Project

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University of California DavisDepartment of Civil and Environmental Engineering

ECI 136 Building Design Spring 2016Final Project

316 Vernon St. Roseville, CA

Negine MalboubiAleksandr SavchukMaksim Bychkov

Phuc HoangSam Ray

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TABLE OF CONTENTS

PAGE

Project Description...........................................................................................................................3

Gravity & Lateral Load Path Processes...........................................................................................3

Structural System Description.........................................................................................................4

Roof System.........................................................................................................................4

Floor System........................................................................................................................5

Reinforcement Required for a Typical 10” Concrete Slab..............................................................9

Reinforcement Required for a 9” Slab Roof……………………………………………………..10

Reinforcement for a Floor Beam………………………………………………………………...10

Roof Beam Calculations................................................................................................................11

Design of Shear Reinforcement for Beams………………………………………………......….12

Column Reinforcement Calculations…………………………………………………………….14

Interior Concrete Column..................................................................................................14

Exterior Concrete Column……………………………………………………………….15

Footing Dimensions......................................................................................................................15

Seismic Design Calculations..........................................................................................................15

Wind Design Calculations……………………………………………………………………….17

Appendix A – Symbology.............................................................................................................21

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Project Description

The office building on 316 Vernon St. in Roseville CA is a four story concrete structure, which will be constructed to replace the existing old building. The new building is mainly designed as an office building with retail space on the first floor, classrooms on the second floor, and various lounges and exercise rooms on the third floor. The rest of the building consists mostly of office space, conference rooms, electrical/IT storage, and miscellaneous rooms. The design live loads, from the 2013 California Building Code, were used for the different types of rooms, in order to create the design of the slab and beams that is necessary to support the weight of each floor.

The overall height of the building, from the slab on grade to the top of the parapets on the roof is 62 feet. The floor heights are as follows: The first floor is 16 feet high. The second and third floors are 14 feet high. The fourth floor is 13 feet and 7 inches. The roof and parapet adds another 4 feet and 5 inches to the total height of the building. The building features an elevator shaft with 2 elevators located close to the center of the building with a set of stairs running up and down the height of the building to either side of the elevator shaft. The office building footprint is approximately 144x144 feet, making the total square footage of the building roughly 82,944 square feet.

The original structural design of the building was chosen to be a two-way concrete slab on top of concrete columns since the smaller distance between columns is ideal for this kind of system. However, due to lack of expertise in designing this type of structure, the building’s structural design was changed into a one-way slab with five-foot wide concrete beams supporting the slab, and 2’ x 2’ concrete columns bringing the load to the ground. The slab on grade will be 5 inches thick with #3 rebar spaced at 18 inches on center each way, underlain by a 10mm vapor barrier on top of 4" of clean crushed rock not passing the #4 sieve. The structures foundation will consist of three-foot deep square footings of varying sizes depending on the location under the building, as recommended by the geotechnical engineering report.

Gravity and Lateral Load Path Process:

Max &Min will use concrete framing for the building’s structural system. The gravity load consists of dead and live loads due to occupancy that generates vertical forces onto the office building.  First, the gravity load accumulates within the roof and the floor of one way slabs, and proceeds to distribute into the beams depending on different tributary areas. The gravity load then travels from the beam into the columns. The same load path is observed on all the other floors. The load gets transferred down the columns to the bottom floor and through the foundation into the ground.

The lateral load consists of wind and seismic forces that impact the building horizontally. The lateral system of the building, meant to support the lateral loading, is going to be a shear wall system. The shear wall will be spaced around the core of the building forming a square around the elevator shafts and stairs. From the shear wall, it will travel into the foundations and then into the ground. This type of lateral system was chosen since it is the preferred lateral system for concrete buildings of similar heights.

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Design Criteria

Design Codes: 2013 California Building Codes American Society of Civil Engineers-ASCE 7-10 Minimum Design Loads for

Buildings and Other Structures American Institute of Steel Construction-Steel Construction Manual, Fourteenth

Edition American Concrete Institute-Building Code Requirements for Structural Concrete

(318-11) Precast Concrete Institute-Precast and Pre-Stressed Concrete, Seventh Edition

Structural System Description-Center

Roof System

The roof of the building is also made of concrete, and is composed of a 9” concrete slab with a ¼” per foot slope on the slab to support drainage. The roof contains 2 concrete panels for heating equipment as well as crickets for water drainage. After consulting with the Senior Engineer, these two loads are neglected because they are deemed insignificant to the loading system as a whole. The roof is supported by concrete beams which rest on the 36 columns that extend from the first floor all the way to the roof. All the weights on the roof, including the parapets, are supported by the concrete beams, and travel through the columns directly into the ground. The table below shows the dead and live loads used to calculate the reinforcement needed in the roof slab and beams. The values of the dead weights were found in a table of Standard Building Material weights compiled by Buehler & Buehler Structural Engineers, and quantities were estimated off of the architectural drawings.

Table 1: Weight Distribution of Roof Loads

Roof Loads

MaterialLoad Type

Magnitude (psf)

Total PSF

Total (kips)

Sprinkler System Dead 1.2    146.4     3035.75Insulation Dead 210" slab Dead 125Mechanical/Electrical/Plumbing Dead 6Roofing Membrane Dead 6Crickets Live 1Misc. Dead 1Acoustic Ceiling Dead 4

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5

Expanded Polystyrene Foam Dead 0.2

Floor System

The building plan has 36 columns evenly spaced out in a square pattern. The dead and live loads on the floors vary between the 4 floors because the designed rooms and occupancy varies floor to floor based on the architectural drawings. Nevertheless, the structural floor plan will be made from 10” one-way concrete slab. The one-way concrete slab will be connected to the beams that will rest on top of the columns. The weight on each slab gets transferred to the beams based on the beams tributary area. The beams carry the load into the columns which is transferred to the square footings which form the foundation for the building.

Table 2: Typical Dead Loads for a Floor

Floor Type

Dead Load (psf)

Reference

1-4

Normal Concrete 8" 100 concreteconstruction.netcarpet tile 1 B&B Material Weights

carpet and pad 1 B&B Material WeightsBeams 20 B&B Material Weights

Columns 5 B&B Material WeightsCeiling 3 B&B Material Weights

Acoustic Fiber Board 1 B&B Material WeightsMechanical Ducts 4 B&B Material Weights

Fibrous Board 1.1 B&B Material WeightsSingle Ply

Waterproofing Membrane

0.7 B&B Material Weights

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Table 3: Live Loads Floors 2-4

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Break 1262 50 63.1 (ASCE 7-10) Chap 4Class Room 8893 40 355.72 (ASCE 7-10) Chap 4

Storage 1168 125 146 (ASCE 7-10) Chap 4Copy 87 50 4.35 (ASCE 7-10) Chap 4Office 1602 50 80.1 (ASCE 7-10) Chap 4

Computer Lab 1266 100 126.6 (ASCE 7-10) Chap 4

Lounge 437 50 21.85 https://sites.google.com/site/boeinghangar/structural

Lobby 423 100 42.3 https://sites.google.com/site/boeinghangar/structural

Bathroom 41.77 0 (ASCE 7-10) Chap 4Corridor 80 0 (ASCE 7-10) Chap 4Janitor 49 50 2.45 (ASCE 7-10) Chap 4

Admissions 178 100 17.8 (ASCE 7-10) Chap 4

Work Room 225 100 22.5 (ASCE 7-10) Chap 4

stairs 100 (ASCE 7-10) Chap 4

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Classroom 1034 40 41.36 (ASCE 7-10) Chap 4Office 9233 50 461.65 (ASCE 7-10) Chap 4Storage 359 120 43.08 (ASCE 7-10) Chap 4

Bathroom 41.77 0 (ASCE 7-10) Chap 4Corridors 80 0 (ASCE 7-10) Chap 4Elevator 300 0 (ASCE 7-10) Chap 4Exercise

Lab 757 100 75.7 (ASCE 7-10) Chap 4

stairs 100 (ASCE 7-10) Chap 4

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Office 8706 50 435.3 (ASCE 7-10) Chap 4Data 21 50 1.05 (ASCE 7-10) Chap 4

Storage 35 125 4.375 (ASCE 7-10) Chap 4

Lockers 428 60 25.68 http://www.eng-tips.com/viewthread.cfm?qid=307407

Break 202 50 10.1 https://sites.google.com/site/boeinghangar/structural

Conference 1816 100 181.6 https://sites.google.com/site/boeinghangar/structural

Bathrooms 42 0 (ASCE 7-10) Chap 4Electrical 100 50 5 (ASCE 7-10) Chap 4

Work Room 159 50 7.95 https://sites.google.com/site/

boeinghangar/structuralCorridors 80 0 (ASCE 7-10) Chap 4

Lobby 213 100 21.3 (ASCE 7-10) Chap 4Print 186 50 9.3 (ASCE 7-10) Chap 4

Janitor 49 50 2.45 (ASCE 7-10) Chap 4stairs 100 (ASCE 7-10) Chap 4

Table 4: Average Live Loads per Floorfloo

rSF Bath

CorridorsLive

Load psfLive Load

(kips)Total Load

(kips)Live Load

psfLive Load

(psf)Live Load

(kips)2 8684.5 80 694.76 1398.865 67.907 70 1441.9653 19892.5 80 1591.4 1637.4 79.487 70 1441.9654 5009.5 80 400.76 1283.53 62.308 62 1283.53

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Table 5: Floor Live Loads

Floor Occupancy/material Area (ft2) Live Load (psf) Live Load (Kip)

=Area*Load Reference

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Classroom 1034 40 41 (ASCE 7-10) Chap 4Office 9233 50 462 (ASCE 7-10) Chap 4

Storage 359 120 43 (ASCE 7-10) Chap 4Exercise Lab 757 100 76 (ASCE 7-10) Chap 4

Corridors9216.5

80737.32

(ASCE 7-10) Chap 4Bathroom 42 (ASCE 7-10) Chap 4

Stairs 100 (ASCE 7-10) Chap 4Average Live Load per Floor (psf) 65

Partition load (psf) 15Total Live Load (psf) 80

Table 6: Typical Dead Load for a Floor

Floor Type Dead Load (psf) Reference

Total Dead (psf) per

floor

Total Load (kips)

1-4

Normal Concrete 10" 125 concreteconstruction.net

221.2 4556.609

carpet and pad 1 B&B Material WeightsBeams 30 B&B Material Weights

Columns 15 B&B Material WeightsCeiling 3 B&B Material Weights

Acoustic Fiber Board 1 B&B Material Weights

Mechanical Ducts 4 B&B Material WeightsSingle Ply Water

Proofing Membrane

0.7 B&B Material Weights

Sprinklers 1.5 B&B Material WeightsCladding 40 B&B Material Weights

Reinforcement Required for a Typical 10” Concrete Slab

Equation Used: Mu=CmWLn2 (1)

All variables are defined in Appendix A of the report.

Table 7: Floor Slab Parameters

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wd (psf) wl (psf) d (in) h (in) ф fy (ksi) f'c (ksi)109 80 9 10 0.9 60 5

Table 8: Floor Slab Reinforcement

Cm Wu Ln (ft)

Mu (lbs*ft/ft)

Mu (kip*inch/ft) Rn m ρ (+) ρ (-) As

(in2) S (in) actual (in)

0.091

258.8 23 12446 149.351 0.17

114.11

80.13

90.00

3 0.314 11.857 11.500

0.063

258.8 23 8557 102.679 0.11

714.11

80.14

00.00

2 0.214 17.361 17.000

Means and Methods

To determine the reinforcement used for a floor, we must consider both the positive and negative moment that results from the loading. The appropriate Cm value is chosen accordingly, as demonstrated in Table 7. The ultimate distributed load, Wu, is determined using the ACI code given the following equation:

wu=1.2 wd+1.6 wl(2)

Once Mu is determined from equation (1), the constant Rn is determined by grouping the following variables:

Rn=M u

12 Dϕ(3)

Next, the parameter is “m” is determined using the following equation:

m=f y

0.85 f c' (4)

When both “Rn” and “m” are determined, the ratio of the area of steel to concrete, or ρ, can be determined. Both a positive ρ and negative ρ are calculated and the lesser value is chosen. The required steel area is then determined by the following formula:

A sreq=( ρ∗12 )

D(5)

A particular bar size is chosen, and we chose a #5 bar so that less bars can be used and assembly is easier for the construction crew. From this bar size, we determined the spacing by the following formula:

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Spacing=( A s

A sreq)∗12(6)

This final number is then rounded down slightly because this final answer represents the maximum spacing. As can be seen in Table 7, where there is positive moment, the spacing used is 17 inches, and for a negative moment, the spacing is 11.5 inches.

Reinforcement Required for a 9” Slab Roof

The calculations for the 9” slab roof are similar to those above for the 10” floor slab. The only change is the dead and live loads. For this reason, only the tables are shown below:

Table 9: Roof Slab Parameters

wd (psf) wl (psf) d (in) h (in) ф fy (ksi) f'c (ksi)133.9 1 8 9 0.9 60 5

Table 10: Roof Slab Reinforcement

Cm Wu (psf) Ln (ft)

Mu (lb*ft/ft)

Mu (kip*inch/ft) Rn m ρ

(+) ρ (-) As (in2) S (in) actual (in)

0.09 162.28 23.00 7804.19 93.65 0.1

4 14.12 0.14

0.00 0.22 16.88 16.50

0.06 162.28 23.00 5365.38 64.38 0.0

9 14.12 0.14

0.00 0.15 24.68 24.50

Reinforcement Required for a Floor Beam

Table 11: Floor Beam Parameters

tbeam (ft) lbeam (ft) bbeam (ft) Atbeam (ft2) Dbeam (psf) Lbeam (psf) hbeam (in) dbeam (in)0.833 28 5 728 109 80 20 19

Table 12: Floor Beam Reinforcement

Mu (kip*in) Wsw (lbs) Wta (lbs) wutotal

(lbs/ft)Mn (kip-

in) As (in2) # of bars actual spacin

g (in)

actual spacing (in)

8795 21000 188406 7479 7916 8.12 8.12 9.00 6.67 6.50

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Means and Methods

We designed the beams to fail in tension using the following formula

M n=As∗f y d (1−0.59 A s f y

f ' c ( bd )). Rearranging this equation and solving for As, we determined the

reinforcement. Mu is determined from the equation M u=wutotal∗Lbeam

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8. The self weight of the

beam is calculated from the following formula, where the density of concrete is assumed to 150 lbs/ft3:w sw=150∗t∗lbeam∗b∗1.2. The distributed load that acts on the tributary area is then determined by w ta=(wd∗1.2+wl∗1.6 )+ Atbeam . Both of these loads are added together to yield the total ultimate load, wultimate. This value is then plugged into the Mu equation presented above. Using the relationshipϕMn=Mu, the needed area of steel As, is determined. An appropriate bar size, a #8 bar is chosen. Dividing the total steel area by the area of each bar, yields the number of

bars. Lastly, the spacing of the bar can be determined from s=bbeam

¿of bars. The spacing is then

rounded down to approximately 6.5" between each bar.

Roof Beam Calculations

The same methods used for the Roof Floor Calculations are used for the reinforcement calculations for the roof, except that the dead and live loads vary. For this reason, they are not elaborated on in this section of the report and tables are presented below.

Table 13: Roof Beam Dimensions

tbeam (ft) lbeam (ft) bbeam (ft) Atbeam (ft2) Dbeam (psf) Lbeam (psf) hbeam (in) dbeam (in)0.833 28 5 728 133.9 1 20 19

Table 14: Roof Beam Spacing

Mu

(kip-in)wsw

(lbs) wta (lbs)wutotal

(lbs/ft)Mn

(kip-in)As

(in2)# of bars

actual

spacing (in)

actual (in)

58442100

0118,14

0 4,969 5,259 5 7 7 9 9

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Design of Shear Reinforcement for Beams:

Given Inputs:

F’c = 4 ksi

Fy = 60 ksi

Beam Effective Depth (d) = 19 in.

Beam Width (bw) = 5 ft = 60 in.

Beam Length (L) = 28 ft.

Wu = 7.479 kip/ft. *dead loads and live loads are found in (psf) and multiplied by the tributary area of 28 x28 (f t 2)

Column Width (w) = 2 ft. = 24 in.

φ = 0.75

λ = 0.75 for light-weight concrete

Means and Methods:

1. Knowing L, Wu, and w, find all reaction forces acting upon the beam and graph the Vu diagram.

Total distributed load = (7.479 kips/ft.) * (28ft.) = 209.412 kips downward

RA=RB=W U L

2=104.706 kips upwards

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2. On the Vu

diagram, V(x) = 104.706 – 7.479x.

Vu at critical section occurs at x = d + 0.5 w

x = 19 + 0.5 (24) = 31 in. = 2.58 ft = distance d from support.

Vu (2.58 ft.) = 85.4 kips

3. To find shear strength of concrete, use the following equation:V C=2 λ√ f ' c bw d

V c=108.15 kips

4. To find shear capacity of stirrups, use the following equation:

V s=V u

φ−V C

V s=5.70 kips

5. Minimum shear reinforcement is required if Vu > 0.5 φ Vc.

0.5φ V c=40.56 kips

Since 85.4 kips > 40.56 kips, stirrups are necessary for minimum shear reinforcement.

6. Determine the required spacing of vertical stirrups based on φ V s. Pick the lowest s.

s=A v f y d

V s

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s=d2∨24

Try #3 Stirrups, s = 44 in.Pick s = 9.5 in.

7. If V s>4φ√ f ' c bwd , thenS ≤ d4∨12∈.

4 (0.75 ) √4000 (60 ) (19 )=3.60Since 5.70 > 3.60, then S ≤ d/4 controls.s ≤ 4.75 in.Use #3 stirrups at 4.5” O.C.

8. Determine spacing of the vertical stirrups based on minimum shear reinforcement. Pick the lowest s.

s=A v f y

50 bw

s=Av f y

0.75√ f ' c bw

s≤ d2

≤ 24∈.

Using #3 stirrups, smin = [4.4 in, 4.64 in] = 4.4 in.

4.4 ≤ 9.5 ≤ 24 in.Round 4.4 inches to 4.5 inchesUse #3 stirrups at 4.5” O.C.

9. Determine the location of stirrups using V(x) = 104.706 – 7.479x.Vu occurs at x = 2.58 ft, Vs occurs at 2.58 ft, φ V c occurs at 3.15 ft, 0.5 φ V c occurs at 8.58 ft.

10. Draw beam with stirrups.

Column Reinforcement Calculations

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The minimum area of steel is 1% Ag. This area of steel is determined to be 5.76 square inches. We chose to use a #8 bar size, and the total number of bars is 7.29 bars. We rounded up to 8 bars, with 8” spacing between each bar and all of them being 4” from the edge of column.

Interior Concrete Column:

Table 15: Interior Column Parameters

wd (psf) wl (psf) wu (psf) At (ft2) Pu (Kip) Ag (in2) Bar #

703.3 241 1229.56 784 964 576 9

Table 16: Interior Column Reinforcement

.65ф As (in2) S (in)0.5525 31 3.1

Exterior Concrete Column:

Table 17: Interior Column Parameters

wd (psf) wl (psf) wu (psf) At (ft2) Pu (Kip) Ag

(in2)Bar #

719 241 1248.4 392 489 576 9

Table 18: Interior Column Reinforcement

.65ф As (in2) S (in)0.5525 15.6 6

Footing Dimensions

Table 19: Footing DimensionsLocatio

nPu

(Kip) BC (kip/ft2) A (ft2)

Side (ft)

Exterior 490 7.5 65 8.1Interior 964 7.5 129 11.3

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Means and Methods

Two footings are designed: one for the exterior column, and one for the interior column. The formula for determining the dimension of one side is as follows:

Footing Dimension=√ ( Total Load onColumnBearingCapacity

)

Dead Loads consist of the slab and beam as well as the column self-weight. The live loads are taken from occupancy and partitions. Outside column also take into account the cladding. All loads are taken in (psf) then multiplied by the appropriate tributary area. Interior columns have a tributary area of 28 x28 ( f t2 )∧28 x 14 ( f t 2 ) for the exterior ones .The thickness of the footing will be 16” and this is determined by making it 1.5 times greater than the size of the footing dimension.

Seismic Design Calculations

Means and Methods:

All variables initially can be found using ASCE7-10 and USGS.com (See Table 20). Because of the classrooms in this building, it is categorized as risk category III. S values are found by location on USGS.com. Because Concrete Shear walls are used, R is taken to be 6. Ta is found using the following equation: T a=C t∗hn

x(See Table 20). Once all these variables are found Cs needs to be found by following the criteria below.

Take the lower of the two values below:

C s=S Ds

RI e

C s=S D1

(T a∗( RIe ))

The first equation is lower so Cs is taken to be .098 (See Table #). Minimum Cs requirements are easily met here so not need to check. W is found by adding up all dead load and live loads for the entire building. In order to find the base shear, the following equation is used

V=C s∗W (See Table 21).

Seismic Redistribution was not required in this building design but values can be found in table #. The seismic is illustrated in Figure 1.

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Table 20: Seismic Constants

S1 0.251Ss 0.506

SM1 0.477SMs 0.706SD1 0.318SDs 0.47

hn (ft) 57.583x 0.9Ct 0.016Ta 0.614TL 12k 1.06R 6

Omega 2.5Ie 1.25Cs 0.098

Table 21: Base Shear

W 19629.39Cs 0.098

V 1924.7795

Table 22: Seismic RedistributionFloor hx (ft) wx (kip) Cvx Fx (kip)

2 16 5450.9 0.1 248.83 30 5427.9 0.2 464.44 44 5427.9 0.4 681.1

roof 57.58 3322.7 0.3 530.5sum   19629.39 1.00 1924.78

Figure 1: Schematic of Lateral Forces

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Wind Calculations

Means and Methods:

Chapter 27 and 26 of ASCE7-10 is used to find all the values and equations found in the tables above. Values for table # can be found using the references found in the reference column. Kz

values can be found using the following equation K z=2.01∗(hx

zg)

2alpha(see table #). qz can be

found using the following equation .00256 K zt Kd K zV 2

(see table #). Cp values can be found using references found in table #. GCpn values for internal pressure can be found in section 27.4.4 (see table #). Pressures can be found using the following equation. External Pressure=G Cp qz (see table #). Internal Pressures can be found using the following equation: Internal Pressure=GC pi qz (see table #). Qz used in the internal pressure equation is taken to be at the roof. Parapet pressure is taken at linear pounds per foot (see table 28)

Table 22: Wind Constants

Step Variable Value Reference

1 Risk  III (Table 1.5-1)

2 V 115 (Risk 3) (Table 26.5-1 B)

3Kd 0.85 (Building) (Table

26.6-1)Exposure Category B (Section 26.7.3)

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Ground Surface

RoughnessB

(Google Earth 316 Vernon

Street Roseville CA) (Section

26.7.2)

Kzt 1(Section 26.8.1)

(doesn't meet conditions)

G 0.85 (Rigid Building) (Section 26.9.1)

Enclosure Classification

Enclosed (Section 26.10)

GCpi 0.18 (Enclosed) (Table 26.11-1)

(-) -0.18 (see above)

α 7 (Exposure B) (Table 26.9-1)

zg 1200 (see above)

Table 23: Velocity Pressure Exposure Coefficient

Step Floor hx (ft) kh or kz

4

1 16 0.592 30 0.703 44 0.78

Roof 57.58 0.84Parape

t 62 0.86

Table 24: Velocity Pressure

Step Floor hx qz or qh

51 16 16.852 30 20.163 44 22.49

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Roof 57.58 24.29Parapet 62 24.81

Table 25: External Pressure CoefficientWall Location Cp or CN Reference

Leeward all -0.5 (27.4-1 cont) (L/B=1)

Windward all 0.8 (All Values) (see above)

Side Wall all -0.7

(see above)Roof0-h -0.9h-2h -0.5>2h -0.3

Table 26: GcCpn values

Windward 1.5Leeward -1

Table 27: External/Internal Pressure

Type Wall Step location Pressure (psf)

External

Windward

7

Floor 1 11.46Floor 2 13.71Floor 3 15.3Roof 16.52

Leeward all -10.54Side all -14.76

Roof0-h -18.580-2h -10.32>2h -6.19

Internal Windward all 4.37Leeward all 4.37

Table 28: Parapet Distributed LoadParapet (plf) 164.35

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Figure 2: Schematic of Wind Profile

Appendix A: Symbology

A−Surface area

Ag−Gross area

α−gust speed exponent

A s−Areaof steel

At−Tributary area

BC−Bearing capacity

C p−External pressure coefficient

C pi−Internal pressure coefficient

C s−Seismic reponse coefficient

C t−building period coefficient

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C vx−Vertical distribution coefficient

d−Effective depthof slab

f ' c−Compressive strength

f y−Yield strength

F x−Portion of seismic baseshear

G−Gust effect factor

G Cpn−Combined net pressure coefficient for a parapet

h−Depth of slab

hn−Height

I e−Importance factor

k−Distributionexponent

Kd−Wind directionality factor

k z−Velocity pressure exposure coefficient

K zt−topographic factor

l−Length ( for slab :center beam¿center beam)

Ln−Clear lengthbetweenbeams

m−Yield∧compressive strength ratio

M u−Ultimate moment

ϕ−Strength factor

Omega−¿ strength factor

ρ−Reinforcemet ratio

Pu−Ultimate Load

qz−Velocity pressure

R−Response modification coefficient

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Rn−Concrete beamdesign ratio

S−Reinforcement spacing

S1−Spectralresponse parameter (1 s)

S D1−Design spectral response parameter (1 s )

S Ds−Design spectral response parameter (short period)

Side−Sidelength

S M 1−Max spectral response parameter (1 s )

S M s−Max spectral response parameter (short period)

Ss−Spectral response parameter (short period )

T a−Apporximate fundamental period

TL−Long period transition period

V−Base shear (for Seismic )

V−Wind Speed ( for wind)

W −weight

wd−Distributed load due¿dead load

w l−Distributed load due¿ live load

wu−Ulitimate distributiveload

w x−weight of given floor

x−distance upwind∨downwind of crest

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24