the column used were
those designed at the 1st, 3rd, 5th, 7th, and 9th floors.
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3.2.4 Seismic Provisions
In addition to the strength design of the Perimeter Moment Resisting Frame columns,
special seismic provisions must be taken into account to ensure the safety of the structure.
We used only the interior perimeter columns for this check because they have two
moment resisting beams framing into them as opposed to only one. The columns must be
strong enough so that plastic hinges will form in the beam before in the column. This can
be accomplished by equation 8-3 of the UBC ’97:
 Z c ( F yc  Puc / Ac )
 Z b F yb
 1. 0 ,
This equation ensures that the plastic strength of the column is larger than that of the
beam.
The columns and beams designed are checked for the strong column-weak beam concept
and where needed redesigned so that they pass.
Another seismic design criterion that had to be checked for the Perimeter Moment
Resisting Frame is the check for “overstrength” during an earthquake, since column
buckling can be a major problem. This provides an extra protection against extra axial
forces in severe earthquakes, which are larger than those used previously in the design.
Since axial loads primarily concern exterior moment frame columns, this check will be
only for those columns. This check should be used when
Pu
 0.4 . We used the
c Pn
following code equation to assure that the exterior perimeter columns were protected
against overstrength:
1.2PDL + 0.5PLL (0.4R)PE ≤ φcPn
In performing this calculation the factored loads were added to 0.4*R*PE = 0.4*8.5* PE =
3.4* PE . This is a large increase in axial load to protect against a rare event. The axial
capacity at each floor is checked so that the above equation is satisfied and the column is
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protected from buckling.
Any column that fails is resized so that it satisfies this
requirement. These results are summarized in Table 3-3.
Table 3-3: Final SMRF Design
EAST - WEST FRAME
Columns
Floor
Roof
Interior
Girders
Exterior
10
W24X131
8
W18X35
W21X44
10
6
Interior
W21X44
9
W21X50
8
W16X40
7
W18X55
6
W24X84
W24X55
W21X44
W21X44
W24X131
W21X50
Girders
Exterior
W14X26
W24X131
W24X68
7
W24X162
Columns
Floor
Roof
W24X55
9
W24x146
NORTH - SOUTH FRAME
W24X55
W21X50
W21X50
W24X146
W24X68
5
W21X55
5
W21X55
4
W18X55
4
W21X55
W21X55
3
W21X55
2
W24X162
W24X104
3
2
W24X162
W24X162
W24X117
1
W24X84
W21X55
W24X55
W24X162
W24X104
1
3.3 Shear Wall Design
Two shear wall staircase cores resist lateral loads in the building. They are 15ft x10.5ft
(centerline dimensions), and have wall thickness of 18 inches (See Figure 3-1). The
strengths of concrete and rebars are 3000psi and 60ksi, respectively. Rebar sizes and
spacings were determined using simplified formulas, assuming a solid core with no
openings. Door openings 3.5’ wide 8’ tall were modeled on each floor in the ETABS
verification model to see the effects of this simplification. Design was performed in
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accordance to applicable ACI 318 provisions. Rebar layouts are shown in Figure 3-5 and
described in Table 3-4.
Figure 3-1: Plan View of Shear Wall Staircase Cores
Table. 3-4: Shear Wall Reinforcement
Shear Wall
15 ft EW core walls (18” thick)
8 ft NS core walls (18” thick)
Reinforcement (on each face of wall)
#4@8” horizontal reinf
#10@12” vertical reinf (story 1-4)
#8@18” vertical reinf (story 5-10)
#4@8” horizontal reinf
#10@12” vertical reinf (story 1-4)
#8@18” vertical reinf (story 5-10)
Choice of Location:
The walls around the staircase were chosen as the lateral load resisting system because
the stair cores were continuous through the structure. Another reason for this choice was
the desire of the architect and the owner to maintain open spaces and unobstructed views.
The locations of stairs were determined by the architect for circulation purposes. The
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atrium above the 5th floor and the location of the elevator made shear walls behind the
elevators infeasible due to the inability to transfer shears near the open space. Additional
walls were also not desirable because of constraints for building modularity (owner), ease
of constructability (contractor) and aesthetics (architect).
Preliminary Thickness:
Since the cores were slender (10.5’ width to 126’ total height), deflection was believed to
control wall thickness. Drift is limited according to UBC section 1630.9:

h

0.02
0.02

 0.003366
0.7 R 0.7(8.5)
Assuming an average interstory drift over the height of the building (126ft or 1512 in),
the total drift limit is 5.08 in.
From the calculated statically equivalent story shear values and assuming (1) 18” thick
core walls with no openings, (2) ½ the load goes to each core and (3) only flexural
deflection of the shear walls, the drift was found to be 4.5in in the NS direction and
3.03in in the EW direction (Ref Appendix D). For these calculations, the moment of
inertia was modified to 0.7I in accordance with ACI Code 10.11.1 for calculating
deflections of an uncracked wall. Table 3-5 gives a summary of the estimated overall
drift of the shear walls.
Limiting drift
5.08 in
Table 3-5: Shear Walls Drift
NS drift
EW drift
4.5 in
3.03 in
Proportioning loads to each core:
Rigidities for each core were determined assuming only flexural deflection. Torsional
rigidities were determined assuming a solid core without openings and a poisson ratio of
0.2. Accidental torsion of 5% was included. From these calculations, it was found that
accidental torsion contributed to moments at each core. The additional shear forces
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caused by torsional moments at the core were determined assuming constant shear flow.
A summary of shear forces is given in Table 3-6.
Table 3-6: Shear Forces to Individual Core
Shear from direct shear
Shear from torsion
Shear on each core
NS
0.5V
0.117V
0.617V
EW
0.5V
0.167V
0.667V
Shear Reinforcement:
Shear strength for the shear wall cores was determined using only concrete shear
strengths and steel shear strengths in the walls in the direction of the load considered
(Ref. Figure 3-2). A  factor of 0.75 was used assuming only flexural failure of the wall.
Shear strength of concrete was determined using:
Vc   c
f c' tLw where
 c  2.0 for H LW  2.0
Figure 3-2. Shear Resisting Portions Considered
For most cases, it was found that minimum horizontal reinforcement was required. This
minimum according to ACI-318 provisions is ρmin =0.0025. Horizontal reinforcement for
all walls was chosen to be #4@8”.
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Bending Reinforcement:
Bending capacity of the shear wall core was determined with many simplifying
assumptions. Distributed rebar forces and compressive rebar forces were neglected. The
distance from tension steel to centroid of concrete stress block was assumed to be 0.9
times the length of wall. Pn was assumed to act 0.4 times the length of wall from the
neutral axis. The factor 0.9 was chosen instead of a smaller value since most of the
moment resisting rebars will be located in the flanges (Ref. Figure 3-3) of the core.
Figure 3-3. Moment Resisting Flanges of the Core
From these assumptions the relationship between axial load, area of steel reinforcement
in one flange and the bending capacity of the core is :
M n  0.9 LW As f y  0.4 LW Pn where
Mn 
P
Mu
and Pn  u
0.85
0.9
Axial loads were determined from tributary areas as shown below:
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Figure 3-4. Tributary Area of Shear Wall Core
Required area of reinforcing steel was determined from overturning moment and axial
load data using the above equations. For both NS and EW walls, #10@12” on each face
were chosen for reinforcement at the flanges.
For ductility reasons it is desired that the bending strength be reached before shear,
therefore a check of Mn/Vn vs Mu/Vu was performed. It was found that at higher stories
(story 6 and higher), the wall fails in shear. For ease of construction, the change of rebar
layout was done at story 5 where the buildings layout also changes. For both NS and EW
walls, #8@18” on each face were chosen for reinforcement at the flanges.
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Figure 3-5. Shear Wall Design
3.4 Connections
Various connections were used in our design and are described in this section. Detail
drawings are shown at the end.
Moment Resisting Frame:
Several connection types suitable for moment resisting frames in seismic regions were
considered. The structural engineer evaluated welded unreinforced flange-welded web
connection (WUF-W), welded flange plate (WFP) connection, and reduced beam section
(RBS) connection. Design procedure and criteria were followed as outlined in FEMA350 document.
The basic design approach of moment resisting connections is to estimate the location of
plastic hinges and determine probable plastic moments and shear forces at the plastic
hinges, at critical sections of the assembly. To be able to form plastic hinges in
predetermined locations, i.e. within beams, connections are strengthened and stiffened or
beam sections are locally reduced as in the case of reduced beam section connection
which were chosen for this project by the structural engineer.
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Column Splices
Close attention was paid to the splices of exterior columns which are part of the moment
resisting frame. These members, in addition to gravity loads, are subjected to relatively
high axial forces that are produced by overturning moments caused by seismic activity.
The structural engineer decided to use a combination of bolted and welded web splices
with complete joint penetration flange welds, which can support axial as well as bending
forces due to earthquake loads.
Shear Connections
Simple bolted shear connections were designed for interior column-to-beam connections,
beams framing into the shear walls, and the two beams framing into cantilever beam
which support the walkway on the 6th through 10th floor.
(Ref: Appendix E for calculation details)
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3.5 Foundation
The foundation of the building serves to transmit gravity and lateral loads as well as
overturning moments to the earth. To accomplish this we have selected a combination
foundation system. Under each gravity column, footings will serve to transfer the gravity
loads to the soil. From preliminary calculations for the base plates of these columns, it
was determined that the footings should be 42 inch square. The second part of the
foundation carries both gravity loads and overturning moments from the moment
resisting frames. This was accomplished using strip footings. The strip footings run the
length of the building along the perimeter and allow a path for the high moments
generated in the moment resisting frame. From similar calculations it was determined
that the footings should be at least 36 inches wide. Finally, the shear walls will be
supported by a mat foundation. The preliminary size of mat required to prevent
overturning of the shear wall base was determined from the overturning moment and the
dead load on the core. Resistance to overturning was assumed to come solely from dead
loads. The required eccentricity and therefore the required half width of the mat was
calculated by dividing the overturning moment by the total unfactored dead load
(including self weight) of the shear wall. A 48’ x 48’ mat was determined. Investigations
on the use of anchors are required to decrease the size.
Table 3-5 to Table 3-7: Calculation of Minimum Mat Foundation Size
Table 3-5
Wall Self weight
thickness
height
perim
Volume
density
Weight
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1.5
126
51
9639
150
1445.85
ft
ft
ft
ft^3
pcf
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Table 3-6
Determine Pu on Wall
10
9
8
7
6
5
4
3
2
1
FLRoof
FL10
FL9
FL8
FL7
FL6
FL5
FL4
FL3
FL2
Dead load
Area (85psf)
Area(50psf)
787.5
612.5
612.5
612.5
612.5
612.5
787.5
787.5
787.5
787.5
Total
(kips)
39.375
52.0625
52.0625
52.0625
52.0625
52.0625
66.9375
66.9375
66.9375
66.9375
567.4
Table 3-7
Total downward load at the
base of the shear wall
2013.288 k
Overturning moment
96698 kft
OR
48349 kft each
Eccentricity required
24.01 ft
Mat under Shear wall
should be 48' x48'
OR smaller with anchors
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4.0 ETABS Modeling - Analysis and Discussion
4.1 Model Discussion
ETABS was used to analyze the building. From the ETABS analysis we were able to
compare some of the actual load effects with the assumptions made in the design process.
We designed the moment resisting frame to be able to resist 25% of the total seismic
loads. However, from the results shown in Table 4-1, it is obvious that this is a very
conservative assumption.
The loads produced by ETABS are consistently lower than
those predicted by the Portal Method. In some cases the predicted values by the Portal
Method are twice of those calculated by ETABS. This discrepancy is accounted for in the
interaction between the moment resisting frame and the shear wall. The stiff shear wall
takes most of the load, so the moment resisting frame takes very little comparatively.
This can be proved by the shear wall frame interaction computations it was found that
only about 5-10% of the total load actually goes to the moment resisting frame.
Table 4-1: EW SMRF
Floor
Roof
Beam Moment
(interior)
Portal
ETABS
171.21
29.28
10
292.57
126.3
9
330.47
126
8
364.16
131.2
7
393.63
129.8
6
418.90
124.1
5
439.05
116.2
4
419.89
91.4
3
431.31
90.7
2
472.80
79.6
Column Moment
(interior)
Portal
ETABS
Column Axial
(exterior)
Portal
ETABS
87.28
99.14
74.81
14.4
138.04
94.06
154.42
66.8
173.83
106.25
236.41
120.04
205.41
102.67
320.48
173.78
232.79
101.91
406.37
227.7
255.95
105.59
493.79
281.57
273.07
74.05
586.24
339.88
272.96
74.44
661.14
384.76
282.47
69.49
741.12
429.46
355.93
53.25
821.51
473.4
1
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Table 4-2: NS SMRF
Beam Moment
(interior)
Floor
Roof
Portal
142.70
ETABS
56.118
10
255.87
155.73
9
297.56
Column Axial
(exterior)
Portal
ETABS
Portal
ETABS
74.66
60.64
44.54
8.14
119.92
89.93
88.85
31.67
155.71
95.37
135.42
57.2
187.30
102.45
183.92
82.71
214.67
110.42
234.04
108.97
237.83
115.77
285.44
135.07
254.96
120.34
340.69
165.12
270.46
113.36
394.06
190.7
279.98
105.52
453.32
215.03
353.44
87.88
513.05
237.62
180.79
8
334.62
180.18
7
367.04
187.47
6
394.84
183.65
5
416.99
204.04
4
439.46
175.5
3
452.02
160.87
2
Column Moment
(interior)
497.66
143.22
1
4.2. Shear Wall-Frame Interaction
We evaluated the frame shear wall interaction using the Component Stiffness Method.
This is used to find out the percentage of lateral load going to the shear wall and the
frame. The assumptions made in the Component Stiffness Method are:
1. Torsion is ignored.
2. No openings in the core
3. Uniform story height has been assumed. In reality we have the 1st and 2nd story at
15 ft each, and all other stories at 12 ft so. An average uniform story height was
assumed to be 12.6 ft
4. Shear deformations are neglected.
5. Calculations showed that seismic deflections governed over wind, thus wind was
ignored in the final calculation of forces, deflection, and moment.
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6. Axial deformations very small, hence ignored.
(Ref: Appendix F for calculations)
Table 4-3. Shear Wall-Frame Interaction Summary
NS
EW
P to each frame
30.10 k
26.27 k
P to each wall
30.10 k
26.27 k
Deflection
2.61 in
1.76 in
Overturning Moment
44683 k-ft
45147 k-ft
Vext.col
5.35 k
4.38 k
Vint.col
9.81 k
8.76 k
ΣMext.col
87.63 k
71.71 k
ΣMint.col
160.69 k
143.42 k
4.3 ETABS Model and Frame- Shear Wall Interaction Comparison
From the story drift data collected from ETABS, we were able to calculate the
deflections. These were compared to the shear wall frame interaction, as can be seen in
the following table.
Table 4-4 to Table 4-6: Interaction Equations Vs. Computer analysis
Table 4-4
Shear wall Frame interaction
ETABS
NS Total Deflection (in)
2.61
3.15
EW Total Deflection (in)
1.76
1.785
From these comparisons, it is seen that the assumptions made in using the shear wall
frame interaction formulas are verified through the computer analysis using ETABS.
Deflections differences in the east west direction were smaller than in the north south
direction. This can be explained by the fact that door openings were modeled in ETABS
whereas they were ignored in interaction calculations.
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Percentage of the overturning moment resisted by the shear wall core was also compared,
as can be seen in the table below. Again, the effects of the door openings account for the
differences between hand calculations and the ETABS model. Since openings were
modeled the walls become less stiff and a lower percentage of the building overturning
moment is resisted by the cores.
Table 4-5
North South
ETABS
Shear wall Frame
interaction
Half the Building
Over turning moment
48349kft
47960.61kft
Overturning
moment one core
40208.38kft
44683 kft
Percentage of load
going to the core
0.83
0.93
Table 4-6
East West
ETABS
Shear wall Frame
interaction
Half the Building
Over turning moment
48349kft
47960.61kft
Overturning
moment one core
39895.68kft
45147 kft
Percentage of load
going to the core
0.825
0.94
Half the building overturning moment for the shear wall frame interaction was obtained
using the story shears calculated from assumed seismic dead loads and the UBC ’97
code. The same values were generated from ETAB’s built-in UBC’97 code calculations
for the same assume period of the structure but with seismic dead loads obtained from the
self weight of the structure. These values are tabulated in the Appendix F.
Interstory drifts limits were also checked against the seismic interstory drift limitation
given by 0.00336. As designed, nowhere are the seismic drifts limits exceeded.
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Floor
Roof
10
9
8
7
6
5
4
3
2
1
EW earthquake interstory drift
0.000638
0.001362
0.001368
0.001366
0.00135
0.001314
0.001251
0.001155
0.001023
0.000852
0.000602
NS earthquake interstory drift
0.000663
0.002466
0.002494
0.002479
0.002448
0.002383
0.002097
0.001858
0.001543
0.001096
0.00448
5.0 Conclusions
For preliminary design of a regular 10 story building, simplifying calculations were
found to provide sufficient accuracy for the initial choice of member sizes. By knowing
the behavior of a structure, few detailed calculations had to be performed.
The
assumption that 100 percent of the lateral loading goes to the cores while 25 percent goes
to the SMRF was also found to be a good conservative approximation.
Assumptions that the cores had no door openings significantly reduced the complexity of
calculations but also reduced the accuracy of the results. In addition, rebar quantities
were only calculated for a core without openings. Rebar layouts in the wall piers as well
as in spandrel beams of the core require more complex calculations which can be
automated using ETABS.
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PART TWO: APPENDIX - DESIGN CALCULATIONS
Appendix A – Load Determination
Appendix B – Gravity System Design
Appendix C – SMRF Design
Appendix D – Shear Wall Design
Appendix E – Connection Details and Calculations
Appendix F – Analysis Results (ETABS and Interaction)
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