Phantom Engineering & Consulting
DESIGN AND ANALYSIS OF PHANTOM TOWER
Design Team: Mohammad Mualla, Xin Tao Liao, Carlos Peralta, Justin Hum
Project Manager: Mohammad Mualla
Respectfully Submitted: December 15, 2016
PAGE 1
Table of Contents
Table of Contents ....................................................................................................................................... 1
Section 1: General Information/Architectural Design ............................................................................. 4
1.1 Building Description ......................................................................................................................... 5
1.2 Architectural Layout Inspiration ..................................................................................................... 6
1.2 Means of Egress ................................................................................................................................. 9
1.3 Parking Lot Design .......................................................................................................................... 10
Section 2: Design Criteria ......................................................................................................................... 15
2.1 Loads ................................................................................................................................................. 15
2.1.1 Gravity Loads .............................................................................................................................. 15
2.1.2 Wind Load ................................................................................................................................. 19
Comparison of hand calculations to ETABs Results .............................................................................. 28
2.1.3 Seismic Loads ............................................................................................................................ 29
2.2 Load Combinations ........................................................................................................................ 29
2.3 Materials Used ................................................................................................................................. 31
2.4 Serviceability .................................................................................................................................. 32
2.4.1 Slab Serviceability ..................................................................................................................... 32
Section 3: Structural System .................................................................................................................... 33
3.1 Gravity System ................................................................................................................................. 33
3.2 Lateral System ................................................................................................................................ 33
3.3 Structural Components .................................................................................................................. 33
3.3.1 Slabs ........................................................................................................................................... 33
3.3.2 Columns .................................................................................................................................... 34
3.3.3 Shear Walls ............................................................................................................................... 37
3.3.4 Transfer Beam .......................................................................................................................... 37
3.3.5 Foundation & Isolated Footing & Strip Footing ..................................................................... 37
Section 4: Analysis & Global Behavior .................................................................................................... 38
4.1 Finite Element Models ................................................................................................................... 38
4.1.1 SAFE: Slab Design...................................................................................................................... 38
4.2 ETABS: Global Analysis .................................................................................................................40
4.2.1 Story Shear Graph ..................................................................................................................... 44
4.2.2 Maximum Story Drifts ............................................................................................................. 46
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4.2.3 Maximum Story Displacements .............................................................................................. 47
4.3 P‐Delta Effects ................................................................................................................................ 56
4.4 Element Types ................................................................................................................................ 56
Appendix A: Transfer Beam Hand Calculations .................................................................................... 57
Appendix B: Column Hand Calculations ............................................................................................... 60
Appendix C: Two‐Way Slab Design ....................................................................................................... 64
Appendix D: ETABS Wind Loading ....................................................................................................... 69
Appendix E: Wind Load Hand Calculations ............................................................................................. 70
Appendix F: Seismic Hand Calculations................................................................................................. 75
Appendix G: Shear Wall Design .............................................................................................................. 81
Appendix H: Isolated Footings ................................................................................................................ 85
Appendix I: Foundation Wall ................................................................................................................. 89
Appendix J: Load Bearing Wall .............................................................................................................. 94
Appendix K: Wall Footing ...................................................................................................................... 96
Appendix L: Snow Loads ........................................................................................................................ 99
Appendix M: Tabulated ETAB WIND & Seismic Results ..................................................................... 103
PAGE 3
Table of Figures/Tables
Table of Figures/Tables .......................................................................................................................... 3
Figure 1. North elevation view. .................................................................................................................. 5
Figure 2. East elevation view. ...................................................................................................................... 5
Figure 3: Layout of Apt 52A at 432 Park Avenue .................................................................................... 67
Figure 4. Ground Floor Architectural Layout .......................................................................................... 7
Figure 5. Typical Floor Architectural Layout ........................................................................................... 8
Figure 6. Penthouse Floor 16 Architectural Layout ................................................................................. 8
Figure 7. Penthouse Floor 17 Architectural Layout .................................................................................. 9
Figure 8. Location of Phantom Tower .................................................................................................... 10
Table 1. Parking Spaces Required Where Group Parking Facilities Are Provided ................................ 11
Figure 9: Basement Vehicle Tracking Simulations & Corresponding Parking Lot Level 1 Layout ...... 12
Figure 10: Subbasement Vehicle Tracking Simulation & Corresponding Parking Lot Level 2 Layout 13
Table 2‐3. Tables taken from the excel used to estimate the weight of the building .......................... 16
Table 4. SDL & LL values used in design ................................................................................................ 18
Table 5. Slab Serviceability, AISC Design Guide .................................................................................... 32
Figure 11. Columns and Footings in Subbasement ................................................................................. 35
Figure 12: This figure shows the shortest clear spans between columns on the ground floor ............ 35
Figure 14: This figure is from the column layout of floor 17, maximum spans are allowed due to
smaller blueprint and larger open spaces. .............................................................................................. 36
Figure 15: This Figure shows the coordinates, column tag and column above symbol for the
respective column. ................................................................................................................................... 36
Figure 18: Ground Floor shear walls subjected to load combination “ENV‐WG” ................................ 42
PAGE 4
Section 1: General Information/Architectural Design
This report addresses the design criteria and the design and analysis of the structural
components in the 17 story luxury apartment complex, Phantom Tower. The Phantom Tower is
located in The Bronx, New York. The report will cover the general information of the building,
architectural layout and its influences, design criteria for the buildings as well as an in depth
analysis of the structural components and their behavior when introduced to several loads.
The building is modeled and design using a various software listed below:
AutoCAD 2016
Revit 2016
ETABS 2015
SAFE 2014
Sample calculations for structural components and loads were completed to validate data from the
analysis software and are attached in the appendix of this report.
The Following References were used in the design:
International Building Code 2012
ASCE 7‐10
ACI‐318‐11
Sample calculations for structural components and loads were completed to
validate data from the analysis software and are attached in the appendix of this
report.
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1.1 BUILDING DESCRIPTION
Phantom Tower is a luxury Residential building. The building is wrapped in a beautiful
limestone veneer and accented with black aluminum window frames. The building is comprised of
two sublevels that hold 60 parking spots. The ground floor includes amenities that are available to
all residents which include a gymnasium, Children’s Daycare, Conference Rooms, and a bike
storage room. There is also a terrace on the 2nd floor where residents can enjoy the sun, have
barbeques, and other types of social gatherings. Floors 2 through 15 are all have a mix of 2 and 3
bedroom apartments, with a total of 8 units on each floor. All units include a Washer/ Dryer room
and an open kitchen that leads to the living rooms. Floors 16 and 17 houses 2 duplex penthouses
that have access to the roof garden.
Each floor is 9 feet tall with the exception of the ground floor which is 14’ tall making the
Phantom Tower stand 158 feet tall at the top of the roof garden. The Phantom Tower has a 189’ X
111’ blueprint on its largest floors and 122’ x 66’ on its smallest floors.
Figure 1. North elevation view.
Figure 2. East elevation view.
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1.2 ARCHITECTURAL LAYOUT INSPIRATION
Floor Layout
Plenty of inspiration was taken from three luxury residences scattered across NYC. The first
residence is the famous 432 Park Avenue. The design team attempted to capture the simplicity of
the layout of 432 Park Ave. Apartment 52A
was used as a template for the layout of the
Phantom Tower. This apartment is
approximately 1600 SF, the typical SF size of
an apartment at the Phantom Tower. The
apartments are designed with privacy in
mind. The Master Bedroom is cornered off,
with a grand view, a walk‐in closet, and a
Master Bathroom. The kitchens were also
modeled near the living room. The
advantage of having the kitchen open to the
living room is that the light provided from
the living room allows the kitchen to function as a true kitchen (by code) and not a closed off
kitchenette. This allowed us to increase the SF of the kitchens to approximately 125 SF. The New
York City Building Code dictates that a kitchen with no window is actually a kitchenette and must
not exceed 80 SF. The idea of having a powder room in the main living area was to divide the
private bedrooms, from the living and entertaining area. A powder room was provided in the main
hall of each apartment so that a guest would be able to use the bathroom, without intruding into
the private rooms. Adjacent Bathrooms were also placed next to one another, so as to use the same
pipe shaft. The same concept was applied for kitchens, the walls separating the apartments houses
a shaft for the plumbing of the kitchens (one kitchen on each side of the wall). Inspiration was also
Figure 3: Layout of Apt 52A at 432 Park Avenue
PAGE 7
taken from 111 W57 St and 70 Vestry St. With similar concepts in mind, the design team was able to
merge ideas from each layout to create similar apartment layouts.
The residence hallways are 5’ wide. The design team also reached out to an Architect
named John Ellis in the NYC area to seek consultation. Mr. Ellis indicated that hallways are usually
4‐5 feet, but 5’ is adequate for a luxury residence. Attached below are the architectural plans for
the Ground floor, typical floor and Penthouse floors respectively.
Figure 4. Ground Floor Architectural Layout
PAGE 8
Figure 5. Typical Floor Architectural Layout
Figure 6. Penthouse Floor 16 Architectural Layout
PAGE 9
Figure 7. Penthouse Floor 17 Architectural Layout
1.2 MEANS OF EGRESS
Referring to Chapter 10 of the International Building Code (2012 edition) we deduced that we
needed 2 means of egress based off our occupancy. We provided a two staircases on each floor to
account for such provisions in this code. All rooms have to be within 200ft of the entrance of one
staircase, and that each staircase must either lead to the exterior of a building or to an exit pathway
that leads to the exterior of the building. With that in mind we placed our staircases strategically in
two scores that were evenly spaced out on each floor so that we can abide by the parameters set by
the code. The code also states that the staircases must have a 2‐hour fire rating. Given that the
stairs are housed in the shear walls of our buildings this requirement was also met.
PAGE 10
1.3 PARKING LOT DESIGN
Parking in NYC is based off of your zoning district and the New York City Zoning Resolution.
According to the zoning map, and based of the latitude and longitude given to us, we can see that
we are in zoning R6.
Figure 8. Location of Phantom Tower
Once the zoning is established, we can then go into the NYCZR to find exactly how many parking
spots we need. The parking spot number is based off residencies. A residence is defined as a unit
and we estimated this number to be 114. Then using the following table of we can see that our
parking spot amount is 70% of the total residencies:
PAGE 11
70% ∗ 114 . 80
Table 1. Parking Spaces Required Where Group Parking Facilities Are Provided
However, after obtaining waivers from Professor Aboumoussa, we are able to reduce the parking
spot requirement to 60 spots. When designing the parking lot for our project we had to keep in
mind the turning radius of each car as well as clearance in between spots. All one way driving lanes
have to be 21 feet wide to accommodate for people pulling out and in to spots, and two way driving
lanes have to be 24’. To ensure that our parking lot satisfies these requirements we used Vehicle
Tracking from Autodesk to simulate the driving lanes and turning radii for cars in our parking lot.
Attached Below are the screenshots for these simulations as well as their respective architectural
layouts.
PAGE 12
Figure 9: Basement Vehicle Tracking Simulations and Corresponding Parking Lot Level 1 Layout
PAGE 13
Figure 10: Subbasement Vehicle Tracking Simulation and Corresponding Parking Lot Level 2 Layout
PAGE 14
Both sublevels have a ceiling height of 12 feet and all ramps are designed to be at the maximum
20 % grade. Higher grade ramps allow for more space in the parking lot for vehicles to turn and
more space for parking. The ramp, connecting the exterior of the building to the basement, is 40
feet long, however the ramp is extended 5 feet out of the building and the ramp starts at the
beginning of the curb directly outside the entrance to the parking lot, thus the ramp inside the
parking is only 35 feet long. All ramps are 24 feet wide to allow for 2 way driving lanes. Similarly, all
landings on each floor are 24 feet wide by 24 feet long to allow for two way lanes and turning radii
of cars. The parking lots will have direction arrows and stop signs added to help circulate traffic in
the parking lot.
PAGE 15
Section 2: Design Criteria
The building was designed adhering to the following codes:
ASCE 7‐10
ACI 318‐14
ACI 318‐11
NYCBC‐2014
Within these codes certain loading, serviceability, and other requirements are established. The
serviceability and loading requirements are explained and proven to be met and satisfied in the
following sections.
2.1 LOADS
2.1.1 Gravity Loads
Dead loads consist of the weight of the construction material incorporated into the
building. For design purposes, the weight of materials and constructions should be used, as well as
mechanical systems. Normal weight concrete was used in the structure with a unit weight of 150
lb/ft3. Live loads are produced by the use and occupancy of the building and do not include
construction or environmental loads. Superimposed dead loads (SDL) are the loads that we will
typically find on the structure once it is completed. Façades are not designed to bear any structural
loads from the building but their weight must be accounted for in the design of the building.
All load cases were modeled as linear static cases. The following table displays the load cases that
were input into the ETABS model.
Table 1. ETABS Model Load Cases
Name Type
Dead Linear Static
LLRED Linear Static
LLNRED Linear Static
LLROOF Linear Static
SDL Linear Static
FACADE Linear Static
WIND Linear Static
EQ Linear Static
EQDRIFT Linear Static
PAGE 16
Height:
Loads Values 14
SDL (psf) SDL Applied Areas (sf) Total: (ksf)
Parking 10 Lobby 3164.63 158.2315
Mechanical/Service/Electrical/Refuse 50 Corridors 2793.29 27.9329
Lobby 50 Residential 5009.37 100.1874
Residential 20 Mail Room 686.23 25.39051
Roof 13 Storage 4243.99 212.1995
Storage 50 Masonry Façade 556.24 13.34976
Mail Room 37
Green Roof 32
Masonry Façade 48
Corridors 10
DL (pcf) Terrace Area (sf) Thickness (ft) Total:
Slab 150 0 0 0
Shear Wall 150 Slab Area (sf) Thickness (ft) Total:
18532.44 0.8333 2316.555
16 x 30 155 Shear Wall Area (sf) Height (ft) Total:
12 x 18 155 226.1 14 474.81
12 x 16 155 Shear Wall Length (ft)
12 x 30 155 226.1
Columns Applicable Area (per column, sf) Total:
Misc. (psf) 12 x 16 1.333333333
Partition Walls 12 12 x 18 1.5
Stairs 155 16 x 30 3.333333333
12 x 30 2.5
Total Weight of Building 52860.6815 Height (ft) # of columns
14 9
5
38
12
Total
Area: (sf) 1760
Stair Area (sf) Height (ft) Total
120 14 130.2
382.2816667
Ground Floor
Columns
Partition Walls
Grand Total: 3862.258237
21.12
Note: Using revit we are able to more accurately get
the areas for partition walls
2.1.1.1Dead loads
The total weight of the building, or the dead load was calculated using material weights. For
example, the weight of the column is taken by:
155 ∗ 14 ∗16 30144
∗ 28 /1000 202.53
Similar calculations are done for other structural elements such as shear walls and the slabs. We
also consider the weight of the elevators, stairs, and super imposed dead loads. The following tables
show the excel that was created to calculate the total DL. Calculations were separated by floor. The
total weight of the building was calculated to be 52860 kips. Below you can see the format that was
used to calculate the weight of a floor:
Table 2‐3. Tables taken from the excel used to estimate the weight of the building
PAGE 17
2.1.1.2 Live Loads & Superimposed Dead Loads
Live loads are produced by the use and occupancy of the building and do not include construction
or environmental loads. The live loads applied and materials weight used to calculate the SDL’s
were taken from the IBC, ASCE 7‐10, NFPA 13, or the AISC 14. Anything other sources will be
identified when used. Values can be seen in table 2 below.
Calculations:
All loads were taken
Parking
We know that our parking lot will have mechanical ducts (5 psf), a sprinkler system (3 psf) and can
allot about 2 psf for lights so we get a total of 10 psf.
Residential
Our residential space will be comprised of hardwood flooring (4 psf), plaster on tile (5 psf), and
partition walls (10 psf) which gives us a total of about 20 psf.
Corridors
Corridors are just linoleum tiles (1 psf), lighting (1 psf), plaster on tile (5 psf), and a sprinkler system
(3 psf) which gives us a total of 10 psf.
Masonry Façade
The façade load is directly given in the code to be 48 psf.
Green Roof
Assuming the usage of an Extensive green roof, from Columbia Green Technologies, they calculate
their roofs to have a saturated load of, at max, 32 psf.
Roof
Assuming four‐ply felt and gravel (6 psf), Water proofing membrane (5.5 psf), and insulation (1 psf)
we get a total of around 13 psf.
PAGE 18
For the remaining loads we took an estimate of half of the current Live Load acting on that area,
given that these particular areas are subject to high and varying loads.
Category SDL (psf)
LL (psf)
Parking 10 40
Mechanical/service/electrical/refuse 50 100
Lobby 50 100
Residential 20 40
Roof 13 20
Storage 50 100
Mail Room 37 100
Green Roof 32 100
Masonry Facade 48 0
Corridors 10
100 (on first floor,
other floors use
same occupancy as use)
Table 4. SDL & LL values used in design
2.1.1.4 Façade loads
Façades are not designed to bear any structural loads from the building but their weight must be
accounted for in the design of the building. The loads given by the facade were applied to the edge
beams, which were modeled with no properties in ETABS.
PAGE 19
2.1.2 Wind Load
Wind loads were calculated using ASCE 7-10 as reference. The wind loads for the Main Wind Force Resisting System(MWFRS) was designed using the directional procedure indicated in chapter 27 of the ASCE 7-10. Before any calculations were done several items have to be addressed; exposure category, building type, building shape and irregularities, risk category, rigidity and basic wind speed. For our project the items and their values are listed below:
Items ValuesExposure Category CBuilding Type Enclosed Building shape and irregularities RegularRisk Category IIRigidity RigidBasic Wind Speed 98(124)
Table 1: List of Items addressed pre-calculations
The exposure category was chosen as C because our building is located in the Bronx in an urban environment, according to Section 27.7-3 of ASCE 7-10 this kind of Surface Roughness falls under Exposure C. Our building is a rigid regular enclosed building, with a risk category II as stated per code. The basic wind speed can be found in Figure 26.5-1A in ASCE 7-10 and was found to be a value of 98 which was then increased to 124 for design purposes. The rigidity of the building was assumed to be rigid because the main lateral wind resisting system is ordinary reinforced concrete shear walls. Thus the gust effect factor maybe conservatively assumed to be 0.85.
After addressing these items we can then define some terms that will be necessary in our calculations later on. These terms are listed in the table below:
ASCE 7-10 Section
Basic Wind Speed V60 Section 26.5-1 98 mph
Basic Wind Speed V700 124 mph
Wind Directionality Factor Kd Section 26.6 Table 26.6-1 0.85
Exposure Category Section 26.7.3 C
Topographic Category Kzt = (1+K1K2K3)^2 Section 26.8.2 1
Gust Effect Factor Section 26.9
0.85
Enclosure Classification Section 26.10
Internal Pressure Coefficient GCpi Section 26.11-1 0.18 -0.18
Risk Category Table 1604.5 NYCBC II
Zg (ft) Table 26.9-1 900
α Table 26.9-1 9.5
Velocity Pressure Exposure Coefficient Kz or Kh
Coefficent 0.00256
PAGE 20
Table 2: List of terms and variables used in calculations of design wind loads
Figure 1: Table 27.2-1(ASCE 7-10) was used as a guide for future calculations.
To find the design load(p) we must first find the respective velocity pressure(q) on each floor. q is defined by the equation below from ASCE 7-10.
0.00256 1
Where:
PAGE 21
27.3 1 7 10
26.8 2 7 10
26.6 7 10
26.5 7 10
Next we also must define the external pressure coefficient based off figure 27.4-1(ASCE 7-10).
Figure 2: Table 27.4-1 from ASCE 7-10 is used to find the Wall pressure Coefficients used in our design
After defining all these values, we can now find the design wind pressure with the following equation.
2
Where:
26.9 7 10
27.4 1 7 10
27.3 1 7 10
26.11 1 7 10
The directional procedure for finding design wind loads for MWFRS requires us to calculate wind pressure for 4 different cases. These four cases show the various types of wind combinations and pressures that our building may encounter. The figure from ASCE 7-10 below will show which four cases we must deal with.
PAGE 22
Figure 3: The four load cases used in directional procedure as defined by Figure 27.4-8 (ASCE 7-10)
Case 1
Case 1 deals with wind pressure acting on each of the orthogonal faces of the building, however pressure each orthogonal face is to be calculated separately.
Values for Case 1
Level
Height Above
Ground Level, z
(ft)
Velocity Pressure
Coefficeint, Kz for
Exposure C
q qi Pwx
(lb/ft^2) Plx
(lb/ft^2) p NET
tributary area (ft^2)
wind force (kip)
Ground Floor
0.00 0.00 0.00 0.00 0.00 0.00 0.00 1337.00 0.00
2 14.00 0.85 28.40 47.17 12.03 ‐11.56 23.59 1840.00 43.40
PAGE 23
3 23.00 0.93 31.08 47.17 13.96 ‐11.56 25.52 1440.00 36.75
4 32.00 1.00 33.31 47.17 15.58 ‐11.56 27.14 1440.00 39.08
5 41.00 1.05 35.10 47.17 16.87 ‐11.56 28.42 1440.00 40.93
6 50.00 1.09 36.60 47.17 17.95 ‐11.56 29.51 1440.00 42.49
7 59.00 1.13 37.89 47.17 18.89 ‐11.56 30.44 1440.00 43.84
8 68.00 1.17 39.04 47.17 19.72 ‐11.56 31.27 1440.00 45.04
9 77.00 1.20 40.08 47.17 20.47 ‐11.56 32.02 1440.00 46.11
10 86.00 1.23 41.02 47.17 21.15 ‐11.56 32.70 1440.00 47.09
11 95.00 1.25 41.89 47.17 21.77 ‐11.56 33.33 1440.00 48.00
12 104.00 1.28 42.70 47.17 22.36 ‐11.56 33.91 1440.00 48.84
13 113.00 1.30 43.45 47.17 22.90 ‐11.56 34.46 1440.00 49.62
14 122.00 1.32 44.16 47.17 23.41 ‐11.56 34.97 1440.00 50.35
15 131.00 1.34 44.82 47.17 23.89 ‐11.56 35.45 1440.00 51.05
16 140.00 1.36 45.45 47.17 24.35 ‐11.56 35.91 1080.00 38.78
17 149.00 1.38 46.05 47.17 24.78 ‐11.56 36.34 1080.00 39.25
Roof Garden 158.00 1.39 46.63 47.17 25.20 ‐11.56 36.75 1080.00 39.69
Top of Bulkhead
167.00 1.41 47.17 47.17 25.59 ‐11.56 37.15 243.00 9.03
Table 3: Show Values for design wind pressure on both windward and leeward Walls in the X direction
Level Height Above
Ground Level, z (ft)
Velocity Pressure
Coefficeint, Kz for
Exposure C
q qi Pwy
(lb/ft^2) Ply
(lb/ft^2) p NET
tributary area (ft^2)
wind force (kip)
Ground Floor
0.00 0.85 28.40 47.17 12.03 ‐3.54 15.57 770.00 9.26
2 14.00 0.85 28.40 47.17 12.03 ‐3.54 15.57 1265.00 15.22
3 23.00 0.93 31.08 47.17 13.96 ‐3.54 17.50 990.00 13.82
4 32.00 1.00 33.31 47.17 15.58 ‐3.54 19.12 990.00 15.42
5 41.00 1.05 35.10 47.17 16.87 ‐3.54 20.41 990.00 16.70
6 50.00 1.09 36.60 47.17 17.95 ‐3.54 21.49 990.00 17.77
7 59.00 1.13 37.89 47.17 18.89 ‐3.54 22.42 990.00 18.70
8 68.00 1.17 39.04 47.17 19.72 ‐3.54 23.26 990.00 19.52
PAGE 24
9 77.00 1.20 40.08 47.17 20.47 ‐3.54 24.00 990.00 20.26
10 86.00 1.23 41.02 47.17 21.15 ‐3.54 24.69 990.00 20.94
11 95.00 1.25 41.89 47.17 21.77 ‐3.54 25.31 990.00 21.56
12 104.00 1.28 42.70 47.17 22.36 ‐3.54 25.89 990.00 22.13
13 113.00 1.30 43.45 47.17 22.90 ‐3.54 26.44 990.00 22.67
14 122.00 1.32 44.16 47.17 23.41 ‐3.54 26.95 990.00 23.18
15 131.00 1.34 44.82 47.17 23.89 ‐3.54 27.43 990.00 23.65
16 140.00 1.36 45.45 47.17 24.35 ‐3.54 27.89 675.00 16.44
17 149.00 1.38 46.05 47.17 24.78 ‐3.54 28.32 675.00 16.73
Roof Garden
158.00 1.39 46.63 47.17 25.20 ‐3.54 28.73 675.00 17.01
Top of Bulkhead
167.00 1.41 47.17 47.17 25.59 ‐3.54 29.13 135.00 3.45
Table 4: Show Values for design wind pressure on both windward and leeward Walls in the Y direction
Case 2
Case 2 is the like case 1 in which the calculations for the design wind loads for each orthogonal axis is done separately. However, these orthogonal wind pressures are reduced to 3/4th of the their original values and a torsional moment is introduced to the calculation of each wind load to account for eccentricity.
Values for Case 2
Level Height Above Ground Level, z (ft) 0.75pwx (lb/ft^2) 0.75plx (lb/ft^2) Mt (lb*ft)
Ground Floor 0.00 0.00 0.00 0.00
2 14.00 9.02 -8.67 96802.75
3 23.00 10.47 -8.67 104732.89
4 32.00 11.68 -8.67 111367.45
5 41.00 12.65 -8.67 116658.39
6 50.00 13.46 -8.67 121098.63
7 59.00 14.17 -8.67 124946.49
8 68.00 14.79 -8.67 128355.52
9 77.00 15.35 -8.67 131425.00
10 86.00 15.86 -8.67 134223.09
11 95.00 16.33 -8.67 136798.75
12 104.00 16.77 -8.67 139188.43
13 113.00 17.18 -8.67 141420.03
14 122.00 17.56 -8.67 143515.44
PAGE 25
15 131.00 17.92 -8.67 145492.15
16 140.00 18.26 -8.67 147364.39
17 149.00 18.59 -8.67 149143.89
Roof Garden 158.00 18.90 -8.67 150840.46
Top of Bulkhead 167.00 19.19 -8.67 152462.37
Table 5: Shows reduced values for windward and leeward pressures as well as the torsional moment for each floor in the X direction
Level Height Above Ground Level, z (ft) 0.75pwx (lb/ft^2) 0.75plx (lb/ft^2) Mt (lb*ft)
Ground Floor 0.00 7.82 -2.15 36894.29
2 14.00 7.82 -1.08 36894.29
3 23.00 8.84 -1.22 41686.77
4 32.00 9.71 -1.34 45811.65
5 41.00 10.43 -1.44 49173.20
6 50.00 11.04 -1.53 52041.90
7 59.00 11.57 -1.60 54562.07
8 68.00 12.05 -1.67 56820.77
9 77.00 12.49 -1.73 58874.94
10 86.00 12.89 -1.78 60764.09
11 95.00 13.26 -1.83 62516.84
12 104.00 13.60 -1.88 64154.68
13 113.00 13.93 -1.93 65694.19
14 122.00 14.24 -1.97 67148.44
15 131.00 14.53 -2.01 68527.96
16 140.00 14.81 -2.05 69841.34
17 149.00 15.08 -2.08 71095.72
Roof Garden 158.00 15.33 -2.12 72297.10
Top of Bulkhead 167.00 15.58 -2.15 73450.54
Table 6: Shows reduced values for windward and leeward pressures as well as the torsional moment for each floor in the Y direction
Case 3
The wind loads for case 3 are applied similarly to case 1 however all the wind loads are reduced to 3/4th of their values and they are also applied to both orthogonal axis simultaneously.
Values for Case 3
PAGE 26
Level Height Above
Ground Level, z (ft) 0.75pwx
(kip/ft^2) 0.75plx
(kip/ft^2) 0.75pwy
(kip/ft^2) 0.75ply
(kip/ft^2)
Ground Floor
0.000 0.000 0.000 0.000 0.000
2 14.000 9.022 -8.668 9.022 -6.501
3 23.000 10.471 -8.668 10.471 -6.501
4 32.000 11.684 -8.668 11.684 -6.501
5 41.000 12.651 -8.668 12.651 -6.501
6 50.000 13.462 -8.668 13.462 -6.501
7 59.000 14.165 -8.668 14.165 -6.501
8 68.000 14.788 -8.668 14.788 -6.501
9 77.000 15.349 -8.668 15.349 -6.501
10 86.000 15.860 -8.668 15.860 -6.501
11 95.000 16.331 -8.668 16.331 -6.501
12 104.000 16.768 -8.668 16.768 -6.501
13 113.000 17.176 -8.668 17.176 -6.501
14 122.000 17.558 -8.668 17.558 -6.501
15 131.000 17.920 -8.668 17.920 -6.501
16 140.000 18.262 -8.668 18.262 -6.501
17 149.000 18.587 -8.668 18.587 -6.501
Roof Garden 158.000 18.897 -8.668 18.897 -6.501
Top of Bulkhead
167.000 19.193 -8.668 19.193 -6.501
Table 7: Shows the reduced values for both orthogonal cases
Case 4
Case 4 is like case 2 in the way the design loads are applied however both torsional moment and the reduced wind loads for both directions are applied simultaneously.
Values for Case 4
Level Height Above
Ground Level, z (ft)
Plx (lb/ft^2)
Pwy (lb/ft^2)
Ply (lb/ft^2)
ex ey Mt (lb*ft)
Ground Floor 0.00 0.00 0.00 0.00 28.65 16.50 0.00
2 14.00 -11.56 12.03 -3.54 24.00 16.50 9697.43
3 23.00 -11.56 13.96 -3.54 24.00 16.50 15849.23
4 32.00 -11.56 15.58 -3.54 24.00 16.50 20995.99
5 41.00 -11.56 16.87 -3.54 24.00 16.50 25100.44
PAGE 27
6 50.00 -11.56 17.95 -3.54 24.00 16.50 28544.96
7 59.00 -11.56 18.89 -3.54 24.00 16.50 31529.93
8 68.00 -11.56 19.72 -3.54 24.00 16.50 34174.48
9 77.00 -11.56 20.47 -3.54 24.00 16.50 36555.63
10 86.00 -11.56 21.15 -3.54 24.00 16.50 38726.25
11 95.00 -11.56 21.77 -3.54 24.00 16.50 40724.32
12 104.00 -11.56 22.36 -3.54 24.00 16.50 42578.11
13 113.00 -11.56 22.90 -3.54 24.00 16.50 44309.28
14 122.00 -11.56 23.41 -3.54 24.00 16.50 45934.79
15 131.00 -11.56 23.89 -3.54 24.00 16.50 47468.22
16 140.00 -11.56 24.35 -3.54 18.00 11.25 25441.79
17 149.00 -11.56 24.78 -3.54 18.00 11.25 26175.04
Roof Garden 158.00 -11.56 25.20 -3.54 18.00 11.25 26874.12
Top of Bulkhead 167.00 -11.56 25.59 -3.54 8.10 4.50 5132.11 Table 8 Shows the values for both reduced loads and the torsional moments calculated in Case 4
Using the design loads calculated in each case we can then verify the design loads outputted by ETABS in the future to prove our analysis was done correct.
The following is a lateral force to stories diagram used to verify results in Etabs.
Figure 4: lateral loads to stories diagram for the x‐direction
0.00 10.00 20.00 30.00 40.00 50.00 60.00
0.00
23.00
41.00
59.00
77.00
95.00
113.00
131.00
149.00
167.00
Wind Force (kips)
Height Above Ground (ft.)
Lateral Loads to stories (x‐direction)
PAGE 28
Figure 5: lateral loads to stories diagram for the y‐direction
These diagrams show the lateral loads acting on each story due to wind. As you can see the load continues to increase as the height of the building increases. However when it reaches the setback floors and the bulkhead the lateral loads decrease since the surface area for the wind to act on becomes lower.
Comparison of hand calculations to ETABs Results
The following is a table that compares the wind loads acting on our building that was calculated
from the excel versus the ETABs model. Besides the setback floors the difference between the two
are very low (below 5%). The setback floors have higher percent of error because the model on
ETABs and the excel may have considered the roof differently. Where ETABS treated the setbacks
as a roof.
comparison
Floor Height Etabs Excel Percent Diff.
Bulkhead 167 4.5 9.02713 100.6028779
Roof 158 33.855 39.69377 17.24640138
Story 17 149 33.59 39.24732 16.84226262
Story 16 140 48.607 38.77904 20.21923102
Story 15 131 48.18 51.04848 5.953666206
Story 14 122 47.73 50.35491 5.499503675
Story 13 113 47.252 49.6197 5.010799696
Story 12 104 46.744 48.83671 4.47695321
0.00 5.00 10.00 15.00 20.00 25.00
0.00
23.00
41.00
59.00
77.00
95.00
113.00
131.00
149.00
167.00
Wind Force, kip
Height Above Ground level (ft.)
lateral loads to stories (y‐direction)
PAGE 29
Story 11 95 46.199 47.99825 3.894558308
Story 10 86 45.612 47.09453 3.250307648
Story 9 77 44.974 46.11277 2.532063996
Story 8 68 44.274 45.03579 1.720622602
Story 7 59 43.495 43.83967 0.792437381
Story 6 50 42.616 42.48958 0.296639036
Story 5 41 41.6 40.93165 1.606615168
Story 4 32 40.386 39.07523 3.245615185
Story 3 23 38.856 36.74737 5.426769181
Story 2 14 47.658 43.39965 8.935216755
Base 0 0 0 0
TOTAL 746.128 759.3315 1.769608798
Table 9: comparison of results between ETABS and Hand calculations
The total error is actually below 2% which assures us that the ETABs model was correct and good
to use for design.
2.1.3 Seismic Loads
In general, seismic load resistance is provided by reinforced concrete shear walls provided
continuously from the roof to the foundations. Shear walls increase stiffness throughout the
structure and decreases the overall fundamental period of vibration. The calculations for these
loads can be found in Appendix I.
2.2 LOAD COMBINATIONS
Load combinations that were entered into the ETABS model can be seen in Appendix A and
were based on the 2014 NYC Building Code. “Where strength design or load and resistance factor
design is used, structures and portions thereof shall resist the most critical effects from the
following combinations of factored loads”:
1. 1.4D
PAGE 30
2. 1.2D + 1.6L + 0.5(
3. 1.2D + 1.6( + ( 0.5
4. 1.2D + 1.0W + 0.5
5. 1..2D + 1.0E+ + 0.2
6. 0.9D + 1.0W
7. 0.9D + 1.0E
Envelopes were created for the wind and gravity loads (ENV‐WG), earthquake drift loads
(ENV DRIFT EQ), and earthquake loads (ENV EQ). A load combination for the service loads was
created as well and later combined into an envelope to determine the worst case loading.
Allowable stress design (ASD) load combinations were also used for further checking of the design:
1. D
2. D + L
3. D + (LR or S or R)
4. D + 0.75L + 0.75(LR or S o R)
5. D + (0.6W or 0.7E)
6. D + 0.75L + 0.75(0.6W) + 0.75(LR or S 0r R)
7. D + 0.75L + 0.75(0.7E) + 0.75S
8. 0.6D + 0.6W
9. 0.6D + 0.7E
PAGE 31
2.3 MATERIALS USED
Throughout the building we will be using 5000psi strength concrete. The concrete will be
reinforced with an ASTM grade 60 strength rebar. Other reinforcement and specific beam
designation can be found in the supporting documents and drawings.
PAGE 32
2.4 SERVICEABILITY
2.4.1 Slab Serviceability
1) Total deflection shall not exceed ∆
a. Dead Load + Superimposed Dead Load + Live Load
2) Deflection that occurs after installation of non‐structural components shall not exceed
∆
3) Slab deflection (façade system)
a. Deflection which occurs prior to installation of façade system shall not exceed
∆ "
b. Deflection from total dead load shall not exceed the minimum of either
i. ∆
ii. ∆
c. Deflection from live load shall not exceed the minimum of either
i. ∆
ii. ∆ in…1
2
Structural Element Deformation Recommendation Loading
Curtain Walls/Spandrels Vertical Deflection 3/8 inch MAX Dead Load Prior to Cladding
Curtain Walls/Spandrels Vertical Deflection L/480 ≤ 5/8 inch MAX TOTAL Dead Load
Curtain Walls/Spandrels Vertical Deflection L/360 ≤ ¼ ‐ ½ inch MAX 0.5 * Live Load
Table 5. Slab Serviceability, AISC Design Guide
PAGE 33
Section 3: Structural System
3.1 GRAVITY SYSTEM
The columns, and slabs resist gravity loads. These structural components take the loads
and transfer them to the foundation where it then transmits that to the earth below. Foundations
are typically compromised of spread footings, combined footings, foundation mats, basement and
retaining walls, and grade beams. All these components work in conjunction to become the
structure’s gravity system. The unbraced length for columns in our building range from 22’‐
27’.Column sample calculations can be found in Appendix D.
3.2 LATERAL SYSTEM
The lateral force system is the system of structural members that, acting jointly, resist and
transmit to the ground the lateral loads arising from seismic motions, wind, and lateral earth
pressure. The forces are transferred to the façade, which transfers the load to the slab edge and the
slab, acting as a diaphragm, transfers the load to the shear wall which once again sends it to the
foundation.
3.3 STRUCTURAL COMPONENTS
3.3.1 Slabs
8" slabs throughout building except 10" slab on GF, Basement, and Subbasement
Continuous bottom reinforcement with additional reinforcement at columns to resist
unbalanced moment
Top reinforcement placed only at critical sections
Edge and panel deflections were checked against Design Guide 3 by AISC
Reinforcement lengths were determined using the spans adjacent to columns. For interior
columns, we took the higher of the two spans that were being looked at (i.e. E‐W spans) and
used the equations: 0.5(ln) + Relevant Column Width/2. For exterior spans we used a similar
PAGE 34
method, however, instead of using a factor of 0.5 we use 0.3. The extra length used both for
staggering and increasing the bar length for alternating layouts is determined via the equation:
0.1(ln)
3.3.2 Columns
After finishing our architectural layout, we were tasked to layout the structural columns for each
floor. Due to various conditions and project requirements we typically have 4 different types of
column layouts in our building. Column spans on each floor were calculated with the aid of span
table 9.5 from ACI 318‐11. We calculated that an 8in thick slab can have an exterior span of 22 feet
and an interior span of 20 feet.
Due to the differing slab thickness and floor layout as previously mentioned we have 4
different types of column layouts in our building. The two sublevel floors which house our parking
lots have a thickness of 10 inches which allows us to extend our span to 27 feet. We placed columns
at the end and the beginning of every 3rd parking spot as a basis of the layout and then
supplemented these columns with other columns to support the rest of the slab above. One thing
we had to keep in mind was a balance between keeping our cost low by having fewer columns,
longer spans, and placing columns in such a way that it didn’t affect the driving lanes set out for
cars. Parking lot levels had to cognizant of small span lengths because any span lengths smaller
than 8 feet required us to design that portion of the slab due to a concentrated load instead of a
uniform load. This concentrated load is used to simulate a jack jacking up a car in the parking lot.
The columns on the subbasement floors will connect to the foundation footings of our
building. The Columns that are attached to our loading bearing foundation wall will also have
buffers to help support the columns above. Attached Below is a section of the column lay out on
our two sublevel parking lots with the architectural underlay displaying the columns and footings.
PAGE 35
Figure 11. Columns and Footings in Subbasement
Columns in our Ground floor are like the column layouts in our typical floors (floors 3‐15).
The only difference is that the Ground floor is about 15 % larger than the typical floors and requires
more columns. Once again, we struggled to maintain a balance of well‐spaced out columns and still
making the building aesthetically pleasing. The two cores in our building was an efficient way to
increase span lengths between columns without the need for extra columns. Most column span
lengths are set at the maximum 20 feet clear span length; however some spans are at 13 feet due to
architectural constraints. Attached below is a portion of the column layout on the ground floor
displaying various span lengths.
Figure 12: This figure shows the shortest clear spans between columns on the ground floor
Lastly our Duplex penthouse floors also have a different column layout. These floors have
the smallest blueprints thus they have the least number of columns. These columns are mostly
spaced at the maximum 20 feet clear span lengths. These span lengths give the owners a lot more
freedom in their use of space. Attached below is a figure displaying large column spans
PAGE 36
Figure 14: This figure is from the column layout of floor 17, maximum spans are allowed due to smaller blueprint and larger open spaces.
All distinct column layouts are dimensioned using a coordinate origin plan style and all
columns are named in a clockwise rotation starting from the outer most corner and spiraling in
towards the middle of each floor. Typical columns are named in the 100 series, columns that are
only on the Ground floor are named in the 200 series and columns that are only in the Sublevels are
named in the 300 series. An example of a column with its respective coordinates and tag as well as
the column above tags is shown below.
Figure 15: This Figure shows the coordinates, column tag and column above symbol for the respective column.
PAGE 37
3.3.3 Shear Walls
Shear Walls were checked in ETABS directly. The building is comprised of 2 central core systems
which resist the lateral loads to the structure (Wind and Seismic). Analysis is ETABS indicated that
the shear walls were cracking from the ground floor to the fourth floor at both cores. The moments
of inertia multipliers for these walls were reduced.
The shear walls were designed every three stories with exception to the first four stories of the
structure (above ground). For both cores, concentrated reinforcement was added to the perimeter
corners, which is where stresses are concentrated. Transverse rebars are spaced every 10”
throughout the walls, and are spliced at each corner. D/C ratios were kept below 0.95 for Shear wall
design.
3.3.4 Transfer Beam
Due to the 4 different types of column layouts in our project the use of transfer beams is necessary
to transfer the loads of columns from one distinct column layout to another. A total of 51 transfer
beams are used in our design. 47 of them are located on the ground floor which transfer the loads
from the 100 series columns down to the 300 series columns. The average size of our transfer beams
were 36”x84”.
Figure: The dashed lines represent the transfer beam that are below slab
Beams were designed using SAFE and then checked via hand calculations. Sample calculations of
the transfer beam can be found in Appendix B.
3.3.5 Foundation & Isolated Footing & Strip Footing
Allowable Soil Pressure = 24 ksf
Continuous top and bottom reinforcement in both directions with additional
reinforcement over core and columns
Service and factored loads obtained from ETABS,SAFE
Square isolated footing
PAGE 38
Section 4: Analysis & Global Behavior
4.1 FINITE ELEMENT MODELS
4.1.1 SAFE: Slab Design
PAGE 39
Initial proportioning of slabs was done in SAFE. Eight different models were created:
basement, ground floor, 2nd floor, typical floor, 16th floor and terrace, 17th floor, roof, and bulkhead.
The slab located at the subbasement is a 5” slab on grade. Moment of inertia of the slabs was not
reduced based on the ACI Code. Slabs were modeled as thick plates, since the length was much
greater than the depth.
Slabs were checked and designed for punching shear, and reasonable shear and flexure
reinforcement within the slab. The roof had the most severe loading (green roof system and
mechanical systems) and as a result the thickest slab in the structure, 11 inches. Floors 2‐17 and the
had slabs of 8 inches and the ground floor was proportioned with a slab of 10 inches.
At locations where punching shear was an issue, the design team has decided it is best to
reinforce the columns using steel fortress reinforcement instead of increasing the slab thickness, as
per the architects request.
The slabs were meshed at a 2’ x 2’ grid in SAFE to capture the most accurate analysis and
values of moment, shear, stresses, etc. Slab deflections were not of concern; the design team used
ACI Code to span column spacing according to Table 9.5:
PAGE 40
4.2 ETABS: GLOBAL ANALYSIS
Shell Stress Analysis: Shear Walls
Load Combination: ENV‐WG
Maximum Allowable Shell Stress:
7.5
1.0
7.5 5,000 530
ACI 318‐14 mandates that the maximum allowable modulus of rupture in the concrete be 530
for 5,000 concrete. Throughout the entire structure, 5,000 psi concrete was used and therefore,
all shell stresses could not exceed 530 psi. Results indicated that under seismic and earthquake
loading, using a combination of 0.9D + 1.0 (W or EQ), the stresses at the base of the building were
nearly 1000 psi. As such, the moments of inertia multipliers from the ground floor to the fourth
floor were reduced from 0,7 to 0.35 as per ACI 318‐14
PAGE 41
PAGE 42
Figure 18: Ground Floor shear walls subjected to load combination “ENV‐WG”
If the shell stresses in the shear walls were to theoretically exceed the limit of 424 psi, ACI 318‐14
suggests to reduce the Moment of Inertia in the shear walls from 0.7 to 0.35 to prevent cracking
in the shear walls. Since the maximum shell stress was significantly below the limit, no reduction in
the moment of inertia of the shear walls was necessary. Table 4 is taken from ACI 318‐14 gives
further insight into the reduction requirements for various members in a structural system:
PAGE 43
Member and Condition
Moment of Inertia
Cross‐Sectional Area
Columns 0.70 lg
1.0 Ag Walls
Uncracked 0.70 lg
Cracked 0.35 lg
Beams 0.35 lg
Flat Plates and flat slabs 0.25 lg
Table 4. Moment of Inertia and cross‐sectional area permitted for elastic analysis at factored level
The moment of inertia of structural sections were reduced as per Table 6.6.3.1.1 (@) from ACI 318‐
14. Stress analysis indicated that the shear walls of both cores were cracking from the Ground Floor
to the 4th floor. The moments of inertia of these sections were changed from 0.7 to 0.35.
A separate model was created in ETABS to satisfy serviceability criteria. The moment of inertia of
structural sections was multiplied by 1.4, increasing the bending moment of inertia in each section.
Serviceability Criteria:
1.4 ∗
:1.4 ∗ 0.7 0.98
:1.4 ∗ 0.35 0.48
:1.4 ∗ 0.25 0.35
PAGE 44
4.2.1 Story Shear Graph
PAGE 45
PAGE 46
4.2.2 Maximum Story Drifts
Figure 21: Maximum Story Drifts under Seismic Loading (Env-EQ Drift)
PAGE 47
4.2.3 Maximum Story Displacements
Figure 23: Maximum story displacement subjected to wind and gravity loads
The maximum lateral deflection that the structure is able to withstand is calculated as:
∆400
PAGE 48
∆167 ∗
121
400
∆ 5.01
The ETABS analysis indicated that under the Wind loads, the maximum deflection is found to be:
0.72
0.35
Figure 24: Maximum Story Displacement subjected to seismic drift loading
The design team ran a global analysis of the structure in ETABS. The deflection of the building
subject to seismic loading was found to be 1.08” at a maximum.
PAGE 49
This deflection occurs at the roof level of the structure. The maximum lateral deflection the
structure can withstand due to seismic loading is 2% of the total building height above the ground.
∆ 2% 0.02 167 ∗121
40.08
Since the maximum deflection recorded is less than the acceptable margin, the structure satisfies
deflection criteria due to seismic loading.
PAGE 50
PAGE 51
Auto Lateral Load to Stories (Strength)
PAGE 52
Overturning Moments (Wind) Strength Model
PAGE 53
PAGE 54
Overturning Moment Seismic (Strength)
PAGE 55
(X‐direction)
PAGE 56
4.3 P‐DELTA EFFECTS
The P‐Delta effect on the structure was analyzed by running the model with and without
P‐Delta effects entered into the model. Only gravity loads were entered into the P‐Delta
calculations, since lateral loads have little effect on the axial force. The P‐Delta was run as an
iterative case. As seen in Appendix I, the P‐Delta effect on the structure is relatively small. The
difference between the moments acting on the structure with and without P‐Delta effects for the
worst case wind loading was around 3% and for the earthquake drift load case, the difference was
around 2%.
4.4 ELEMENT TYPES
Our slabs were modeled in ETABS as membranes. This is to represent how the slab would
handle the loads acting on its edge by transferring the forces to a supporting structural objects. In
this case, 100% of the load is transferred to the shear wall. This causes the moments in the slab to
be significantly higher as well. This is opposed to Shell modelling which gives the slab some flexural
deformation to help resist a portion of the loading.
The walls in the building were modeled as thin‐shells. Thin‐shells neglect transverse shear
deformation. Transverse shear deformation tends to be important when shell thickness is greater
than approximately 1/5 to 1/10 of the span of the plate‐bending curvature. Shearing may also
become significant in locations of bending‐stress concentrations, which occur near sudden changes
in thickness or support conditions, and near openings or re‐entrant corners. Thick‐plate
formulation is best for such applications. Thick shell plates are used in the slabs of the isolated
footings and the mat.
In general, the contribution of shear deformation becomes significant when ratio between the span
of plate‐bending curvature and thickness is approximately 20:1 or 10:1. The formulation itself is
adequate for ratio down to 5:1 or 4:1. In that this ratio is dependent upon the projected span of
curvature, shell thickness may be greater than the actual plan dimensions of a shell object.
PAGE 57
Appendix A: Transfer Beam Hand Calculations
The following calculations were done for beam CB19 as seen on the respective set of structural
drawings.
Preliminary:
Applicable design code is ACI 318‐11
Concrete compressive strength, 5
Reinforcement yield strength, 60
Length of beam, 27.5
Assumed depth, 36 33.5
Assumed width, 84
Max moment and shear obtained from software:
2842.01
548.41
Assuming max possible tensile steel with no compression steel and computing
beam’s nominal moment strength (When 0.005 :
0.0181
Assume 0.90 :
2842.01 12 /0.90 84 33.5
0.402 401.97
.1 1
.
. ,
, 1 1
.
. , 0.00705
0.00705 84 33.5 19.84
. .
0.0181.
. 0.00777 0.0035
OK
.
. ,
. , 3.68
0.90 21.87 60,000 33.5.
37,389,826 3115 2843
OK
PAGE 58
Shear Reinforcements:
548.41
Assume #5 stirrups
If then stirrups are needed:
2 0.90 2 1.0 5,000 84 33.5 358,164
358
54812358 179
Stirrups needed because
Theoretical spacing:
548.41 3580.90
211.4 211,384.4
2 0.31 60,000 33.5211,384.4
5.90
Maximum spacing to provide minimum area of shear reinforcement, :
0.75
2 0.31 60,000
0.75 5,000 848.35
502 0.31 60,000
50 848.86
Maximum spacing:
211,384 4 5,000 84 33.5 795,920
2
33.52
16.75 24
PAGE 59
Shear Reinforcements:
Length of beam, l 27.5
Distance from Face of support ft 0 13.75 27.5
Maximum Shear, Vu lb 358738 509095 548412
Input Stirrup # #5 #5 #5
Av in^2 0.31 0.31 0.31
Steel strength, fy psi 60000 60000 60000
Concrete Strength, f'c psi 5000 5000 5000
Beam Width, bw in 84 84 84
Beam depth, h in 36 36 36
Assumed effective depth, d in 33.5 33.5 33.5
1 1 1
ϕVc lb 358163.7268 358163.7268 358163.7268
Vu>1/2 ϕVc Stirrup is needed
Stirrup is needed
Stirrup is needed
Design of Stirrups
Vs lb 638.081326 167701.4147 211386.9702
Theoretical spacing, s in 1953.04 7.43 5.90
Maximum spacing provided minimum area of shear reinforcements, s in 8.35 8.35 8.35
s cannot be more than (Av fyt)/(50bw) OK OK OK
Maximum spacing, s in 16.75 16.75 16.75
Stirrup Size #5 #5 #5
theoretical spacing, s in 8.0 7.0 5.0
Number of stirrups 13 15 22
From face of support
Middle of beam End of beam
Stirrup Size #5 #5 #5
theoretical spacing, s in 8.0 7.0 5.0
Number of stirrups 13 15 22
From face of support Middle of beam End of beam
PAGE 60
Appendix B: Column Hand Calculations 1. Compute the factored load
Factored Loads:
. . . .
1.2 1.6
1.2 156.81 1.6 38.87 250.36
From SAFE Analysis, the moment at the top and the bottom of the column are found to be:
Moment at top of column: 47.33 k‐ft
Moment at the bottom of column: 19.89 k‐ft
By definition, is the larger end moment in the column. Therefore, 47.33 and
19.89 . The ratio of is taken to be positive, because the column is bent in single
curvature. Thus 0.420
2. Estimate the column size, assuming that .
/ 0.40
250.36 ∗10001
0.40 5000 60000 ∗ 0.010111.77
111.77 10.57
This suggests that an 11” x 11” column would be satisfactory. It should be noted that the above
equation used to calculate the gross area of the column was derived for short columns and will
underestimate the required sizes of slender columns.
3. Is the column slender?
A column in a non‐sway frame is short if:
34 12 40
For the 11” x 11” section selected, k =1.0 because the column is pin‐ended, and where:
PAGE 61
0.3 0.3 11 3.3
1.0 17 ∗121
3.361.82
For 0.420,
34 12 34 12 0.420 28.96
Because 61.82 28.96, the column is not slender, and the column size is
adequate.
Check whether the moments are less than the minimum
ACI Code Section 10.10.6.5 requires that a braced column be designed for a minimum eccentricity
of 0.6+0.03h = 1.08 in. because the maximum end eccentricity exceeds this, design for the moments
from step 1.
4. Compute EI
At this stage, the area of reinforcement is unknown. Additional calculations are needed before it is
possible to use:
0.401
Where:
57,000 57,000 5,000 4.03 ∗ 10
1211)(1112
1220.08
The term is the ratio of the factored sustained (dead) load to the total factored axial load:
1.2
1.2 ∗ 156.81250.36
0.752
Thus,
0.4 4.03 ∗ 10 1220.081 0.752
1.123 ∗ 10
PAGE 62
5. Compute the magnified moment
Where
1 0.75
1.0
0.6 0.4
0.6 0.4 0.420 0.768
Where k = 1.0 because the column is pin‐ended
1.123 ∗ 10 ∗
1.0 ∗ 17121
54331204.6 54331.2
And
0.768
1250.36
0.75 54331.2
.773 1.00
Normally, if exceeds 1.75 to 2.0, a larger cross section should be selected. Continuing without
selecting a larger column, the magnified moment is
.773 47.33 36.59
6. Select the column reinforcement. We will use the tied‐column interaction diagram.
Assuming an equal distribution of longitudinal bars in two opposite faces of the
column. The parameters required for entering the interaction diagrams are
2
20" ‐ (2)(1.5"))/(11") = 1.55
Assuming 250.36 ,
250.3611in x 11
2.07
Assuming 36.59
36.59121
11 20 3.63
PAGE 63
From both Fig. A‐7b ( 0.75 and Fig. A‐7c ( 0.90), the required value for is less than 0.01.
Therefore to satisfy the minimum column longitudinal reinforcement ratio from ACI Code Section
10.9.1, use 0.01. Thus,
0.01 11 in. x 11 in. 1.21
However, due to design constraints this column’s actual size was changed to be 12”x26” for
constructability reasons. Columns were designed from bottom up and then using further analysis of
SPcolumns we could decrease the column sizes as we went up. These column sizes are very
conservative.
This is example was based off column 120 on the 10th‐15th floors. The final reinforcement chosen for
this column was 8#8 bars
PAGE 64
Appendix C: Two‐Way Slab Design
The following steps are taken in the design of the two‐way slab:
1. The layout and type of slab are chosen.
2. The slab thickness is chosen with deflection and shear in mind.
3. A method for computing the design moments is chosen.
4. We then calculate the distribution of the moments across the width of the slab.
5. Reinforcement is designed.
6. Check shear strength at a critical section around the columns.
For architectural and practical reasons, a flat plate was chosen. Flat plates are usually employed in
residential buildings where light loads are usually present. The thickness of the slab was chosen to
match desired spans between columns which in turn was affected by the architectural layout of the
building. Therefore, for a typical floor, a slab thickness of 8” was chosen.
For this sample calculation we will be using the Direct Design method to calculate the design
moments.
Direct Design Method (DDM)
Requirements:
‐ Three continuous spans in each direction
‐ Successive span lengths (measured center‐to‐center) shall not differ by more than one‐
third the longer span
‐ Panels shall be rectangular, with the ratio of longer to shorter panel dimensions, measured
center‐to‐center of supports does not exceed 2
‐ All loads shall be due to gravity only and uniformly distributed over an entire panel
‐ Unfactored live load shall not exceed two times the Unfactored dead load
‐ For a panel with beams between supports on all sides, Apply equation 8.10.2.7a for beams
in the two perpendicular directions
0.2 5.0
Where:
PAGE 65
For the particular section of the typical floor slab that we will be analyzing the requirements are
met, thus, we are allowed to employ the DDM. This particular slab section is 8” thick, supports a
live load of 40psf and a SDL of 20. The story height is 9ft. We will be calculating the moment in the
short direction of the panel.
First, we compute the factored loads:
1.2812
∗ 150 20 1.6 40 208
Now, by creating our middle and column strips, we can calculate our moment.
80.208 ∗ 17.67 ∗ 16
8117.61
L2 = 17’ ‐ 8”
L = 16’
PAGE 66
Next, we divide M0 into negative and positive moments per ACI 8.10
0.65 76.44
0.35 41.16
Next, we further divide the moment into column and middle strips positive and negative moments.
αf = 0 because no beams are present. Values are taken from the tables shown above.
0.75 ∗ 76.44 57.33
0.25 ∗ 76.44 19.11
We do the same for the positive moments.
0.60 ∗ 41.16 24.70
0.40 ∗ 41.16 16.46
PAGE 67
We can now move onto choosing reinforcement. Because we have spans lower than 25’ we can
make the following assumption:
≃ 1.1 8 1.1 6.9
We then compute As assuming J = 0.95 and using Mu = ‐28.67 kip‐ft
, ∗ ∗ ∗
57.33 ∗ 12000
0.9 ∗ 60000 ∗ 0.95 ∗ 6.91.94
Now we can check if the section is tension controlled or not.
0.851.94 ∗ 60
0.85 ∗ 5 ∗ 7.83 ∗ 120.25
0.250.85
0.29
38
2.58, ∅ 0.9
Using the following table we can determine the number of reinforcement needed:
PAGE 68
We want to use #5 bars so we can see that we need 7 bars. Dividing the width of the column strip
by the number of bars needed we can get the spacing. We get that we need #5 bars spaced at 12”
o.c.
We know from ACI that the minimum area of steel can be taken as follows:
0.0018 ∗ ∗ 0.0018 ∗ 9.25 ∗ 12 ∗ 8 1.60 ^2
PAGE 69
Appendix D: ETABS Wind Loading
ASCE 7-10 Auto Wind Load Calculation
This calculation presents the automatically generated lateral wind loads for load pattern WIND
according to ASCE 7-10, as calculated by ETABS.
Exposure Parameters
Exposure From = Diaphragms
Exposure Category = C
Wind Direction = 0 degrees
Basic Wind Speed, V [ASCE 26.5.1] V 124 mph
Windward Coefficient, Cp,wind [ASCE 27.4.1] C , 0.8
Leeward Coefficient, Cp,lee [ASCE 27.4.1] C , 0.5
Wind Case = All Cases
Top Story = BULKHEAD
Bottom Story = GF
Include Parapet = No
Factors and Coefficients
Gradient Height, zg [ASCE Table 26.9-1] z 900
Emperical Exponent, α [ASCE Table 26.9-1] α 9.5
Velocity Pressure Exposure Coefficient, Kz; [ASCE Table 27.3-1] K 2.01 for15ft z z
K 2.01 forz15ft
Topographical Factor, Kzt [ASCE 26.8.2] K 1
Directionality Factor, Kd [ASCE 26.6] K 0.85
Gust Effect Factor, G [ASCE 26.9] G 0.85
Lateral Loading
Velocity Pressure, qz [ASCE 27.3.2 Eq. 27.3-1] q 0.00256K K K V
Design Wind Pressure, p [ASCE 27.4.2 Eq. 27.4-2] p qGC , q GC ,
PAGE 70
Appendix E: Wind Load Hand Calculations
1. Determining the risk category
According to table 1.5-1, our building is considered to have a Risk Category of II
2. Next we are asked to determine the basic wind speed, V, for the applicable risk category.
According to NYCBC we have a V50 = 98mph
Our V700 is found by applying the following formula:
√1.6 98 √1.6 124
3. Next, we determine the wind load parameters:
Wind Directionality Factor, Kd [Table 26.6-1]: 0.85
Exposure Category [Section 26.7]: Exposure C
Topographic Factor, Kzt [Figure 26.8-1]: 1
Gust-effect factor, G [Section 26.9]: 0.85 [Assuming our building is considered rigid;
natural frequency is greater than or equal to 1Hz]
Enclosure classification [Section 26.10]: enclosed
Internal pressure coefficient, GCpi [Table 26.11-1]: +0.18;-0.18
4. Determine velocity pressure exposure coefficient, Kz or Kh [Table 27.3-1]:
5. Velocity Pressure, qz [Eq. 27.3-1]
6. 0.00256 0.00256 ∗ 0.77 ∗ 1 ∗ 0.85 ∗ 124 25.63
7.
0.00256 0.00256 1.41 0.85 124 47.17 /
0.00256 2 / 2 27.3 1
where
Kd = wind directionality factor, see Section 26.6
Kz = velocity pressure exposure coefficient, see Section 27.3.1
PAGE 71
Kzt = topographic factor, see Section 26.8.2
V = basic wind speed, see Section 26.5
qz = velocity pressure calculated using Eq. 27.3-1 at mean roof height h
From ASCE 7‐10, Wind Directionality Factor from Table 26.6‐1 is 0.85.
The wind speed‐up effect shall be included in the calculation of design wind loads bu using the
factor 1
2.01
2.0115
, ∝ 9.5, 900 26.9 1 of ASCE 7‐10
Sample Calculation:
at 41ft elevation
2.01 ∗ 2.01 ∗411200
0.77
Wind Loads‐ Main Wind Force‐Resisting System
Section 27.4.1 Enclosed and Partially Enclosed Rigid Buildings
PAGE 72
Design wind pressures for the MWFRS of buildings of all heights shall be determined by the
following equation:
, , ,
= for windward walls, side walls, leeward walls, and roofs of enclosed buildings and for
negative internal pressure evaluation in partially enclosed buildings
= for positive internal pressure evaluation in partially enclosed buildings where height z is
defined as the level of the highest opening in the building that could affect the positive internal
pressure. For buildings sited in wind‐borne debris regions, glazing that is not impact resistant or
protected with an impact‐resistant covering shall be treated as an opening in accordance with
Section 26.10.3. For positive internal pressure evaluation, qi may conservatively be evaluated at
height h(qi = qh)
G = gust‐effect factor, see Section 26.9
= external pressure coefficient from Figs. 27.4‐1, 27.4‐2, and 27.4‐3
(G ) = internal pressure coefficient from Table 26.11‐1 q and qi shall be evaluated using exposure
defined in Section 26.7.3. Pressure shall be applied simultaneously on windward and leeward walls
and on roof surfaces as defined in Figs. 27.4‐1, 27.4‐2, and 27.4‐3.
PAGE 73
Sample Calculation
External Pressure Coef., Cp
Use
With
Windward
Wall 0.8 qz
Leeward
Wall ‐0.5 qh
Side Wall ‐0.7 qh
Roof
‐0.9
qh ‐0.18
25.63 ∗ 0.85 ∗ 0.85 25.63 ∗ 0.18 13.9
Leeward wind load is calculated the same except the internal pressure coefficient is now ‐0.18 and is
done for the highest elevation of the building.
In some cases, we must find the torsional moment of each floor (case 2 and 4) below is the sample
calculations for the torsional moment on floor 5:
0.75 0.75 13.90 6.28 ∗ 110 ∗ 0.15 ∗ 110 16309.74 ∗
Where:
0.15
PAGE 74
PAGE 75
Appendix F: Seismic Hand Calculations
Seismic Loads
Samples from the site have determined that the soil can be classified as D.
Now we need to find the MCEg spectral response acceleration parameters at short periods and at a
period of 1 second. To do this we must look at the spectral response accelerations shown in chapter
22 of ASCE 7‐10.
SS = 0.25
S1 = 0.073
Next, we need to establish Site Coefficients and Risk‐Targeted Maximum Considered Earthquake
(MCER) Spectral Response Acceleration Parameters.
0.25 1.6 0.4 . 11.4 1
2.4 0.073 0.1752 . 11.4 2
where:
Fa = Site Coefficient = 1.6
FV = Site Coefficient = 1.7
PAGE 76
Design Spectral Acceleration Parameters
23
23
0.4 0.27 . 11.4 3
23
23
0.1752 0.1168 . 11.4 4
Using tables 11.6‐1 and 11.6‐2 we can determine that our seismic design category is B. However,
further site inspection and recommendations from project owners indicate to us that our Seismic
Design Category should be C.
Then we can develop our Design Response Spectrum:
PAGE 77
Equivalent Lateral Force Procedure
The seismic response coefficient, Cs, shall be determined using the following equation:
0.2751
0.054
where:
SDS = the design spectral response acceleration parameter in the short period range as
determined from section 11.4.4 or 11.4.7 = 0.2 g
R = the response modification factor in table 12.2‐1 = 5 (assuming ordinary reinf. conc. shear wall)
IC = the importance factor determined in accordance with section 11.5.1 = 1
The effective seismic weight (w) is defined as the dead load above the base, 25% of LL’s in areas
used for storage,
The seismic base shear, V, in a given direction shall be determined in accordance with the following
equation:
0.054 ∗ 52860 2854 [12.8‐2]
where:
Cs = the seismic response coefficient determined in accordance with section 12.8.1.1 = 0.054
W = the effective seismic weight per section 12.7.2 = 52860kips
For seismic weight we do not need to add the live load because it is not more than 5% of the floors
seismic weight.
If any irregularities exist, we will have to amplify the load in order to account for them. Note that
we are inly checking the irregularities that are applicable to buildings with a seismic design
category of B.
Horizontal Irregularities
1a: Torsional Irregularity – Story drift does not point towards any irregularities
1b: Extreme Torsional Irregularity ‐ Story drift does not point towards any irregularities
4: Out‐of‐Plane Offset Irregularity – Does not apply to this building. This irregularity only occurs
when the lateral forces in a lateral force resisting element are transferred to an element that is not
in the same plane as that element.
PAGE 78
Ta 0.93 [Eq. 12.8‐7]
Ct 0.02 [Table 12.8‐2]
x 0.75 [Table 12.8‐2]
Estimated Period
Variables
5: Nonparallel System Irregularity – Does not apply to this building. This irregularity only occurs
when any element of the lateral load resisting system is not parallel to one of the orthogonal axes of
the lateral load resisting system of the entire structure.
Vertical Irregularities
4. In‐Plane Discontinuity In Vertical Lateral Force‐Resisting Element – Does not apply to this
building. Only applies when there is an in‐plane offset of the vertical seismic force‐resisting system
element.
5b. Discontinuity in Lateral Strength‐Extreme Weak Story Irregularity – Story lateral strength values
from SAFE suggest this irregularity is not applicable here
The Shear Story Graph was created using the following equation:
[12.8‐11]
∑ [12.8‐12]
where:
V = total design lateral force or shear at the base of the structure (kip or kN)
Wx = portion of the total effective seismic weight of the structure (W) located or assigned to Level x or
i
Hx = the height from the base to Level i or x (ft)
K = an exponent related to the structure period = 2 [when period is between 0.5 and 2.5]
Note: Period was found using the following equation and variables:
PAGE 79
Vert. Dist. Factor
Floor Height Height from base w CVX Fx Vx
GF 0 0 3862.3 0.0 0.00000 0.0 0.0
2 14 14 3698.9 1956702.2 0.00406 16.2 16.2
3 9 32 3037.61086 3110513.5 0.00646 25.8 42.0
4 9 41 3037.61086 5106223.9 0.01060 42.4 84.4
5 9 50 3037.61086 7594027.2 0.01577 63.0 147.4
6 9 59 3037.61086 10573923.4 0.02195 73.1 220.5
7 9 68 3037.61086 14045912.6 0.02916 97.1 317.6
8 9 77 3037.61086 18009994.8 0.03739 124.5 442.2
9 9 86 3037.61086 22466169.9 0.04664 155.3 597.5
10 9 95 3037.61086 27414438.0 0.05692 162.5 760.0
11 9 104 3037.61086 32854799.1 0.06821 194.7 954.7
12 9 113 3037.61086 38787253.1 0.08053 229.9 1184.6
13 9 122 3037.61086 45211800.0 0.09387 223.3 1407.9
14 9 131 3037.61086 52128440.0 0.10823 257.5 1665.3
15 9 140 3037.61086 59537172.9 0.12361 294.0 1959.4
16 9 149 2868.4 63681233.8 0.13222 314.5 2273.9
17 9 158 1632.1 40744930.7 0.08460 201.2 2475.1
Roof 9 167 1310.1 36536793.2 0.07586 252.6 2727.7
BH 9 167 67.5 1881419.8 0.00391 11.2 2738.9
SUM= 481641748
After using the above equation, we get the following table and graph for story shear.
Then, by summing the shears corresponding to each floor we can create the Lateral Force Resisting
System Shear.
PAGE 80
0
20
40
60
80
100
120
140
160
180
0.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.0
Height (ft)
VLFRS (kips)
LFRS Shear
PAGE 81
Appendix G: Shear Wall Design
Shear Wall Design on Ground Floor
Ground floor 36.421
Wall thickness (h) = 12” (the reinforcement will be placed on both faces of the wall)
Check the maximum allowed shear strength of the wall.
The effective depth, 0.8 0.8 24 230.4
ACI Code requires the design shear strength, to be greater than or equal to the required shear
strength or factored shear strength or factored shear .
10 11.9.3
Where:
0.8 0.8 24121
230.4 11.9.4
10 5,000 12 0.8 24121
11000
1,955
0.75 1,955 1,466.25
PAGE 82
1392
1392 1466.25
2
2 0.75 5,000 12 0.8 24121
11000
293
Because 305 293 ,shear reinforcement is therefore required in the wall.
Required Horizontal Shear Reinforcement:
305 2930.75 60 230.4
0.00116
0.00116
The corresponding horizontal reinforcement ratio provided is:
0.0011612
0.000096667 0.0025
Try #5 Horizontal bars on both faces of the wall; therefore, 2 ∗ 0.31 0.62 . Try
18” spacing.
The maximum spacing of the horizontal reinforcement that is allowed by the Code (s maximum) is
the smallest of the following:
5
24121
557.6 .
3 3 12 36
PAGE 83
Therefore Use #5 bars HEF at 18” o.c. for horizontal reinforcing
Vertical Reinforcing:
If 0.5 , The minimum ratio of distributed vertical or longitudinal reinforcement, in the
wall to the gross cross‐sectional area of the wall perpendicular to the reinforcement is given in ACI
11.6.2:
0.0025 0.5 2.5 0.0025 0.0025
Wall Type Type of
nonprestressed
reinforcement
Bar/Wire Size , psi Minimum
longitudinal
Minimum
transverse
Cast‐in‐
place
Deformed bars >No. 5 Any 0.0015 0.0025
0.0025 0.5 2.5177 24
0.0025 0.0025 0.0025
0.0025
0.0025
0.0025 12 0.03
Try #5 vertical bar reinforcing both face of the wall;
PAGE 84
2 ∗ 0.31 0.62
Therefore, the required spacing of the vertical shear reinforcement is:
0.620.03
20.67
The maximum spacing of the longitudinal reinforcement that is allowed by the Code (s maximum)
is the smallest of the following:
3
24121
396 .
3 3 12 36
Therefore, use #5 reinforcing bars VEF spaced at 18 in. o.c.
Concentrated Reinforcing:
Design the shear wall for flexure or bending and determine the end zone vertical reinforcement.
The maximum factored bending moment at the base of the wall due to the factored seismic lateral
load is:
13500 ∗
PAGE 85
The limit states design equation for flexure requires that . Initially, we will
assume 0.9 (this will be checked later fater is determined) and then calculate the required
as follows:
13500121
0.9 12 0.8 24121
0.28257
Using Table A‐11 ( 5000 and 60 )
0.0049
From Table A‐11 of Reference 1, we obtain a 0.0049. Since 0.005, 0.9, as initially assumed. The concentrated vertical reinforcement required at each end zone of the shear wall is:
0.0049 12 230.4 13.55
The minimum area of concentrated steel required for bending at the ends of the shear wall is:
,3
200
,3 500060.000
12 230.4 9.78
20060,000
12 230.4 9.22
Therefore, 13.55
Use 14 No. 9 bars ( 14.00 vertical reinforcement at each end of the wall (i.e., 7 No.9 bars
VEF)
Appendix H: Isolated Footings
Isolated Footing Sample Calculations:
Column Size: 30 x 16
Concrete Strength: 5000 psi
PAGE 86
Dead Load: 562.42 k
Live Load: 166.47 k
Allowable Soil Pressure: 24 ksf
Assume Thickness: 24 inches
Assume soil cover of: 24 inches
Floor thickness of: 8 inches
Soil density: 100 lb/ft3
Initially Sized for Soil Bearing Strength
812
∗150
.100
242412
∗0.15
2 ∗. 100
0.67 ∗0.15
23.4
562.42 166.47
23.431.15 6′ 0" 24
Two way Shear Check
1.2 562.42 1.6 166.47
626.146
24 398 19.875
30 19.875 ∗112
4.16
16 19.875 ∗112
2.99
26.146 6 4.16 ∗ 2.99 616.38
Shear strength of concrete checks
2 ∗ 30 19.875 16 19.875 171.5
3016
1.875
1. 2 ∗ ∗ ∗ 996.223
40
PAGE 87
2. ∗
2 ∗ ∗ ∗∗ .
.2 ∗ √5000 ∗ 171.5 ∗ 19.875 1599.32
3. 4 4 ∗ 1 5000 ∗ 171.5 ∗ 19.875 964.09 Choose the smallest of the 3:
964.09 ∗ 0.75 723.07
723.07 616.38
Two way shear check: OK
One way shear check
2
2
0.922
26.146 ∗ 70.922 ∗ 6 144
2 0.75 ∗ 2 ∗ 1 5000 ∗ 72 ∗ 19.875 151.78
O.K in one way shear
Flexure
33012
1.75
26.15 ∗ 1.75 ∗1.752
∗ 6 240.22
240.22 ∗ 120.9 ∗ 72 ∗ 19.875
0.11261
Table A‐3 from McGregor, R value below minimum steel ratio:
_min 0.0033
In tension controlled section.
0.0033 ∗ 72 ∗ 19.875 5. .0085
Average d was used, so use same reinforcement in both directions.
. 10.5.4 7.12.2.1 0.0018 0.0018 ∗ 72 ∗ 24 3.11
Max Spacing (ACI Code Sect. 7.6.5.) = 18in
Try 7#8 bars each way, As=5.53 in2
Check moment capacity again
5.53 ∗ 600.85 ∗ 5 ∗ 72
1.08
PAGE 88
0.9 ∗ 5.53 ∗60 ∗ 18
0.8962
12434.44
Moment strength is adequate.
Design Column footing joint
Pu=941.26k
2 2
0.85 ∗ 2 0.85 ∗ 0.65 ∗ 5 ∗ 39.99 ∗ 2 2652
Minimum Dowels needed
. ∗ .
Based on ACI‐318 Table 25.3.1 for tension bars:
Inside bend diameter=6db=6.75in
Dowels will be extended a length of 25.44in as per #6bar development lengths.
Tie specification for bottom of column is stated in 10.7.6.2 of ACI‐318
PAGE 89
Appendix I: Foundation Wall
Exterior basement and foundation wall
Preliminary:
Applicable design code is ACI 318‐11
ACI 14.5.3 Minimum wall thickness 7.5
Assume wall thickness 12
Vertical Distance between supports 12
Under gravity loads, self‐weights, and lateral soil pressure
Soil surface to basement top of slab 24
Sits on fractured rock layer with 24,000 / allowable bearing capacity
Unit weight of soil backfill 116
Angle of internal friction 34° Concrete compressive strength, 5000
Reinforcement yield strength, 60,000
No water pressure applied on wall due to perimeter drainage system installed
Minimum reinforcement requirement are in accordance to:
Vetical reinf. – assume 0.15 % of horizontal gross concrete area
Horizontal reinf. – assume 0.25% of vertical gross concrete area
Vertical shear reinf. – larger of equation 11‐30 and 0.25% of horizontal gross
concrete area
Horizontal shear reinf. – 0.25% of vertical gross concrete area
Loading:
a) Soil pressure is calculated with Rankine expressions for the active pressure
coefficient.
Rankine active pressure coefficient: °
°0.2827
Assume linear pressure variation, the active pressure at any height:
0.2827 116 32.8 /
Max active pressure at 18 below soil surface:
32.8 24 787.2
b) Soil surcharge based on minimum uniformly distributed sidewalk loads around
building:
300
0.2827 300 84.814
c) Gravity loads:
1 strip of wall
Both basement and sub‐basement heights are 12
Tributary width of slab 12.5
10" Slab self‐weight:
PAGE 90
150 12.5 1562.5 /
Self‐weight of basement wall:
150 24 3600 /
Weight of masonry façade on ground floor:
198 14 2772 /
Superimposed dead loads of miscellaneous:
100 12.5 1250 /
Total dead load:
1562.5 3600 2772 1250 9,185
Total occupancy live load:
100 20 2,000
Total axial load:
1.2 9,185 1.6 2,000 7401.4 7.40
From SAP2000 software:
, 8744 8.74
, 34,276 / 34.28 /
Figure 1 ‐ Foundation Wall Shear Diagram
Figure 2 ‐ Foundation Wall Moment Diagram
Shear Design:
Shear design shall be in accordance with ACI 11.9 (provision for walls)
Design wall with pinned base, roller at mid‐support and top
Assume slabs are in place and has achieved full strength prior to
backfilling
PAGE 91
Use center‐to‐center of supports dimension of 9 for both moment and
shear calculations
Assume no eccentricities associated with vertical load
Factored Shear and moment from soil pressure at base of wall (ACI. 9.2.1 &
9.2.5):
Factored Shear: 1.6 8.74 13.98
Factored Moment: 1.6 34.28 54.85
Factored Vertical Axial Force from building, elevated slab above and self‐
weight:
Axial load: 7.40
ACI 14.4 Walls designed as compression members is to be used as the
method of design for this example.
Assume 14 thick wall
Concrete shear strength(ACI 11.9.1, 11.11.2.1, & Eq 11‐3, 11‐31):
For normal weight concrete 1.0 Unit length approach, 12 /
Assume 11.5 , 2 . 7.7.1.
2 2 1 5000 12 11.5 19,516
19.52
Nominal Sher strength (Eq 11‐2):
Nominal shear strength, is neglected
0.75
19.52
0.75 19.52 14.64
Required strength (Eq 11‐1):
14.64 13.98 OK
⸫ Thick wall is adequate for shear
Flexure and Axial Design:
Vertical reinforcement at base of wall
Use ACI 14.4 design method for walls designed as compression members
Area of outside face:
Assume #4 0.20 @12
0.20
0.20
Check minimum reinforcement for both faces:
Length, 12
PAGE 92
Wall thickness, 14 .
0.0024 0.0015 OK
Check wall slenderness (ACI 10.10):
Effective length factor, 1.0 Unbraced length, 12 144
Radius of gyration, 0.3 14 4.2 .
. 34
For compression members braced against sidesway (Eq 10‐7):
Smaller & larger factored end moments, 0
34 34 12 34 40
⸫ Slenderness effects may be ignored
Strain compatibility analysis:
Assume wall section is tension controlled (ACI 10.3.4 & 9.3.2.1)
0.005 and 0.90 0.85
.
.8.22
8.22 0.85 5 / 12 0.20 / 60 /
0.396 in In accordance to ACI 10.2.7.1, 0.80
.
.0.496
. .
. 11.5 0.496 0.0666
0.0666 0.005
⸫ Wall section is tension controlled, assumption verified. (ACI 10.3.4)
Design strength:
Distance from compression fiber to extreme tension reinf. layer
11.5
0.90 0.85
0.90 0.85 5 / 12 0.396142
0.3962
0.20 60 /142
11.5
172.25 / 14.35 /
13.35 / 3.24 / OK
⸫ #4@12” vertical reinf. In each face at base is adequate
PAGE 93
Check maximum spacing:
Maximum spacing is lesser of 3 and 18 for strength requirements
3 14 42 18
OK
Horizontal reinforcement
Minimum reinforcement required is 0.25% of gross cross section. Try #4
bars at 10 in. Use on both faces
#4 , 0.20
0.20
0.24
.
0.0029 0.0025 OK
⸫ #4@10” horizontal reinf in each face is adequate
Dowel Length
According to ACI, the development length should be larger of the lap
splice in tension of the thinner bar or the development length of the thick
bar
Basic Tension Development Equation (Eq. 12‐1):
12
: bar‐location factor (ACI 12.2.4) = 1.0 : epoxy coating factor (ACI 12.2.4) = 1.0 : bar‐size factor (ACI 12.2.4) = 1.0
λ: lightweight concrete factor (ACI 12.2.4(d)) = 1.0 cb: min (smallest distance measured from the surface of the concrete to
the center of a bar being developed, one half of the center‐to‐center
spacing of the bars or wires being developed)
Ktr: transverse reinforcement factor (ACI 12.2.3)
is limited to 2.5 or smaller, to prevent pull‐out bond failures
∗ . √
. ∗ . ∗ .
.15.9 12
For a tension lap splice: 1.3 1.3 ∗ 15.9 20.7
⸫ #
.
. ∗ .
21.2
⸫ from the wall into the floor slab or the basement slab
PAGE 94
Appendix J: Load Bearing Wall
Design of Load Bearing Wall
Preliminary:
Applicable design code is ACI 318‐11
Wall height 12
Concrete compressive strength, 5
Reinforcement yield strength, 60
Total service load:
Takes load from Concrete Beam 10, 30, 44, 45
10, 1260
30, 915
44, 756
45, 532
135 , 40 , 1.2 1.6 200 45
, 1260 915 756 532 45 3508
Determine minimum wall thickness:
5.76
4
Try 12 in thick wall
Bearing strength of wall:
Beam bearing width 84
0.85 0.65 0.85 5 12 84 2784.6 3508
N.G.
Try 16 in thick wall
0.85 0.65 0.85 5 16 84
3712 3508
Use 16 in thick wall
Horizontal length of wall to be considered as effective in supporting each
concentrated load:
4 84 4 16 148
Design strength of wall:
PAGE 95
0.55 1 0.55 0.65 5 16 148 1
.
4231.3 3508
OK
Vertical Reinforcements per foot (ACI 14.3.2, 14.3.3, 14.3.5):
Maximum spacing is the smaller of 3 3 16 48 18
Vertical Reinforcements, for No.5 deformed bars or smaller, 0.0012
0.0012 12 16 0.23 /
Use minimum vertical reinf. #4 @ 10 in spacing (0.24 / )
Horizontal Reinforcements, for No.5 deformed bars or smaller, 0.0020
0.0020 12 16 0.39 /
Use minimum horizontal reinf. #5 @ 8 in spacing (0.46 / )
PAGE 96
Appendix K: Wall Footing
Design of Wall Footings
Preliminary:
Applicable design code is ACI 318‐11
Basement wall thickness 14 ; concrete cover 2 11.5
Soil surface to basement top of slab 24
Sits on fractured rock layer with allowable bearing capacity,
24,000 24 /
Unit weight of soil backfill 116
Concrete compressive strength, 5
Reinforcement yield strength, 60
Assume depth of footing, 12 1
Concrete cover = 3”
Total service load:
Tributary width of slab 12.5
10" Slab self‐weight:
150 12.5 1562.5 /
Self‐weight of basement wall:
150 24 3600 /
Weight of masonry façade on ground floor:
198 14 2772 /
Superimposed dead loads of miscellaneous:
100 12.5 1250 /
Total dead load:
1562.5 3600 2772 1250 9,185
Total occupancy live load:
100 20 2,000
Total axial load:
1.2 9,185 1.6 2,000 14,222 14.22
Footing weights, 1 150 150
Soil fill on top of footing, 23 116 2,668
Effective soil pressure, 24,000 150 2,668 21,182
PAGE 97
Width of footing required, . /
. 0.67 → .
Bearing pressure for strength design for a 12 width:
14.225.00
2.85
Depth required for shear at a distance d from face of wall:
. 2.85 2.73
. √ 4.29
4.29 3.5 7.79
7.79 12
⸫ Use 12 in total depth of footing
2 0.75 2 1√5000 12 8.5 10,818.7
10.82
10.82 2.73
⸫ Shear Check OK
Required steel area:
Cantilever length
1.92
Moment at face of wall:
2.85 1.92 5.25
.
. . 80.8
Steel percentage:
.1 1
.
. ,
, 1 1
.
. ,
0.0014 0.0035
0.0035 12 8.5 0.357
⸫ Use # @ . /
Development length:
1.0
3.5 ←
0.5 10 5.0
PAGE 98
0.
/5.6 2.5 → 2.5
,
. , / . 25.46 /
25.46.
. 24.57 /
24.5758 15.35 16
Available development length assuming bars are cut off 3 in from edge of footing
52
122
112
3.0112
1.75 21
21 16
⸫ Use .
Temperature and Shrinkage steel (Perpendicular to the #7 bars) (ACI 7.12.2.1):
0.0018 0.0018 60 12 1.296
⸫ Use # .
Connection between the wall and the footing:
PAGE 99
Appendix L: Snow Loads
A snow load can be defined as the vertical force placed on a building’s roof by the weight of snow.
Snow loads for our building were calculated using ASCE 7‐10. The flat roof snow load (pf) can be
found using the following equation:
0.7
Where:
Ce = Exposure Factor (Table 7‐2, ASCE 7‐10) = 1.0 (assuming Exposure B, and partially
exposed)
Ct = Thermal Factor (Table 7‐3, ASCE 7‐10) = 1.1
Is = Importance Factor (Table 1.5‐1, ASCE 7‐10) = 1 (Assuming a Risk Category of II)
Pg = Ground Snow Loads (Fig. 7‐1, ASCE 7‐10) =20 psf
0.7 0.7 1 1.1 1 20 15.4
Next, we will need to know the height of our balanced snow load (hb). This can be found by
employing the following equation:
15.416.6
11.13"
where:
ps = Slope roofed balance snow load (we can assume this to be equal to pf) = 15.4 psf
γ = snow density = 0.13(pg) + 14 = = 0.13(20) + 14 =16.6 pcf
Using this we can now begin to take into account the snow that forms from drifts coming from a
higher roof or that comes with the wind from the opposite direction, from the roof on which the
drift is located. These two drifts are known as the windward drift and the leeward drift.
PAGE 100
For this sample calculation, we will be looking at Section A in the roof garden plan view.
For Leeward drift, the drift height can be determined from the following graph. Where lu = upper
roof length. The windward drift height is found by using the same graph, however, the upper roof
length is substituted by the lower roof length and only three‐quarters of the drift height are used.
The higher drift height from both leeward and windward are used for the design.
PAGE 101
Using the drift height equation, we find the actual drift height to be 1.23’, but we will round up to
1.5’ to be conservative. For this particular roof section, both sections have the same roof lengths,
therefore the leeward drift height will be used for design. Drift height can be estimated to be
around 1’‐6”. The drift width is equal to 4hd (4 * 1.5’ = 6’), and now with both the drift height and
drift weight we can calculate the maximum intensity of the drift surcharge load, pd, which is equal
to the drift height multiplied by the snow density. Doing so we get that pd is equal to 24.9 psf. The
final snow load layout can be seen in appendix A.
The remaining sections are done in a similar manner. This time we’ll be using the drift height
equation for simplicity. All snow layouts can be found in the Appendices. Starting with Sections B:
Leeward:
0.43 10 1.5 0.43√20√20 10 1.5 1.23′
Windward:
0.43 10 1.534
0.43√22.67√20 10 1.534
1.01′
Leeward controls design, with hd = 1.23’, which we can round up to 1.5’
Because hd ≤ hc , w = 4hd = 4(1.5’) = 6’
PAGE 102
Now with both the drift height and drift weight we can calculate the maximum intensity of the drift
surcharge load.
∗ 1.5 16.6 24.9
Sections C
Leeward:
0.43 10 1.5 0.43√9.083√20 10 1.5 0.25′
Windward:
0.43 10 1.534
0.43√28√20 10 1.534
1.17′
Windward controls design, with hd = 1.17’, which we can round up to 1.25’
Because hd ≤ hc , w = 4hd = 4(1.25’) = 5’
Now with both the drift height and drift weight we can calculate the maximum intensity of the drift
surcharge load.
∗ 1.25 16.6 20.75
Section D
Leeward:
0.43 10 1.5 0.43√9.083√20 10 1.5 0.25′
Windward:
0.43 10 1.534
0.43√33.5√20 10 1.534
1.31′
Windward controls design, with hd = 1.31’, which we can round up to 1.5’
Because hd ≤ hc , w = 4hd = 4(1.5’) = 6’
Now with both the drift height and drift weight we can calculate the maximum intensity of the drift
surcharge load.
∗ 1.5 16.6 24.9
PAGE 103
Appendix M: Tabulated ETAB WIND & Seismic Results
Auto Lateral Load to Diaphragm
Story Elevation (ft) Location
X‐direction
Y‐direction
Bulkhead 167 Top 4.357 0
Roof 158 Top 74.526 0
Story 17 149 Top 44.113 0
Story 16 140 Top 84.127 0
Story 15 131 Top 74.212 0
Story 14 122 Top 67.306 0
Story 13 113 Top 60.587 0
Story 12 104 Top 54.065 0
Story 11 95 Top 47.749 0
Story 10 86 Top 41.653 0
Story 9 77 Top 35.79 0
Story 8 68 Top 30.177 0
Story 7 59 Top 24.835 0
Story 6 50 Top 19.789 0
Story 5 41 Top 15.071 0
Story 4 32 Top 10.726 0
Story 3 23 Top 6.817 0
Story 2 14 Top 3.956 0
Base 0 Top 0 0
Seismic lateral loads to Diaphragm
Auto Lateral Load to Diaphragm
Story Elevation (ft) Location
X‐direction
Y‐direction
Bulkhead 167 Top 4.5 0
Roof 158 Top 33.855 0
Story 17 149 Top 33.59 0
Story 16 140 Top 48.607 0
Story 15 131 Top 48.18 0
Story 14 122 Top 47.73 0
Story 13 113 Top 47.252 0
Story 12 104 Top 46.744 0
Story 11 95 Top 46.199 0
Story 10 86 Top 45.612 0
Story 9 77 Top 44.974 0
Story 8 68 Top 44.274 0
PAGE 104
Story 7 59 Top 43.495 0
Story 6 50 Top 42.616 0
Story 5 41 Top 41.6 0
Story 4 32 Top 40.386 0
Story 3 23 Top 38.856 0
Story 2 14 Top 47.658 0
Base 0 Top 0 0
Wind lateral Loads on diaphragms
Overturning Moment Wind Strength X
Story Elevation (ft) Location X‐direction
Y‐direction
Bulkhead 167 Top 0 0
Roof 158 Top 93.0891 ‐0.0698
Story 17 149 Top 824.9076 ‐0.6585
Story 16 140 Top 1956.7654 ‐1.6058
Story 15 131 Top 3756.7149 ‐3.2235
Story 14 122 Top 6135.4126 ‐5.4887
Story 13 113 Top 9026.8666 ‐8.3973
Story 12 104 Top 12368.4999 ‐11.9418
Story 11 95 Top 16101.2145 ‐16.1118
Story 10 86 Top 20169.4664 ‐20.8936
Story 9 77 Top 24521.3496 ‐26.27
Story 8 68 Top 29108.6914 ‐32.2193
Story 7 59 Top 33887.1613 ‐38.7146
Story 6 50 Top 38816.3967 ‐45.7219
Story 5 41 Top 43860.1515 ‐53.1983
Story 4 32 Top 48986.4718 ‐61.0876
Story 3 23 Top 54167.9077 ‐69.3157
Story 2 14 Top 59381.7625 ‐77.7808
Base 0 Top 67518.5856 ‐91.137
Overturning Moment due to wind in the x‐direction
Overturning Moment Wind Strength Y
Story Elevation (ft) Location
X‐direction Y‐direction
Bulkhead 167 Top 0 0
Roof 158 Top 0.0237 ‐112.8312
Story 17 149 Top 0.749 ‐1014.0488
Story 16 140 Top 1.9693 ‐2419.0201
Story 15 131 Top 4.1219 ‐4684.4258
Story 14 122 Top 7.1759 ‐7712.5974
PAGE 105
Story 13 113 Top 11.1271‐
11433.4147
Story 12 104 Top 15.9675‐
15778.6056
Story 11 95 Top 21.6853‐
20681.8373
Story 10 86 Top 28.2648‐
26078.8206
Story 9 77 Top 35.6858 ‐31907.428
Story 8 68 Top 43.923‐
38107.8338
Story 7 59 Top 52.945‐
44622.6787
Story 6 50 Top 62.7125‐
51397.2705
Story 5 41 Top 73.1753‐
58379.8316
Story 4 32 Top 84.266 ‐65521.816
Story 3 23 Top 95.8853‐
72778.3317
Story 2 14 Top 107.8609 ‐80108.742
Base 0 Top 126.477‐
91580.8802
Overturning Moment due to wind in the x‐direction
Overturning Moment Wind Strength
Story Elevation (ft) Location
X‐direction Y‐direction
Bulkhead 167 Top 0 0
Roof 158 Top 0.0167 ‐41.2208
Story 17 149 Top 0.5105 ‐392.4984
Story 16 140 Top 1.3415 ‐1049.7471
Story 15 131 Top 2.8092 ‐2151.1985
Story 14 122 Top 4.8933 ‐3692.7022
Story 13 113 Top 7.5912 ‐5670.0769
Story 12 104 Top 10.8979 ‐8078.8727
Story 11 95 Top 14.8059‐
10914.3337
Story 10 86 Top 19.3052‐
14171.3507
Story 9 77 Top 24.3825‐
17844.4005
Story 8 68 Top 30.0211‐
21927.4672
PAGE 106
Story 7 59 Top 36.2‐
26413.9376
Story 6 50 Top 42.8926 ‐31296.454
Story 5 41 Top 50.0646‐
36566.7019
Story 4 32 Top 57.6694‐
42215.0771
Story 3 23 Top 65.6384‐
48230.1209
Story 2 14 Top 73.8525‐
54597.4196
Base 0 Top 86.6184‐
65172.5055
Overturning wind strength
Overturning Moment Wind Strength X
Story Elevation (ft) Location
X‐direction kip‐ft
Y‐direction kip‐ft
Bulkhead 167 Top 0 0
Roof 158 Top 54.8639 ‐0.1071
Story 17 149 Top 634.8425 ‐1.0114
Story 16 140 Top 1730.7949 ‐2.4681
Story 15 131 Top 3591.6424 ‐4.9592
Story 14 122 Top 6210.0553 ‐8.4515
Story 13 113 Top 9578.9169 ‐12.9406
Story 12 104 Top 13690.6451 ‐18.4166
Story 11 95 Top 18537.1236 ‐24.8655
Story 10 86 Top 24109.6211 ‐32.2682
Story 9 77 Top 30398.6893 ‐40.5999
Story 8 68 Top 37394.0318 ‐49.829
Story 7 59 Top 45084.3299 ‐59.9149
Story 6 50 Top 53457 ‐70.806
Story 5 41 Top 62497.8422 ‐82.4357
Story 4 32 Top 72190.4909 ‐94.7162
Story 3 23 Top 82515.4728‐
107.5301
Story 2 14 Top 93448.3507‐
120.7161
Base 0 Top 111675.395‐
141.5183
Overturning Moment Wind Strength X
PAGE 107
Overturning Moment vs Elevation
0
20
40
60
80
100
120
140
160
180
0 0.0002 0.0004 0.0006 0.0008
Elevation (ft)
Overturning Moment, kip‐ft
Story Overturning Moment
Global X
Global Y
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