Frame Shear wall Interaction - cee285 / FrontPagecee285.pbworks.com/f/Report0322.doc · Web viewShear Wall-Frame Interaction 52 4.3 ETABS Model and Frame- Shear Wall Interaction Comparison

CEE 285 BEHAVIOR OF STRUCTURAL SYSTEMS FOR BUILDINGS

DESIGN PROJECT

Professor H. KrawinklerStanford University

Submitted: March 22, 2006Team Members:

Jimmy ChanAsphica ChhabraJennifer MooreJana TetikovaNick Wann

CEE 285 BEHAVIOR OF STRUCTURAL SYSTEMS FOR BUILDINGS

DESIGN PROJECT

Professor H. KrawinklerStanford University

Team Members:Jimmy ChanAsphica ChhabraJennifer MooreJana Tetikova

Nick Wann

BD Inc. Project: Palo Alto Office Tower 2

Table of ContentsPART ONE: SYSTEM ASSESSMENT.................................................................4

1.0 Introduction................................................................................................................41.1 Project Proposal.....................................................................................................41.2 Individual Roles.....................................................................................................4

2.0 Load Determination...................................................................................................82.1 Gravity...................................................................................................................82.2 Lateral..................................................................................................................20

3.0 Structural Design.....................................................................................................243.1 Gravity System....................................................................................................243.2 Perimeter Moment Frames..................................................................................303.3 Shear Wall Design...............................................................................................353.4 Connections.........................................................................................................413.5 Foundation...........................................................................................................49

4.0 ETABS Modeling - Analysis and Discussion.........................................................514.1 Model Discussion................................................................................................514.2. Shear Wall-Frame Interaction.............................................................................524.3 ETABS Model and Frame- Shear Wall Interaction Comparison........................53

5.0 Conclusions..............................................................................................................55PART TWO: APPENDIX - DESIGN CALCULATIONS...............................................56

Appendix A – Load Determination...................................................................................Appendix B – Gravity System Design...............................................................................Appendix C – SMRF Design.............................................................................................Appendix D – Shear Wall Design.....................................................................................Appendix E – Connection Details and Calculations..........................................................Appendix F – Analysis Results (ETABS and Interaction)................................................


PART ONE: SYSTEM ASSESSMENT

1.0 Introduction

1.1 Project Proposal

To build a 10 story office building in Palo Alto according to 1997 UBC specifications

keeping the following constraints in mind:

Site Constraints:

Seismic Loads: the building is located at 7 km from the San Andreas fault.

Soil profile SD

Architectural Constraints:

Clear Story height should be at least 8.5 ft.

80 ft x 140 ft floor plan

Other Considerations:

Insure elastic behavior of structure under strong motion earthquake

Consider foundation system

1.2 Individual Roles

Individual roles were given to each team member:

Owner: Jennifer Moore

Architect: Nick Wann

Structural: Jimmy Chan

Mechanical: Jana Tetikova

Contractor: Ashpica Chhabra

The responsibilities of each are outlined below. Each person performed research in

his/her own area in order to guide the building system design.


1.2.1 Owner

The owner wanted to have flexibility in the use of functional spaces that can support the

unknown future demands on the structure as wells as to entice sales of spaces. Specific

areas were chosen and designed for heavier loads in order to meet this flexibility

requirement. To increase demand, the owner also requested specific physical

characteristics such as an atrium on the first floor and a restaurant. Commercial space on

the first floor was also set as a hard constraint in order to rent to retailers. Minimizations

of costs were also important to the owner, who desired to have a cost efficient building

system.

1.2.2 Architect

The architect responded to the owner’s vision of the building through an innovative and

practical extension of the atrium to improve the overall space. Instead of having the

atrium at the first floor level, he reversed the sequence and added a large opening running

through the building from the 6th to 10th floor. This large open space leads to a reduction

in the functional space of the building, however it allows ample natural light to enter the

building, creating a livelier atmosphere and increasing the productivity of its occupants.

The ceilings at the first floor were increased to 15 ft in order to increase the grandeur and

aesthetic appeal of the commercial area. The architect opted against a basement. The lack

of basement and commercial use of the first floor required that mechanical systems be

placed on the second floor, increasing the 2nd floor story height to 15 ft.

The architect designed two continuous shear wall cores, one on each side of the opening.

He has also provided for a restaurant on the fifth floor level, which provides for more

retail space in the building. This floor was chosen because its central location would be

more accessible to the building occupants, which would hopefully increase use. Also, the

restaurant’s location on the 5th floor would allow diners to look up through the opening,

improving the quality of the lunchtime experience. Additionally, people at the top floors

would be able to look down at the decorated restaurant.


1.2.3 Structural Engineer

The mechanical and architectural requirements posed as the primary structural challenges

for the structural engineer. Owners concerns were addressed through the architect and not

the owner herself.

One of the most important decisions that the structural engineers made was the type of

lateral load resisting system. The structural engineers decided on a dual system

consisting of concrete shears walls and steel special moment resisting frames (SMRF) in

both the EW and NS directions. Ductile shear walls provide excellent resistance to high

lateral loads that are probable in highly seismic regions. To achieve this ductility,

however, special attention had to be paid to the detailing of the walls’ reinforcement.

Additionally, the special moment resisting frames (SMRF) act as a “backup” system

providing necessary redundancy to the system.

Special attention also had to be paid to key areas for the heavy loads imposed by the

mechanical system components. These areas were strategically placed in locations

approved by the architect, so as not to interfere with the flow of the building, yet provide

efficient service throughout. One of the most notable structural challenges in the building

has to do with the large open core running down the center of the building. This

architectural detail provided many structural challenges, beginning with the diaphragm

that was assumed to be rigid in this building design. With a plan discontinuity such as

this, the engineers would have to analyze the diaphragm further to validate the rigid

diaphragm assumption. Many other structural decisions had to be made throughout the

design process including the use of composite beams, shored construction, and

fireproofing around the stairways.

1.2.4 MEP

The structural engineers collaborated with the mechanical engineers to come up with a

scheme for the ductwork, which will primarily run along the interior corridor deck that

surrounds the opening. On the 1st through 5th floor, ductwork will run under the floor

beams which are not very deep. The mechanical engineer specified that two chillers and


cooling towers are required for the building. Chillers and other Origination systems will

be housed in the two mechanical rooms on the second floor next to the cores. Coolers at

the roof are also located next to the cores. Four elevators are located in the building. The

shear core is housed around the stairway, allowing for most of the vertical pipes to also

run along the core. The transformer and generator which account for heavy concentrated

loads will be housed outside the building and hence do not affect the structural decisions.

Typical MEP features and loads can be found in Table 2-2.

1.2.5 Contractor

The primary role of the contractor was to promote efficiency of the structural design.

This affected decisions on member sizing, steel member and shear wall connections, and

concrete work. The more similar the connections and member sizes, the more cost

efficient the design. Also, connections and members that are readily available in the

market are more desirable. Labor was also a concern especially related to the installation

of the doubler plates which was avoided by increasing the interior column sizes. The

contractor participated in the design process.


2.0 Load Determination

Gravity loads were computed based on MEP load requirements, typical dead loads, and

live loads based on varying functional uses. Wind and seismic loads were determined to

compute total lateral load effects.

2.1 Gravity

Table 2-1. Dead Load & Live Loads

Loads ksfConcret+deck+misc. 0.065Partitions 0.02DL 0.085

Exterior Cladding 0.02Roofing system 0.05 Self Weights klfFloor Beams 0.05Girders 0.1Columns 0.2 Live Loads ksfOffices 0.05Corridors, exits 0.1File Rooms 0.15Roof 0.02

The chillers, which may weigh up to 10,000 lbs, were placed on the second floor. The

cooling towers are in general placed on the roof for they require a continuous flow of air

and are quite noisy. Since at the time of conceptual design no decision was made as to

where exactly on the roof cooling towers would be placed, four areas of about 150 square

feet where designed to support loads up to 300 psf (Ref. Roof Load Key Sheet).

In addition to chillers and cooling towers, another important consideration is the chilled

water loop and condenser loop which will produce a reaction of about 80,000 lb. at the

base of the building.


Other geometric constraints arise from providing the building with plumbing, storm, and

electrical system. Table 2-2 summarizes the MEP loads and considerations.

Table 2-2. MEP Loads and Considerations

Category Related Constraints Vertical Load

1. Elevator system

Elevators and dumbwaiters (DL and LL) accessibility and fireproofing 2 x10000 lb

2. HVAC System

i) Origination System - -

Chillers

area of 10 ft. x 20 ft.

4(+) thick raised concrete pad

12 - 15 ft. ceiling height

300 psf

Cooling towers

area of 15 ft. x 20

ft. height of 15 ft. - 20 ft.

raised above deck

300 psf

Condenser loop (2 loops needed) - 80000 lb

Chilled water loop (2 loops needed) - 80000 lb

Masonry wall enclosures and

increased slab thickness for pumps and

compressors

- 100 psf - 130 psf

ii) Distribution System

Ductwork - 5 psf

3. Electrical System

Transformers concrete encasing 2 ft. x 6 ft. 300 psf

Emergency Generator 80000 lb

4. Plumbing System

Tanks and boilers - -

5. Fire Protection System

Distribution lines and sprinkler heads - -

A summary of the gravity loads along with the architectural renderings of the typical

floor plans are included herein.












2.2 Lateral

Once the gravity loads are computed and finalized the lateral loads can be determined.

The lateral loads are applied in addition to the gravity loads and typically control the size

of the members. In our case, the lateral loads are resisted by a shear wall and moment

resisting frame system. Wind loads can be very high in some regions such as near the

shoreline of a major body of water, such as the Pacific Ocean or the Gulf of Mexico.

However, the seismic forces imposed on our building were much greater than the wind

forces, and therefore controlled the design. Other forms of lateral load, such as blast

loading or impact loading are not relevant for the design of an office building and

therefore were not considered in this preliminary design.

2.2.1 Wind Loads

The loads imposed on the building were calculated using the UBC formula 20-1. A

design wind speed of 90 mph and an exposure category B were used in the formulation of

the lateral wind loads. Using the following equation as well as Table 16-G of the UBC,

containing values for Ce, the wind pressure at each story and at each mid-story was

interpolated:

p = CeΣCqqsI where ΣCq = 0.8 + 0.5 = 1.3

Then, as shown in Figure 2-1, the values of the wind pressure, p, are averaged at each

interval and this value is then used as the design wind pressure over the entire half-story.

The design wind load was then represented as a line load over the width of the floor by

multiplying the wind pressure of the half-story above and below each floor by their

respective half-story heights and summing.


Figure 2-1: Distribution of the Wind Pressures over the Height of the Building.

This line load, W in k/ft, was then multiplied by the width of the building to calculate the

total force imposed on each floor by the wind. These story forces were then summed

cumulatively down the building to arrive at the story shear force. Each story shear force

was then multiplied by the story height and again summed cumulatively down the

building to determine the overturning moment imposed by the wind loading. The

calculations are summarized in Appendix A. As expected, the NS wind produces higher

base shear forces and overturning moments of 428 kips and 31,142 kip-ft, respectively.

This is nearly twice the loads imposed by an EW wind producing a base shear of 245 kips

and an overturning moment 17,950 kip-ft. However, while these lateral load effects are


notably large due to the close proximity to the Pacific Coast, they were ultimately

neglected in place of the even larger seismic loads.

2.2.2 Seismic Loads

The seismic loads imposed on structures in the Palo Alto area are expected to be

significant. The seismic loads were calculated according to the UBC (1997). As

prescribed by the code, the total base shear is calculated according to design parameters,

such as proximity to an active fault, seismic zone, soil profile, type of lateral system,

period and the effective seismic weight of the building. The seismic weight was

determined in Appendix A using many preliminary assumptions for material and

mechanical weights. These assumptions were later verified as conservative averages.

The elastic fundamental period of vibration of the structure was determined using code

Method A (equation 30-8):

T = Ct(hn)3/4,

where Ct = 0.035 for steel moment-resisting frame was used. Then, the base shear was

calculated using equations UBC (1997) 30-4 through 30-7:

Once the total base shear was determined, the forces were distributed to each floor. Since

the natural fundamental period was determined to be 1.3 sec > 0.7 sec, the whiplash

force, Ft was determined according to:

Ft = 0.07TV< 0.25V,

This force was applied to the roof of the building to account for the wave reflection

which causes a higher inertia force on the top floor. The rest of the base shear was then

distributed to the individual floors based on their seismic weight and height. As was the

case with the wind loading, the seismic shear story forces were summed cumulatively


down the building to determine the individual story shears and the base shear at the

ground level. The story shear was then multiplied by the story height and cumulatively

summed once more to determine the overturning moment. The results of these

calculations can be observed in Figure 2-2.

Figure 2-2: Distribution of the Seismic Forces over the Height of the Building.

As can be easily seen from the results in the Appendix A, the base shear for the building

is 1,038 kips and the overturning moment at the ground floor is 96,698 kip-ft. These

results are nearly 3 times the largest values obtained from the wind loading, thus the wind

loads were ignored and the seismic loads were used as the controlling design lateral

loads. Additionally, unlike the wind loading, the lateral systems in both directions

experience the same loading and thus must both be designed for the same load effects.


3.0 Structural Design

3.1 Gravity System

3.1.1 Gravity Columns

The gravity columns which make up all of the interior columns were designed for axial

load only. These columns have beams framing into them and have simple shear

connections, which are modeled as pins so that virtually no moment is transferred into the

column. Thus, in order to design the columns we first had to determine the axial loads

due to dead and live loads only. These loads were based on the tributary area of the

column and gravity loads including the column self-weight. The resulting loads are

summarized in Appendix B.

The dead and live axial loads were summed cumulatively from the roof down to

determine the total axial load at each floor. These loads were then factored according to

the load combinations provided in the UBC (1997) to obtain a design load, Pu. However,

before we could continue with the design, two engineering decisions were made. First,

due to the column layout and symmetry of the building we determined that we could

reduce all of the interior gravity columns down to two typical columns; one on the corner

next to the elevators, and the other towards the middle of the building closer to the shear

wall. This consistency provides a simplification during construction. The second

engineering decision is that the columns would be spliced at 4 feet above every second

level. This decision is based on the transportation constraints of the columns as well as

the constructability of the building.

With these decisions in mind, the columns were then designed using a K= 1, F y = 50 ksi

and = 0.85 for compression. Column sizes at each story were chosen so that the ratio

of axial compression from the loads to the axial compression capacity of the size,

, was less than or at most equal to 1.00. We used W14 sections for the gravity


columns. The final preliminary design of the gravity columns were taken as the sizes

designed at the 1st, 3rd, 5th, 7th, and 9th floors. These are summarized in Table 3-1.

Table 3-1. Gravity Column Design

GRAVITY COLUMNS

Floor Column 5 Column 6Roof

10 W14X53 W14X539 8 W14X90 W14X907 6 W14X120 W14X1095 4 W14X159 W14X1453 2 W14x211 W14X1761

3.1.2 Interior Girders

The interior girders are designed for 1.2 D + 1.6 L. Refer to the previous load key sheets

for the various load areas. For interior girders only, we analyzed the girders with

distributed loads and tributary areas. We looked at both the strength and deflection,

calculating the minimum section modulus as well as the minimum Ix before deciding the

girder sections. The deflection limits for live loads and dead loads are L/240 and L/360

respectively. Sample calculations can be found in Appendix B.


3.1.3 Floor Beams

Floor beams and slab were designed as a fully composite system to reduce beam sizes

and to take advantage of the concrete floor strength. Floor beams were designed with the

following properties:

Total floor depth - 6.25 inches

Concrete fill - Lightweight concrete (fc’= 3ksi, 110pcf density)

Steel strength - fy = 50ksi

Shear studs - ¾ inch diameter 3 inches long

Shored and unshored construction was evaluated with the following assumed

construction loads:

Wet concrete - 60 psf live load

Additional const. load - 20 psf live load

Finally, the choice of using composite beams was verified by performing a cost

comparison between composite and non-composite beams, detailed in Appendix B.

Loads:

Loads were obtained from the load key sheets. Three typical loadings and three floor

beam lengths/spacings were used in calculations.

Dead Load - 85psf

Live Load - Heavy =(150psf), Medium = (100psf) and Light = (50psf)

Floor beams - 30'Long @10' spacing, 25'@10' and 25' @8'-4"

Required Flexural Strength:

The flexural resistance required was obtained from:


where w is the load per linear foot of beam obtained from tributary widths (half the

distance to adjacent beams) and L is the span of the beam.

Select Section and Properties:

Assuming the depth is the concrete stress block, a, is less than the thickness of the

concrete slab, the design flexural strength, Mn is:

where As is the area of the steel beam required, d is the depth of the steel beam (assumed

to be 10” for the first iteration), yconc is 6.25 inches, a is the depth of the concrete block

(assumed to be 2” for the first iteration).

A value of Y2 , distance from top of the steel flange to the center of the concrete stress

block, is also required. Assuming the depth of the concrete stress block is less then the

thickness of the slab, Y2 was obtained from:

Using these two values sections were chosen from the AISC LRFD Steel Design Manual

3rd edition Table 5-14 Composite W-Shapes.

Flexural capacity was check using:

where

and

Compute number of Shear Studs Required:

The nominal strength of 1 stud was obtained from:


where Asc is the cross-section of the shear stud (0.44in2) , Ec is the modulus of elasticity

of concrete given below (2085.3 ksi) and w is the unit weight of concrete (110pcf).

For a ¾ in diameter stud the strength is 17.47 kips. The number of studs required from

the point of max moment to its connected ends for full composite action was obtained

from:

Since the beams are simply supported this number is for half the beam length. Total

number of studs required is then twice #stud.

Construction Phase Strength Check:

A flexural demand for an unshored beam was checked using the construction loads

assumed. For floor beams where the flexural capacity of the steel is exceeded, a larger

section was chosen and the number of shear studs recalculated.

Deflection Calculations:

Beams that are unshored were checked for deflection under dead loads using:

where unfactored load per linear foot of beam and E and I are the modulus of elasticity

and moment of inertia for the unshored beam. Where deflection are large (δ>L/360)

adequate cambering is required.

Beams that are composite were checked for deflections under live loads using:

where I is the lower bond elastic moment of inertia given Table 5-15 of the AISC LRFD

Steel Design Manual 3rd edition.


Comparison to a Non-Composite Section:

Beam sections were chosen by comparing flexural capacity of the steel section to the

calculated flexural strength required. Sections chosen were also checked for live load

deflections as (Δ<L/360). Assuming 7lbs per stud (in cost) the amount of steel increase

due to the beam size increase was compared.

Sizes for each of the 3 loadings (heavy, medium and light) and for each of the 3

spans/spacings as described in A, are tabulated below. A sample calculation can be

found in Appendix B.

Table 3-2: Section Design

Heavy (LL = 150psf) 30'@10' Type of Const Section Stud Stud Spacing Mu [kft] φMn [kft]Shored W12x35 3/4" every 6" 384.75 439.5Unshored W12x35 3/4" every 6" 144 192Non-Composite W16x57 384.75 394 Heavy 25'@10' Type of Const Section Stud Stud Spacing Mu [kft] φMn [kft]Shored W14x22 3/4" every 8" 267.2 280Unshored W14x22 3/4" every 8" 100 124.5Non-Composite W16x40 267.2 274 Heavy 25'@8.333' Type of Const Section Stud Stud Spacing Mu [kft] φMn [kft]Shored W10x22 3/4" every 8" 222.57 255Unshored W10x22 3/4" every 8" 83.3 97.5Non-Composite W16x36 222.57 240 Medium(LL = 100psf) 30'@10' Type of Const Section Stud Stud Spacing Mu [kft] φMn [kft]Shored W10x26 3/4" every 8" 294.75 302.1Unshored W12x30 3/4" every 7" 144 161.6Non-Composite W16x45 294.75 308.6 Medium 25'@10' Type of Const Section Stud Stud Spacing Mu [kft] φMn [kft]Shored W10x19 3/4" every 9" 204.7 224Unshored W10x26 3/4" every 6" 100 117.4Non-Composite W14x34 204.7 204.75


Medium 25'@8.333' Type of Const Section Stud Stud Spacing Mu [kft] φMn [kft]Shored W10x15 3/4" every 11" 170.5 176.4Unshored W10x22 3/4" every 8" 83.3 97.5Non-Composite W14x34 170.5 204.75 Light (LL = 50psf) 30'@10' Type of Const Section Stud Stud Spacing Mu [kft] φMn [kft]Shored W10x19 3/4" every 11" 204.75 226.72Unshored W12x30 3/4" every 7" 144 161.6Non-Composite W14x34 204.75 204.75 Light 25'@10' Type of Const Section Stud Stud Spacing Mu [kft] φMn [kft]Shored W10x12 3/4" every 14" 142.2 142.34Unshored W10x26 3/4" every 6" 100 117.4Non-Composite W14x26 142.2 139.5 Light 25'@8.333' Type of Const Section Stud Stud Spacing Mu [kft] φMn [kft]Shored W10x12 3/4" every 14" 118.4 142.34Unshored W10x22 3/4" every 8" 83.3 97.5Non-Composite W12x26 118.4 139.5

3.1.4 Elevator Beams

Specials beams were designed above the roof to support the weight of the elevator and its

components. These beams, called sheave beams, were designed to carry 10,000 lbs each

as a centered point load. Additional beams were designed to support the sheave beams.

Limitations on deflection called for a W12x16 for the sheave beams, and W24x55 for the

support beams. Refer to Appendix B for calculations.

3.2 Perimeter Moment Frames

3.2.1 Fixed End Moments

The Perimeter Moment Resisting Frame of the building undergoes large moments

imposed both by lateral and gravity loading. These moments are transferred through the

beams to the columns and eventually to the foundation, where they are dispersed into the

earth. Therefore, each member of this chain must be strong enough to resist the

maximum moments imposed on it if the system is to carry the loads safely. However,


before we can design the members we must know the maximum loads that each would be

likely to experience. Thus, we can start with the perimeter girders to determine the

maximum moments imposed on them from the gravity loads. These can be calculated by

assuming the ends of the perimeter girders are fixed and calculating the fixed end

moments.

In our system, none of the perimeter girders carry distributed loads other than their own

self-weight or the exterior cladding which was assumed to be 0.34 k/ft along the length of

the beam. Additionally, there are two point loads caused by two beams framing into the

girders. Thus, before the fixed end moments can be calculated, the reactions from the

framing beams must be determined according to the load key sheet and beam layout

geometry. These calculations are shown in Appendix C.

3.2.2 Girder Design

The perimeter girders provide majority of the stiffness in the Perimeter Moment Resisting

Frames. However, we did not need to design the girders for stiffness since the moment

frame is the secondary or “backup” system. The primary shear wall system instead

provides the required stiffness. The moment frame hence only needs to be designed for

strength. The design load was taken as the maximum fixed end moments (gravity loads)

and moments due to earthquake loading, which were determined using the Portal Method.

The fixed end moments were factored by 1.1 and used for a preliminary estimate of the

gravity moments. These assumptions would later be checked by computer analysis.

Also, the ρ factor used in UBC ’97 for redundancy was ignored in this design, but the

load combinations provided in the code were utilized. The maximum moment obtained

from the load combinations and the determined moments was used for the preliminary

design.

Using the design moment, we were able to calculate the minimum plastic section

modulus, Zx that was required. The appropriate factor of 0.9 was used for bending.

The equation used to perform this calculation was:


Zx,min = Max Moment(from load combinations)*12/(0.9*50(ksi))

At this point, it was decided to use the same girder size for all three of the girders in each

moment frame. This consistency simplifies the construction process and thus reducing

the chance of beams placed in the wrong location. The results of the preliminary girder

design are shown in Appendix C.

3.2.3 SMRF Column Design

The columns in the SMRF undergo both axial compression and bending moments. It is

assumed that there’s no biaxial bending expected since the interior gravity beams framing

into the columns are shear connected. The perimeter columns were oriented such that

strong axis of the column would occur. We utilized symmetry and only two columns in

each direction of the moment resisting frame were designed. Also, we decided to use

W24 sections due to their large bending moment resistance.

Among the loads imposed on the perimeter columns are moments and axial loads from

dead, live, and seismic loads. To determine all of these components we began by

calculating the axial loads due to the dead and live loads. The procedure for this was

exactly the same as for the gravity columns, using the tributary area of the columns and

the gravity loads due to all possible sources including the self-weight of the column. A

moment distribution of the moment resisting frames was also completed to determine

how the fixed end moments determined earlier were actually distributed to the columns

of the frame. To compute the stiffness of each member in the moment distribution of the

frame, the moment of inertia of the columns was assumed to be 1.2 times the moment of

inertia of the beams. In performing the moment distribution, a concentrated moment of

100 kip-ft was used so that a simple percentage of the moments applied due to the fixed

end moment could be used to calculate the actual distribution of moment in columns due

to gravity loads. Also, an unbalanced loading was used in the moment distribution to

represent possible scenarios of live load. Another load effect obtained during the

moment distribution was a continuity shear that resulted from the unbalanced moments in

the adjacent columns. This shear was computed by dividing the difference in moments in

the adjacent columns by the length of the beam. This shear in the beam is converted to


an axial load in the interior column and is added to the axial load due to dead loads. The

axial loads due to dead and live loads were cumulatively summed as before to determine

the total axial load at each floor due to the dead and live loads. Finally, the axial loads

and moments determined in the Portal Method are used to determine the ultimate loading

on the columns. These loads are summarized in Appendix C.

All of the load cases used in this design were considered. However, since rx/ry is large in

our case, we can ignore the first case (1.2D + 1.6L) and use the second case (1.2D + 0.5L

+ 1.0E) assuming Kx = Ky = 1.0, which is permitted by the seismic code, to determine the

ultimate axial load and bending moment on each column. The results of this factoring

are shown in Appendix C.

Using the following interaction equations sizes were determined from the factored loads:

Mu = B1Mnt + B2Mlt

Mnt= come from factored gravity loads

Mlt = come from factored lateral loads

Once again the columns were spliced at every 2nd level, so that the column used were

those designed at the 1st, 3rd, 5th, 7th, and 9th floors.

3.2.4 Seismic Provisions

In addition to the strength design of the Perimeter Moment Resisting Frame columns,

special seismic provisions must be taken into account to ensure the safety of the structure.

We used only the interior perimeter columns for this check because they have two

moment resisting beams framing into them as opposed to only one. The columns must be


strong enough so that plastic hinges will form in the beam before in the column. This can

be accomplished by equation 8-3 of the UBC ’97:

,

This equation ensures that the plastic strength of the column is larger than that of the

beam.

The columns and beams designed are checked for the strong column-weak beam concept

and where needed redesigned so that they pass.

Another seismic design criterion that had to be checked for the Perimeter Moment

Resisting Frame is the check for “overstrength” during an earthquake, since column

buckling can be a major problem. This provides an extra protection against extra axial

forces in severe earthquakes, which are larger than those used previously in the design.

Since axial loads primarily concern exterior moment frame columns, this check will be

only for those columns. This check should be used when . We used the

following code equation to assure that the exterior perimeter columns were protected

against overstrength:

1.2PDL + 0.5PLL (0.4R)PE ≤ φcPn

In performing this calculation the factored loads were added to 0.4*R*PE = 0.4*8.5* PE =

3.4* PE . This is a large increase in axial load to protect against a rare event. The axial

capacity at each floor is checked so that the above equation is satisfied and the column is

protected from buckling. Any column that fails is resized so that it satisfies this

requirement. These results are summarized in Table 3-3.

Table 3-3: Final SMRF Design

EAST - WEST FRAME NORTH - SOUTH FRAME

Columns Girders Columns GirdersFloor Interior Exterior Floor Interior Exterior Roof W18X35 Roof W14X26


10 W21X44 10 W16X40 W24X131 W24X55 W24X131 W24X55 9 W21X44 9 W21X44 8 W21X50 8 W21X44 W24x146 W24X68 W24X131 W24X55 7 W21X50 7 W21X50 6 W18X55 6 W21X50 W24X162 W24X84 W24X146 W24X68 5 W21X55 5 W21X55 4 W18X55 4 W21X55 W24X162 W24X104 W24X162 W24X84 3 W21X55 3 W21X55 2 W21X55 2 W24X55 W24X162 W24X117 W24X162 W24X104 1 1

3.3 Shear Wall Design

Two shear wall staircase cores resist lateral loads in the building. They are 15ft x10.5ft

(centerline dimensions), and have wall thickness of 18 inches (See Figure 3-1). The

strengths of concrete and rebars are 3000psi and 60ksi, respectively. Rebar sizes and

spacings were determined using simplified formulas, assuming a solid core with no

openings. Door openings 3.5’ wide 8’ tall were modeled on each floor in the ETABS

verification model to see the effects of this simplification. Design was performed in

accordance to applicable ACI 318 provisions. Rebar layouts are shown in Figure 3-5 and

described in Table 3-4.


Figure 3-1: Plan View of Shear Wall Staircase Cores

Table. 3-4: Shear Wall Reinforcement

Shear Wall Reinforcement (on each face of wall)15 ft EW core walls (18” thick) #4@8” horizontal reinf #10@12” vertical reinf (story 1-4)

#8@18” vertical reinf (story 5-10)8 ft NS core walls (18” thick) #4@8” horizontal reinf

#10@12” vertical reinf (story 1-4)#8@18” vertical reinf (story 5-10)

Choice of Location:

The walls around the staircase were chosen as the lateral load resisting system because

the stair cores were continuous through the structure. Another reason for this choice was

the desire of the architect and the owner to maintain open spaces and unobstructed views.

The locations of stairs were determined by the architect for circulation purposes. The

atrium above the 5th floor and the location of the elevator made shear walls behind the

elevators infeasible due to the inability to transfer shears near the open space. Additional


walls were also not desirable because of constraints for building modularity (owner), ease

of constructability (contractor) and aesthetics (architect).

Preliminary Thickness:

Since the cores were slender (10.5’ width to 126’ total height), deflection was believed to

control wall thickness. Drift is limited according to UBC section 1630.9:

Assuming an average interstory drift over the height of the building (126ft or 1512 in),

the total drift limit is 5.08 in.

From the calculated statically equivalent story shear values and assuming (1) 18” thick

core walls with no openings, (2) ½ the load goes to each core and (3) only flexural

deflection of the shear walls, the drift was found to be 4.5in in the NS direction and

3.03in in the EW direction (Ref Appendix D). For these calculations, the moment of

inertia was modified to 0.7I in accordance with ACI Code 10.11.1 for calculating

deflections of an uncracked wall. Table 3-5 gives a summary of the estimated overall

drift of the shear walls.

Table 3-5: Shear Walls DriftLimiting drift NS drift EW drift5.08 in 4.5 in 3.03 in

Proportioning loads to each core:

Rigidities for each core were determined assuming only flexural deflection. Torsional

rigidities were determined assuming a solid core without openings and a poisson ratio of

0.2. Accidental torsion of 5% was included. From these calculations, it was found that

accidental torsion contributed to moments at each core. The additional shear forces

caused by torsional moments at the core were determined assuming constant shear flow.

A summary of shear forces is given in Table 3-6.


Table 3-6: Shear Forces to Individual Core

NS EWShear from direct shear 0.5V 0.5VShear from torsion 0.117V 0.167VShear on each core 0.617V 0.667V

Shear Reinforcement:

Shear strength for the shear wall cores was determined using only concrete shear

strengths and steel shear strengths in the walls in the direction of the load considered

(Ref. Figure 3-2). A factor of 0.75 was used assuming only flexural failure of the wall.

Shear strength of concrete was determined using:

where

for

Figure 3-2. Shear Resisting Portions Considered

For most cases, it was found that minimum horizontal reinforcement was required. This

minimum according to ACI-318 provisions is ρmin =0.0025. Horizontal reinforcement for

all walls was chosen to be #4@8”.

Bending Reinforcement:


Bending capacity of the shear wall core was determined with many simplifying

assumptions. Distributed rebar forces and compressive rebar forces were neglected. The

distance from tension steel to centroid of concrete stress block was assumed to be 0.9

times the length of wall. Pn was assumed to act 0.4 times the length of wall from the

neutral axis. The factor 0.9 was chosen instead of a smaller value since most of the

moment resisting rebars will be located in the flanges (Ref. Figure 3-3) of the core.

Figure 3-3. Moment Resisting Flanges of the Core

From these assumptions the relationship between axial load, area of steel reinforcement

in one flange and the bending capacity of the core is :

where

and

Axial loads were determined from tributary areas as shown below:


Figure 3-4. Tributary Area of Shear Wall Core

Required area of reinforcing steel was determined from overturning moment and axial

load data using the above equations. For both NS and EW walls, #10@12” on each face

were chosen for reinforcement at the flanges.

For ductility reasons it is desired that the bending strength be reached before shear,

therefore a check of Mn/Vn vs Mu/Vu was performed. It was found that at higher stories

(story 6 and higher), the wall fails in shear. For ease of construction, the change of rebar

layout was done at story 5 where the buildings layout also changes. For both NS and EW

walls, #8@18” on each face were chosen for reinforcement at the flanges.


Figure 3-5. Shear Wall Design

3.4 Connections

Various connections were used in our design and are described in this section. Detail

drawings are shown at the end.

Moment Resisting Frame:

Several connection types suitable for moment resisting frames in seismic regions were

considered. The structural engineer evaluated welded unreinforced flange-welded web

connection (WUF-W), welded flange plate (WFP) connection, and reduced beam section

(RBS) connection. Design procedure and criteria were followed as outlined in FEMA-

350 document.

The basic design approach of moment resisting connections is to estimate the location of

plastic hinges and determine probable plastic moments and shear forces at the plastic

hinges, at critical sections of the assembly. To be able to form plastic hinges in

predetermined locations, i.e. within beams, connections are strengthened and stiffened or

beam sections are locally reduced as in the case of reduced beam section connection

which were chosen for this project by the structural engineer.


Column Splices

Close attention was paid to the splices of exterior columns which are part of the moment

resisting frame. These members, in addition to gravity loads, are subjected to relatively

high axial forces that are produced by overturning moments caused by seismic activity.

The structural engineer decided to use a combination of bolted and welded web splices

with complete joint penetration flange welds, which can support axial as well as bending

forces due to earthquake loads.

Shear Connections

Simple bolted shear connections were designed for interior column-to-beam connections,

beams framing into the shear walls, and the two beams framing into cantilever beam

which support the walkway on the 6th through 10th floor.

(Ref: Appendix E for calculation details)








3.5 Foundation

The foundation of the building serves to transmit gravity and lateral loads as well as

overturning moments to the earth. To accomplish this we have selected a combination

foundation system. Under each gravity column, footings will serve to transfer the gravity

loads to the soil. From preliminary calculations for the base plates of these columns, it

was determined that the footings should be 42 inch square. The second part of the

foundation carries both gravity loads and overturning moments from the moment

resisting frames. This was accomplished using strip footings. The strip footings run the

length of the building along the perimeter and allow a path for the high moments

generated in the moment resisting frame. From similar calculations it was determined

that the footings should be at least 36 inches wide. Finally, the shear walls will be

supported by a mat foundation. The preliminary size of mat required to prevent

overturning of the shear wall base was determined from the overturning moment and the

dead load on the core. Resistance to overturning was assumed to come solely from dead

loads. The required eccentricity and therefore the required half width of the mat was

calculated by dividing the overturning moment by the total unfactored dead load

(including self weight) of the shear wall. A 48’ x 48’ mat was determined. Investigations

on the use of anchors are required to decrease the size.

Table 3-5 to Table 3-7: Calculation of Minimum Mat Foundation Size

Table 3-5

Wall Self weight thickness 1.5 ft height 126 ft perim 51 ft Volume 9639 ft^3 density 150 pcf Weight 1445.85 k


Table 3-6

Determine Pu on Wall Dead load Area (85psf) Area(50psf) (kips)10 FLRoof 787.5 39.375

9 FL10 612.5 52.06258 FL9 612.5 52.06257 FL8 612.5 52.06256 FL7 612.5 52.06255 FL6 612.5 52.06254 FL5 787.5 66.93753 FL4 787.5 66.93752 FL3 787.5 66.93751 FL2 787.5 66.9375

Total 567.4

Table 3-7

Total downward load at thebase of the shear wall 2013.288 k Overturning moment 96698 kftOR 48349 kft each Eccentricity required 24.01 ft Mat under Shear wall should be 48' x48' OR smaller with anchors


4.0 ETABS Modeling - Analysis and Discussion

4.1 Model DiscussionETABS was used to analyze the building. From the ETABS analysis we were able to

compare some of the actual load effects with the assumptions made in the design process.

We designed the moment resisting frame to be able to resist 25% of the total seismic

loads. However, from the results shown in Table 4-1, it is obvious that this is a very

conservative assumption. The loads produced by ETABS are consistently lower than

those predicted by the Portal Method. In some cases the predicted values by the Portal

Method are twice of those calculated by ETABS. This discrepancy is accounted for in the

interaction between the moment resisting frame and the shear wall. The stiff shear wall

takes most of the load, so the moment resisting frame takes very little comparatively.

This can be proved by the shear wall frame interaction computations it was found that

only about 5-10% of the total load actually goes to the moment resisting frame.

Table 4-1: EW SMRF

Floor

Beam Moment (interior)

Column Moment (interior)

Column Axial (exterior)

Portal ETABS Portal ETABS Portal ETABSRoof 171.21 29.28

87.28 99.14 74.81 14.410 292.57 126.3 138.04 94.06 154.42 66.89 330.47 126 173.83 106.25 236.41 120.048 364.16 131.2 205.41 102.67 320.48 173.787 393.63 129.8 232.79 101.91 406.37 227.76 418.90 124.1 255.95 105.59 493.79 281.575 439.05 116.2 273.07 74.05 586.24 339.884 419.89 91.4 272.96 74.44 661.14 384.763 431.31 90.7 282.47 69.49 741.12 429.462 472.80 79.6 355.93 53.25 821.51 473.41


Table 4-2: NS SMRF

Floor

Beam Moment (interior)

Column Moment (interior)

Column Axial (exterior)

Portal ETABS Portal ETABS Portal ETABSRoof 142.70 56.118

74.66 60.64 44.54 8.1410 255.87 155.73 119.92 89.93 88.85 31.679 297.56 180.79 155.71 95.37 135.42 57.28 334.62 180.18 187.30 102.45 183.92 82.717 367.04 187.47 214.67 110.42 234.04 108.976 394.84 183.65 237.83 115.77 285.44 135.075 416.99 204.04 254.96 120.34 340.69 165.124 439.46 175.5 270.46 113.36 394.06 190.73 452.02 160.87 279.98 105.52 453.32 215.032 497.66 143.22 353.44 87.88 513.05 237.621

4.2. Shear Wall-Frame InteractionWe evaluated the frame shear wall interaction using the Component Stiffness Method.

This is used to find out the percentage of lateral load going to the shear wall and the

frame. The assumptions made in the Component Stiffness Method are:

1. Torsion is ignored.

2. No openings in the core

3. Uniform story height has been assumed. In reality we have the 1st and 2nd story at

15 ft each, and all other stories at 12 ft so. An average uniform story height was

assumed to be 12.6 ft

4. Shear deformations are neglected.

5. Calculations showed that seismic deflections governed over wind, thus wind was

ignored in the final calculation of forces, deflection, and moment.


6. Axial deformations very small, hence ignored.

(Ref: Appendix F for calculations)

Table 4-3. Shear Wall-Frame Interaction Summary

NS EW

P to each frame 30.10 k 26.27 k

P to each wall 30.10 k 26.27 k

Deflection 2.61 in 1.76 in

Overturning Moment 44683 k-ft 45147 k-ft

Vext.col 5.35 k 4.38 k

Vint.col 9.81 k 8.76 k

ΣMext.col 87.63 k 71.71 k

ΣMint.col 160.69 k 143.42 k

4.3 ETABS Model and Frame- Shear Wall Interaction Comparison

From the story drift data collected from ETABS, we were able to calculate the

deflections. These were compared to the shear wall frame interaction, as can be seen in

the following table.

Table 4-4 to Table 4-6: Interaction Equations Vs. Computer analysis

Table 4-4

NS Total Deflection (in) EW Total Deflection (in)Shear wall Frame interaction 2.61 1.76ETABS 3.15 1.785

From these comparisons, it is seen that the assumptions made in using the shear wall

frame interaction formulas are verified through the computer analysis using ETABS.

Deflections differences in the east west direction were smaller than in the north south

direction. This can be explained by the fact that door openings were modeled in ETABS

whereas they were ignored in interaction calculations.


Percentage of the overturning moment resisted by the shear wall core was also compared,

as can be seen in the table below. Again, the effects of the door openings account for the

differences between hand calculations and the ETABS model. Since openings were

modeled the walls become less stiff and a lower percentage of the building overturning

moment is resisted by the cores.

Table 4-5

North South Half the Building Over turning moment

Overturning moment one core

Percentage of load going to the core

ETABS 48349kft 40208.38kft 0.83Shear wall Frame interaction

47960.61kft 44683 kft 0.93

Table 4-6

East West Half the Building Over turning moment

Overturning moment one core

Percentage of load going to the core

ETABS 48349kft 39895.68kft 0.825Shear wall Frame interaction

47960.61kft 45147 kft 0.94

Half the building overturning moment for the shear wall frame interaction was obtained

using the story shears calculated from assumed seismic dead loads and the UBC ’97

code. The same values were generated from ETAB’s built-in UBC’97 code calculations

for the same assume period of the structure but with seismic dead loads obtained from the

self weight of the structure. These values are tabulated in the Appendix F.

Interstory drifts limits were also checked against the seismic interstory drift limitation

given by 0.00336. As designed, nowhere are the seismic drifts limits exceeded.


Floor EW earthquake interstory drift NS earthquake interstory driftRoof 0.000638 0.00066310 0.001362 0.0024669 0.001368 0.0024948 0.001366 0.0024797 0.00135 0.0024486 0.001314 0.0023835 0.001251 0.0020974 0.001155 0.0018583 0.001023 0.0015432 0.000852 0.0010961 0.000602 0.00448

5.0 Conclusions

For preliminary design of a regular 10 story building, simplifying calculations were

found to provide sufficient accuracy for the initial choice of member sizes. By knowing

the behavior of a structure, few detailed calculations had to be performed. The

assumption that 100 percent of the lateral loading goes to the cores while 25 percent goes

to the SMRF was also found to be a good conservative approximation.

Assumptions that the cores had no door openings significantly reduced the complexity of

calculations but also reduced the accuracy of the results. In addition, rebar quantities

were only calculated for a core without openings. Rebar layouts in the wall piers as well

as in spandrel beams of the core require more complex calculations which can be

automated using ETABS.


PART TWO: APPENDIX - DESIGN CALCULATIONS

Appendix A – Load Determination

Appendix B – Gravity System Design

Appendix C – SMRF Design

Appendix D – Shear Wall Design

Appendix E – Connection Details and Calculations

Appendix F – Analysis Results (ETABS and Interaction)


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