Simplified Analysis Model for Modern Skyscrapers With

Mega-Diagonal Lateral Force Resisting System

Russell Irion

A project submitted to the faculty of Brigham Young University

in partial fulfillment of the requirements for the degree of

Master of Science

Richard Balling, Chair Fernando Fonseca

Alan Parkinson

Department of Civil & Environmental Engineering

Brigham Young University

April 2015

Copyright © 2015 Russell Irion

All Rights Reserved

ABSTRACT

Simplified Analysis Model for Modern Skyscrapers With a Diagrid Lateral Force Resisting System

Russell Irion Department of Civil & Environmental Engineering, BYU

Master of Science

Modern skyscrapers are reaching higher and are more innovative than ever before. The

standard form of skyscrapers from the early 20th century has structural elements that include a

concrete core, columns, belt trusses and outriggers. Dr. Richard Balling and Jacob Lee produced

a simplified skyscraper analysis model (SSAM) with the aforementioned structural elements.

The 1960s brought about a change to the status quo of skyscrapers, introducing diagonal braces,

which contribute to both the lateral and vertical stiffness of the overall structural system. With

the addition of external diagonal braces came more open floor space and an optimal design that

performs well even at high elevations.

The John Hancock Center in Chicago Illinois was the first of many to adopt the external

diagonal brace structure. Fazlur Khan was the designer who produced this innovative design. It

was determined to be the best configuration for new skyscrapers at the time. Advances in

technology allow us to now model the entire skyscraper, which would have been too

computationally expensive for Khan back in the 1960s. A full model of the building was created

in SAP 2000 to measure the total displacement due to wind and earthquake loads.

The purpose of this project is to discuss how the SSAM was modified to include diagonal

braces. The diagonal elements impacted the size of the columns and the overall stiffness of the

structure. The lateral displacement of structure was calculated in the spreadsheet and compared

with the model created in SAP 2000.

The displacement due to wind loads between the two structures on average was .03m.

The greatest difference was located at the top story of the building and the difference between

the two was .098m. Earthquake loads were calculated and the average difference in displacement

from the two analyses was .34m and the worst case was 1.0m. In each case the SSAM predicts a

building that is less stiff than what the finite element model calculated.

Keywords: SSAM, Diagonal, John Hancock Center, SAP 2000

 

ACKNOWLEDGEMENTS

Many hours of hard work have been put in to producing a Masters Project that I can be

proud of. Oftentimes I met walls that seemed insurmountable. Many hours were spent wrestling

SAP 2000 or dissecting the stiffness matrix. Dr. Balling provided advice and assured me that I

would be able to figure it out. I’m very grateful for his council and guidance through this project.

Additionally I’m grateful for Changheon Yi and the listening ear he gave when I needed to talk

through a problem.

Most important however is the confidence and support I received from my loving family.

Ellen has been a constant support for me through it all. On a number of occasions I would wake

her up by sleep talking, teaching some engineering principle to her. While lifting the pillow, I

gestured to each corner and proceeded to explain to her “each corner has a value.” After getting

frustrated that she didn’t understand me I shook my head and went back to bed. Needless to say,

she is very sweet for putting up with the long hours I have put in at school and was always very

positive through it all. Lastly my parents and siblings have always been supportive and I’m lucky

that we get to be together forever.

v

TABLE OF CONTENTS

LIST OF FIGURES ................................................................................................................... viii  

1   Introduction ............................................................................................................................. 1  

2   The John Hancock Center, Chicago IL. USA ...................................................................... 4  

2.1   Building Characteristics ..................................................................................................... 5  

3   Finite Element Model ............................................................................................................. 7  

3.1   Structural Members ............................................................................................................ 7  

3.2   Loads .................................................................................................................................. 8  

3.3   Execution ........................................................................................................................... 9  

4   Simplified Skyscraper Analysis Model (SSAM) ................................................................ 10  

4.1   Simplifications ................................................................................................................. 10  

4.2   Vertical Stiffness Contribution of Diagonals ................................................................... 11  

4.3   Horizontal Stiffness Contribution of Diagonals .............................................................. 12  

4.4   Strain and Stress in Diagonal Members ........................................................................... 14  

4.5   Analysis Results ............................................................................................................... 14  

5   Conclusions ............................................................................................................................ 20  

REFERENCES ............................................................................................................................ 21  

vi

LIST OF TABLES

Table 1 Diagonal Member Stiffness Matrix ..........................................................................13  

Table 2 Displacement Results. ...............................................................................................15  

vii

viii

LIST OF FIGURES

Figure 1 Braced Tube and Diagrid Structure Diagrams. .......................................................2  

Figure 2 Diagonal Tower, Seoul, South Korea. (Dezeen 2012) ............................................3  

Figure 4 High Rise Design vs Height. ...................................................................................5  

Figure 6 Displaced vs Undisplaced Shape. ............................................................................9  

Figure 7 Vertical Displacement. ............................................................................................12  

Figure 8 Horizontal Displacement. ........................................................................................12  

Figure 9 Wind Displacement Results. ...................................................................................15  

Figure 10 Earthquake Displacement Results. ........................................................................16  

Figure 11 Force on Building. .................................................................................................17  

Figure 12 Colored Frame Undisplaced and Displaced. .........................................................19  

1

1 INTRODUCTION

This work is an extension of the work of Dr. Richard J. Balling and Jacob S. Lee and

their simplified skyscraper analysis model (SSAM) to include mega diagonals and tapered

buildings. The extended model is applied to the John Hancock Center in Chicago, IL USA. The

John Hancock Center was one of the first to implement an external mega-diagonal structural

system. A computer model was created in order to compare results and draw conclusions about

the accuracy of the SSAM.

Using a SSAM in lieu of a space frame or detailed finite element model (DFEM) results

in faster execution, an iterative optimization technique, simpler data preparation and

straightforward data extraction (Lee and Balling 2014). It also presents an effective way to teach

engineering students some of the analysis and calculations that are required when designing a

skyscraper. Using the SSAM, conventional skyscrapers were analyzed, with configurations

involving concrete cores, columns, outriggers and belt-trusses. The purpose of this document is

to develop a skyscraper spreadsheet model that includes diagonal cross braces and a tapered

profile. The spreadsheet will be compared to a full-scale computer model in order to determine if

the calculations closely mimic real life. The paper will culminate with the production of a

spreadsheet that models the John Hancock Building to display how the SSAM is now upgraded

to better model modern skyscrapers.

2

Mega-diagonal structural members have become a viable option as a part of the lateral

force resisting system of a structure. The sloping orientation of the member results in

components parallel to both the lateral forces as well as the gravity loads of a structure.

Figure 1 Braced Tube and Diagrid Structure Diagrams.

As displayed in Figure 1, structural systems that include mega-diagonal braces may

require column elements, but they are not required if engineered appropriately. Systems

composed solely of diagonal members are called diagrid buildings (Panchal and Patel 2014). The

structure analyzed herein has a combination of core, column and mega-diagonal elements. Some

examples of this type of structure include the Diagonal Zero Zero in Barcelona, Spain, The

Diagonal Tower in Seoul, South Korea, and the John Hancock building in Chicago, IL. These

buildings “can be seen as one enormous vertical truss or integrated structural frame” (Priwer and

Phillips 2014).

3

Figure 2 Diagonal Tower, Seoul, South Korea. (Dezeen 2012)

Architects and designers hope to create structures that are unique and expressive.

Oftentimes those types of structures are not perfectly symmetric or follow perfect patterns. One

unique form of a skyscraper is a gradual taper in order to produce an elongating effect. By doing

so, numerous other benefits result which will be discussed in the next section.

4

2 THE JOHN HANCOCK CENTER, CHICAGO IL. USA

The John Hancock building in Chicago

Illinois was the first skyscraper to employ the use

of external diagonal structural cross braces. Doing

so presented some geometric advantages. The

revolutionary designer who determined this

structure was the most efficient form was Fazlur

Khan of Skidmore Owings and Merrill. This

building was the start of new heights and

possibilities for modern skyscrapers. The

conceptual design and planning stages for this

building started in 1965 and the building was

finally completed in 1970. Around this same time,

the world saw a shift away from the less efficient

vierendeel structural composition towards a

cantilevered column type system (Takabatke 2012). These vierendeel structures were comprised

mainly of beams and columns with rigid connections. By changing to hinge connected braces,

the diagonal elements only experience axial forces and become a more efficient shape.

Figure 3 Image of Hancock Center.

5

Figure 4 High Rise Design vs Height.

Figure 4 was produced by Fazlur Khan in the mid 1900s (Iyengar 2000). It displays the

shift toward truss-tubed structures that resulted in taller buildings.

2.1 Building Characteristics

The John Hancock Building is a mixed use structure, utilizing floor space for residential

and commercial use. The structural system used is the truss-tube without interior columns system

as depicted in Figure 4. The bottom floor is rectangular, 262’ wide and roughly 164’ long. The

top floors are also rectangular, 160’ wide and 100’ long (Iyengar 2000). The Hancock center has

a slight taper all the way to the top, thus causing onlookers to believe the structure is even taller

than it actually is (Hearn 2015). The total height of the structure is 1128 ft. Not only does the

6

tapered form produce an elongation effect, it also decreases the surface area on which wind can

act and decreases the seismic weight of the structure at the critical top levels (Khushbu Jania

2013) (Montuori, Mele et al. 2013). It was designed such that under 60 mph wind loading, the

structure would sway only five to eight inches (Hearn 2015).

Figure 5 John Hancock Center (Iyengar, 2000)

7

3 FINITE ELEMENT MODEL

3.1 Structural Members

Typical megadiagonals would be a concrete filled steel tube or some other steel brace.

The megadiagonal members used to model the John Hancock Center were all assumed to be

concrete members. This assumption is made to more closely match the SSAM model that will be

discussed later. Material properties of each of the columns and concrete core were also assigned

to match what is found in the SSAM. The cross sections of diagonal and column members were

assumed to be circular. The moment of Inertia was calculated for the different members at each

interval. The moment of inertia for the concrete core is found in the SSAM. The torsional

stiffness was arbitrarily set to 1000. This assumption did not affect the results and was verified. It

is also worth noting that the diagonal members were assumed to span the entire interval instead

of connecting at each intermediate column.

SAP 2000 allows users to create “area elements.” For the façade and floor members, area

elements were used and properties such as unit weight, thickness, stiffness and other

characteristics were applied appropriately. The use of area elements may more accurately

represent real life behavior. It proved difficult to produce similar results when modeling the

concrete core. Thus a column element was used that shared the same characteristics (moment of

8

inertia, area. . . etc.) as found for the concrete core in the SSAM. In order to be able to see other

elements, the diaphragms have been removed from the display in Figure 6.

3.2 Loads

The loading on the structure was taken directly from the SSAM. Instead of potentially

introducing more error into our model by using the SAP 2000 built in wind analysis, horizontal

point loads and moments about the assumed axis of rotation were placed at the top of the core in

the center of the building. This project is not created to determine the accuracy of the forces

calculated in the spreadsheet, instead the response of the system is the main objective. Thus

forces were copied straight from the spreadsheet into the DFEM.

9

3.3 Execution

The SAP 2000 model required over 28 minutes to run analysis on average. The underlying

mathematical model had 6 degrees of freedom at each column and core for every level. The

diagonal members only had degrees of freedom at critical intervals. That results in over roughly

10,2000 degrees of freedom for the system. The SAP 2000 model said the model had over

92,616 equilibrium equations to satisfy. The file containing all the information was over 120

MB. In order to make any changes the whole structure needed to be re analyzed.

Figure 6 Displaced vs Undisplaced Shape.

10

4 SIMPLIFIED SKYSCRAPER ANALYSIS MODEL (SSAM)

As was mentioned earlier, the SSAM is an analysis tool that results in faster execution, an

iterative optimization technique, simpler data preparation and straightforward data extraction.

The spreadsheet makes it simple to change member properties & see immediate results when

determining how much material to allocate between columns, core, and other structural

members. Without it, a modeling expert would require a lot of time and effort to provide a

collection of optimized designs to the client. Implementing this spreadsheet, in conjunction with

the optimization capabilities in excel or other outside sources could enable the designer to

converge onto a pareto front of optimized designs. These benefits are what have led to further

development of this tool. The following sections will describe the improvements that have been

made to the SSAM.

4.1 Simplifications

The configuration that has been selected is a single X brace for each side of the building

spanning the entire interval. Using this configuration results in a symmetric structure. Wind and

earthquake forces produce a lateral force, which can then be further simplified and analyzed as a

symmetric structure with anti-symmetric loading. Initially it was hoped that a very general,

modular method could be created which allows for multiple X’s on each interval or other

configurations. Complications came in developing the stiffness matrix, due to the dependence

11

that adjacent intervals and their degrees of freedom have on each other. It is possible that a

macro could be created that would automatically fill in the stiffness matrix given some input

parameters, but this has not been explored yet.

4.2 Vertical Stiffness Contribution of Diagonals

Unlike most of the other components of this structure, the diagonal members will

contribute to both the vertical and horizontal stiffness of the structure (Moon, Connor et al.

2007). The size of the concrete core, columns and diagonals depend on each other. With each of

these components, strain in the core must equal the strain of the outer column and diagonals,

otherwise a large displacement discrepancy will propagate through each level and result in

cracks. The thickness of the concrete and the area of the diagonal members were determined as

the two independent variables and would be used to calculate the required area of columns.

Equating equations of strain and solving for the dependent variable resulted in:

𝑨𝒊𝒄𝒐𝒍𝒋 =  𝑨𝒊𝒄𝒐𝒓𝒆 ∗

𝑭𝒊𝒄𝒐𝒍𝒋

𝑭𝒊𝒄𝒐𝒓𝒆 −

𝑽𝒊𝒅𝒊𝒂𝒈

𝒉𝒊𝐬𝐢𝐧𝜽𝒊

𝒅𝒊𝒂𝒈 𝟒 𝑭𝒊𝒄𝒐𝒍𝒋

𝑭𝒊𝒄𝒐𝒍𝒋 𝟏 + 𝜸𝒉𝒊𝑨𝒊

𝒄𝒐𝒓𝒆

𝑭𝒊𝒄𝒐𝒓𝒆 4-1

where A = area F = Axial force in member 𝑉!!"#$ = Total volume of diagonals on interval

ℎ! = Height of interval 𝛾 = Unit weight of concrete core

For the new model, the diagonal members were assumed to be concrete tube members instead of

steel members. This assumption was made to simplify the model. Oftentimes these diagonal

members are concrete filled steel tubes. It wasn’t deemed necessary to go into such depth to

determine the stiffness of a composite structure. If a designer would like to determine an

12

appropriate amount of steel, the ratio of stiffness provided by a steel tube of the desired radius

and thickness could be subtracted from the calculated area of concrete. The spreadsheet could be

manipulated to assume the diagonals are pure steel if that is what the designer desires.

4.3 Horizontal Stiffness Contribution of Diagonals

Using principles of virtual work and mechanics of materials in conjunction with anti-

symmetry, the following equations were derived:

Figure 7 Vertical Displacement.

Figure 8 Horizontal Displacement.

13

𝑲𝑳𝑽 =  𝑬𝑨𝑳

𝟏 − 𝒔𝒊𝒏𝟐 𝜽 4-2

𝑲𝑳𝑳 =  𝑬𝑨𝑳(𝟏 − 𝒔𝒊𝒏𝟐 𝜽) 4-3

𝑲𝑽𝑽 =  𝑬𝑨𝑳𝒔𝒊𝒏𝟐 𝜽 4-4

E is the youngs modulus of the diagonal members, A is the area and L is the total length of the

diagonal member. Implementing the formulas from above results in the following stiffness

matrix:

Table 1 Diagonal Member Stiffness Matrix

DOF’s 𝑯𝒐𝒓𝒊 𝑽𝒆𝒓𝑨𝒊 𝑯𝒐𝒓𝒊!𝟏 𝑽𝒆𝒓𝑨𝒊!𝟏

𝐻𝑜𝑟! 𝐾𝑳𝑳 −𝐾𝑳𝑽 −𝐾𝑳𝑳 −𝐾𝑳𝑽

𝑉𝑒𝑟𝐴! −𝐾𝑳𝑽 𝐾𝑽𝑽 𝐾𝑳𝑽 𝐾𝑽𝑽

𝐻𝑜𝑟!!! −𝐾𝑳𝑳 𝐾𝑳𝑽 𝐾𝑳𝑳 𝐾𝑳𝑽

𝑉𝑒𝑟𝐴!!! −𝐾𝑳𝑽 𝐾𝑽𝑽 𝐾𝑳𝑽 𝐾𝑽𝑽

14

4.4 Strain and Stress in Diagonal Members

By inverting the stiffness matrix and multiplying by the calculated lateral loads, the

product is the total displacement of the structure. Diagonal members are going to be strained

when the building is displaced both horizontally and vertically. The difference between

horizontal displacements on neighboring intervals equals the horizontal component of the strain

in the diagonal member. By anti-symmetry, the sum of the vertical displacements on neighboring

intervals is the vertical component of the strain in the diagonal member.

𝒕𝒐𝒕𝒂𝒍  𝒔𝒕𝒓𝒂𝒊𝒏 =  𝜺 = 𝜺𝒉𝒐𝒓𝒊𝒛 + 𝜺𝒗𝒆𝒓𝒕 ∗ 𝒔𝒊𝒏𝟐𝜽 4-5

Stress in the diagonal members can be calculated from the equation:

𝝈 = 𝑬 ∗ 𝝐 4-6

where 𝜎 = stress and E = Young’s modulus. Comparing that calculated stress to the allowable

stress is the resulting design constraint.

4.5 Analysis Results

Executing both the SSAM and DFEM for the John Hancock center produced similar

results. The overall drift due to wind on average for the structure was within .1m between the

two programs. Unfortunately, stresses calculated by the SAP 2000 did not correspond to what the

SSAM calculated. Overall displacement was however observed and recorded with closer

correlation.

15

Table 2 Displacement Results.

Figure 9 Wind Displacement Results.

0  

50  

100  

150  

200  

250  

300  

350  

400  

450  

0   0.05   0.1   0.15   0.2   0.25   0.3   0.35  

Height(m

)  

X  Displacement  (m)  

Wind  Displacement  

DFEM  

SSAM  

WIND DISPLACEMENT EARTHQUAKE DISPLACEMENT

ELEVATION (M) SSAM DFEM Δ SSAM DFEM Δ

80 .0199 .033 .131 .113 .123 .01

160 .0699 .075 .005 .411 .301 .11

240 .140 .122 .018 .843 .512 .33

320 .221 .168 .052 1.35 .721 .63

400 .305 .207 .098 1.90 .893 1.001

16

Figure 10 Earthquake Displacement Results.

A comparison between the deflections found in each model can be found in both Figure 9

and Figure 10. The results agree with the statements made earlier regarding the allowable drift

for which the building was designed. It is said that under 60 mph winds the building would

deflect only roughly 5-8” (Hearn 2015). The wind load considered by our models was of higher

magnitude, thus the higher deflections.

Earthquake displacements deviate from one another. In the top level of the building, the

displacement calculated in the SSAM is double the displacement calculated in the DFEM. It is

possible that the DFEM model was set up incorrectly, and would produce better results if a more

experienced designer had entered data and constructed the model. Measures were taken to ensure

the two models had the same material and cross sectional properties. The connection between

elements however was not always clear in the SAP 2000 model and could have introduced some

error.

0  

50  

100  

150  

200  

250  

300  

350  

400  

450  

0   0.5   1   1.5   2  

Height(m

)  

X  Displacement  (m)  

Earthquake  Displacement  

DFEM  

SSAM  

17

Figure 11 Force on Building.

One unique observation for this structure is the force exerted by the wind. Because of its

tapered shape, the lateral force decreases with height after about 175 m (see Figure 11). The

equations used for lateral wind pressure can be found in ASCE 7-05

𝑷𝒌𝒘𝒊𝒏𝒅 =  . 𝟎𝟎𝟐𝟓𝟔 𝟐. 𝟎𝟏

𝑯𝒌𝑯𝒈

𝟐𝒂

𝒗𝟐   4�-­‐7

P = wind pressure at story k

v = design wind speed in mph

Hk = height of story k above the ground

Hg = reference height parameter reflecting exposure (274 m)

a = another exposure parameter (9.5m)

The final execution required over 28 minutes to analyze. In comparison, the SSAM

spreadsheet produces results that are essentially instantaneous. The spreadsheet does not need to

go through the thousands of degrees of freedom found in the structure. Instead it utilizes some

0

50

100

150

200

250

300

350

400

0 100 200 300 400 500 600

Hei

ght (

m)

Lateral Force (KN)

Wind

Wind

18

simplifications and must only analyze a structure with thirty degrees of freedom. Doing so

results in much faster execution.

Easier data extraction is the final result. Instead of sifting through thousands of numbers,

the SSAM produces results that are easily deciphered. Graphs are automatically populated

showing overall force and displacement. Unity checks are provided which show exactly what

parts of the structure are overstressed or if the governing drift constraints come from wind or

earthquake loads. The DFEM proved to be more difficult to work with than originally

anticipated. Many hours of exposure to such programs are required in order to master the art of

structural modeling and analysis. The SSAM can be seen as a more user-friendly tool created to

help teach skyscraper analysis principles in a manageable way.

19

Figure 12 Colored Frame Undisplaced and Displaced.

20

5 CONCLUSIONS

It is much simpler to make changes and understand what is going on in the SSAM than in

the DFEM. Users inexperienced in SAP 2000 or any other commercial software will find it

difficult to portray the structure and loading the user intends. However, one must understand the

simplifications and assumptions made in the SSAM in order to use it correctly. The claim has

never been made that the SSAM can replace full structural analyses, but instead can be a tool in

determining sizes and forces in a structure. Further research will need to be done on the

calculation of stress in diagonal members.

Calculations from the SSAM estimate that the total lateral displacement on the top floor

of the structure will be roughly .3m. That is about .1m greater than the deflection results

provided by the DFEM. On average the two calculated wind displacements differed .03m.

Earthquake loads are estimated to displace the structure 1.8m at the top level. That displacement

is roughly 1 m greater in magnitude than the displacement provided by the DFEM. On average,

the difference between the two analyses with respect to earthquake displacement is .34m.

The Hancock Center in Chicago Illinois has proven to be an optimal shape for

skyscrapers. The tapered profile of the structure reduces the loads that an un-tapered structure

would react to. The external diagonal brace system was the first of its kind. The diagonals help

resist both vertical and lateral loads. The results of both the SSAM and the DFEM model closely

reflect the findings online regarding the overall drift one can anticipate being present. The

likeness in overall displacement between the two analyses, although not perfect, produced results

that help justify the use of the SSAM for preliminary skyscraper analysis.

21

REFERENCES

Dezeen (2012). Diagonal Tower by SOM. Hearn, C. (2015). johnhancockcenterchicago. Retrieved 03-20-15, 2015, from http://www.johnhancockcenterchicago.com/facts.html. Iyengar, H. (2000). "Reflections on the Hancock Concept." CTBUH(1). Khushbu Jania, P. V. P. (2013). "Analysis and Design of Diagrid Structural System for High Rise Steel Buildings." Procedia Engineering 51: 92-100. Lee, J. S. and R. J. Balling (2014). "Simplified Model for Analysis and Optimization of Skyscrapers with Outrigger and Belt Trusses." Journal of Structural Engineering. Montuori, G. M., et al. (2013). "Design criteria for diagrid tall buildings: Stiffness versus strength." Wiley Online Library(23): 1294-1314. Moon, K.-S., et al. (2007). "DIAGRID STRUCTURAL SYSTEMS FOR TALL BUILDINGS: CHARACTERISTICS AND METHODOLOGY FOR PRELIMINARY DESIGN." The Structural Design of Tall and Special Buildings 16(2). Panchal, N. B. and V. R. Patel (2014). "DIAGRID STRUCTURAL SYSTEM: STRATEGIES TO REDUCE LATERAL FORCES ON HIGH-RISE BUILDINGS." IJRET 03(04): 374-378. Priwer, S. and C. Phillips (2014). Skyscrapers and High Rises, Routledge. Takabatke, H. (2012). "A Simplified Analytical Method for High-Rise Buildings." INTECH.

APPENDIX

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Concreteallowable stress (KPa) 48000modulus (KPa) 43400000density (KN/m^3) 21.7cost ($/m^3) 157

Steelallowable stress (KPa) 207000modulus (KPa) 200000000density (KN/m^3) 77cost ($/m^3) 5390

Weight Datafloor dead load (KPa) 4.34floor live load (KPa) 2.4cladding weight (KPa) 1.3

Wind Dataspeed (m/s) 55air density (Kg/m^3) 1.226reference height (m) 274exponent 9.5drift allowable 0.002778

Seismic Dataspectral acceleration (g) 0.2ductility factor 3exponent 2drift allowable 0.02

80 m

80 m

80 m

80 m

80 m

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Design Variables config 8 Design Constraints Design Objectivestories core t outrig V belt V diag V wind drift 0.38171318 concrete cost 15637095.3

81 to 100 0.32719329 0 0 50 seismic drift 0.33888699 steel cost 061 to 80 0.83919412 0 0 80 core stress 0.65074505 total cost 15637095.341 to 60 1.36217332 0 0 120 column stress 0.4791928321 to 40 1.87311318 0 0 170 outrigger stress 01 to 20 2.35789651 0 0 200 belt stress 0

diagonal stress 371.71106Core Section Properties

stories d y sin n d y sin n area inertia81 to 100 25 0 1 2 25 12.5 0 2 32.7193289 3408.2634361 to 80 25 0 1 2 25 12.5 0 2 83.9194121 8741.6054341 to 60 25 0 1 2 25 12.5 0 2 136.217332 14189.305421 to 40 25 0 1 2 25 12.5 0 2 187.311318 19511.59561 to 20 25 0 1 2 25 12.5 0 2 235.789651 24561.422

Outrigger Superelement Belt Superelementstory mem length mem sine mem area stiffness mem length mem sine mem area stiffness100 14.8408221 0.5390537 0 0 10.1519703 0.78802437 0 080 14.8408221 0.5390537 0 0 10.1519703 0.78802437 0 060 14.8408221 0.5390537 0 0 10.1519703 0.78802437 0 040 14.8408221 0.5390537 0 0 10.1519703 0.78802437 0 020 14.8408221 0.5390537 0 0 10.1519703 0.78802437 0 0

Long Side Diagonal Superelement Short Side Diagonal Superelementstory mem length mem sine mem area stiffness story mem length mem sine mem area stiffness100 95.37 0.83883821 0.13106847 41969.3831 100 86.33 0.92667671 0.14479324 62507.589780 98.9 0.80889788 0.20222447 58065.0137 80 87.87 0.91043587 0.22760897 93183.108460 102.7 0.77896787 0.29211295 74904.7198 60 89.5548 0.89330778 0.33499042 129549.42440 106.724 0.74959709 0.39822345 90993.4763 40 91.37408 0.87552181 0.46512096 169342.73320 110.9528 0.72102732 0.45064207 91640.3294 20 93.3209 0.85725706 0.53578566 183115.047

Tributary Perimeter Tributary Areastories core column A column B/D column C/E core column A column B/D column C/E

81 to 100 0 10.0625 10.0625 10.0625 837.4 23.25 46.5 46.561 to 80 0 11.609375 11.609375 11.609375 1190.55 33.0625 66.125 66.12541 to 60 0 13.15625 13.15625 13.15625 1543.7 42.875 85.75 85.7521 to 40 0 14.703125 14.703125 14.703125 1896.85 52.6875 105.375 105.3751 to 20 0 16.25 16.25 16.25 2250 62.5 125 125

Interval Dimensions Dead, Live, and Cladding Loadstories # stories height core column A column B/D column C/E

81 to 100 20 80 112881.52 4180.6 7314.7 7314.761 to 80 20 80 160486.14 5664.2 10121.025 10121.02541 to 60 20 80 208090.76 7147.8 12927.35 12927.3521 to 40 20 80 255695.38 8631.4 15733.675 15733.6751 to 20 20 80 303300 10115 18540 18540

Axial Force Column Areastories core column A column B/D column C/E column A column B/D column C/E

81 to 100 112881.52 4180.6 7314.7 7314.7 1.17410209 1.88831534 1.8877318561 to 80 330168.415 11883.0412 20713.8404 20712.8275 2.82212245 4.957252 4.9563178741 to 60 683943.274 23930.0458 42246.9799 42244.3453 4.5240517 8.04346495 8.0423255921 to 40 1176111.94 40415.1995 71944.11 71939.4975 6.15532526 11.0308707 11.02965251 to 20 1804584.39 61215.8442 109633.702 109626.974 7.7258427 13.9113447 13.9101203

Core Superelement Column Superelementsstories EI 2EI/L 4EI/L 6EI/L^2 12EI/L^3 column A column B column C column D

81 to 100 3.7021E+10 925533933 1851067865 34707522.5 867688.062 636950.384 1024411.07 512047.264 1024411.0761 to 80 9.5129E+10 2378212899 4756425799 89182983.7 2229574.59 1531001.43 2689309.21 1344401.22 2689309.2141 to 60 1.5469E+11 3867373425 7734746850 145026503 3625662.59 2454298.05 4363579.73 2181480.82 4363579.7321 to 40 2.1309E+11 5327308471 1.0655E+10 199774068 4994351.69 3339263.95 5984247.36 2991793.25 5984247.361 to 20 2.687E+11 6717565889 1.3435E+10 251908721 6297718.02 4191269.67 7546904.53 3773120.12 7546904.53

LONG Diagonal Superelement - Stiffness Matrix Contribution (PARALLEL TO LOAD) SHORT Diagonal Superelement - Stiffness Matrix Contribution (PERP TO LOAD)stories KLL KLV KVV stories KLL KLV KVV

81 to 100 17675.91 27236.8691 41969.3831 81 to 100 10283.1714 25353.0326 62507.589761 to 80 30676.5633 42204.6806 58065.0137 61 to 80 19235.5692 42337.1011 93183.108441 to 60 48539.3118 60297.7906 74904.7198 41 to 60 32793.457 65179.5478 129549.42421 to 40 70946.6491 80347.2603 90993.4763 21 to 40 51576.0413 93456.0206 169342.7331 to 20 84631.6173 88066.2778 91640.3294 1 to 20 66058.478 109983.187 183115.047

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hor 100 rot 100 ver A 100 ver B 100 ver C 100 ver D 100 hor 80 rot 80 ver A 80 ver B 80hor 100 885363.972 -34707522 -27236.869 0 0 0 -885363.97 -34707522 -27236.869 0rot 100 -34707522 1851067865 0 0 0 0 34707522.5 925533933 0 0

ver A 100 -27236.869 0 741427.357 0 0 0 27236.8691 0 -594981 0ver B 100 0 0 0 1024411.07 0 0 0 0 0 -1024411.1ver C 100 0 0 0 0 512047.264 0 0 0 0 0ver D 100 0 0 0 0 0 1024411.07 0 0 0 0

hor 80 -885363.97 34707522.5 27236.8691 0 0 0 3145615.13 -54475461 -14967.812 0rot 80 -34707522 925533933 0 0 0 0 -54475461 6607493664 0 0

ver A 80 -27236.869 0 -594981 0 0 0 -14967.812 0 2423676.91 0ver B 80 0 0 0 -1024411.1 0 0 0 0 0 3713720.28ver C 80 0 0 0 0 -512047.26 0 0 0 0 0ver D 80 0 0 0 0 0 -1024411.1 0 0 0 0

hor 60 0 0 0 0 0 0 -2260251.2 89182983.7 42204.6806 0rot 60 0 0 0 0 0 0 -89182984 2378212899 0 0

ver A 60 0 0 0 0 0 0 -42204.681 0 -1472936.4 0ver B 60 0 0 0 0 0 0 0 0 0 -2689309.2ver C 60 0 0 0 0 0 0 0 0 0 0ver D 60 0 0 0 0 0 0 0 0 0 0

hor 40 0 0 0 0 0 0 0 0 0 0rot 40 0 0 0 0 0 0 0 0 0 0

ver A 40 0 0 0 0 0 0 0 0 0 0ver B 40 0 0 0 0 0 0 0 0 0 0ver C 40 0 0 0 0 0 0 0 0 0 0ver D 40 0 0 0 0 0 0 0 0 0 0

hor 20 0 0 0 0 0 0 0 0 0 0rot 20 0 0 0 0 0 0 0 0 0 0

ver A 20 0 0 0 0 0 0 0 0 0 0ver B 20 0 0 0 0 0 0 0 0 0 0ver C 20 0 0 0 0 0 0 0 0 0 0ver D 20 0 0 0 0 0 0 0 0 0 0

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ver C 80 ver D 80 hor 60 rot 60 ver A 60 ver B 60 ver C 60 ver D 60 hor 40 rot 40 ver A 40 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0

-512047.26 0 0 0 0 0 0 0 0 0 00 -1024411.1 0 0 0 0 0 0 0 0 00 0 -2260251.2 -89182984 -42204.681 0 0 0 0 0 00 0 89182983.7 2378212899 0 0 0 0 0 0 00 0 42204.6806 0 -1472936.4 0 0 0 0 0 00 0 0 0 0 -2689309.2 0 0 0 0 0

1856448.49 0 0 0 0 0 -1344401.2 0 0 0 00 3713720.28 0 0 0 0 0 -2689309.2 0 0 00 0 5934453.05 -55843520 -18093.11 0 0 0 -3674201.9 -145026503 -60297.7910 0 -55843520 1.2491E+10 0 0 0 0 145026503 3867373425 00 0 -18093.11 0 4341001.74 0 0 0 60297.7906 0 -2379393.30 0 0 0 0 7052888.94 0 0 0 0 0

-1344401.2 0 0 0 0 0 3525882.04 0 0 0 00 -2689309.2 0 0 0 0 0 7052888.94 0 0 00 0 -3674201.9 145026503 60297.7906 0 0 0 8739500.24 -54747564 -20049.470 0 -145026503 3867373425 0 0 0 0 -54747564 1.8389E+10 00 0 -60297.791 0 -2379393.3 0 0 0 -20049.47 0 6258352.350 0 0 0 0 -4363579.7 0 0 0 0 00 0 0 0 0 0 -2181480.8 0 0 0 00 0 0 0 0 0 0 -4363579.7 0 0 00 0 0 0 0 0 0 0 -5065298.3 199774068 80347.26030 0 0 0 0 0 0 0 -199774068 5327308471 00 0 0 0 0 0 0 0 -80347.26 0 -3248270.50 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0

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ver B 40 ver C 40 ver D 40 hor 20 rot 20 ver A 20 ver B 20 ver C 20 ver D 20 wind force wind disp0 0 0 0 0 0 0 0 0 1330.09094 0.305535860 0 0 0 0 0 0 0 0 -17008.525 0.001050170 0 0 0 0 0 0 0 0 0 0.011607550 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 2660.51415 0.221071050 0 0 0 0 0 0 0 0 -848.48204 0.001048720 0 0 0 0 0 0 0 0 0 0.010597980 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 2784.47627 0.139842950 0 0 0 0 0 0 0 0 -451.34945 0.000955970 0 0 0 0 0 0 0 0 0 0.00886057

-4363579.7 0 0 0 0 0 0 0 0 0 00 -2181480.8 0 0 0 0 0 0 0 0 00 0 -4363579.7 0 0 0 0 0 0 0 00 0 0 -5065298.3 -199774068 -80347.26 0 0 0 2810.08274 0.069930340 0 0 199774068 5327308471 0 0 0 0 236.584562 0.000762190 0 0 80347.2603 0 -3248270.5 0 0 0 0 0.0063923

10347827.1 0 0 0 0 0 -5984247.4 0 0 0 00 5173274.06 0 0 0 0 0 -2991793.2 0 0 00 0 10347827.1 0 0 0 0 0 -5984247.4 0 00 0 0 11447648 -52134653 -7719.0175 0 0 0 2620.79527 0.019897620 0 0 -52134653 2.409E+10 0 0 0 0 2104.36895 0.000454520 0 0 -7719.0175 0 8065625.21 0 0 0 0 0.00329004

-5984247.4 0 0 0 0 0 13531151.9 0 0 0 00 -2991793.2 0 0 0 0 0 6764913.37 0 0 00 0 -5984247.4 0 0 0 0 0 13531151.9 0 0

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wind non wind non' seis force seis disp seis non seis non'0 46.7046386 9306.10303 1.89602416 0 298.37390 -558.38003 -112144.19 0.00673127 0 -3558.990 0 0 0.07316596 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 114.064882 17953.8115 1.35604505 0 717.05030 -310.51632 -26843.668 0.00666551 0 -1875.340 0 0 0.06645574 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 130.955641 16467.9074 0.84264804 0 784.69330 33.7479847 15805.0665 0.00598282 0 505.49610 0 0 0.05510068 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 62.8330392 10234.9953 0.4106056 0 303.12540 634.43305 35138.1663 0.00462206 0 4102.2390 0 0 0.03933276 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 -149.55284 3494.08303 0.11303739 0 -944.5840 1606.30861 29244.2567 0.00262882 0 8784.4380 0 0 0.02003899 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

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story story height total height int position int height floor area perimeter conc vol steel vol weight axial force pressure width lat force F bot F top M bot M top disp disp I disp II total disp rot I rot II total rot drift P moment P F bot P F top P M bot P M topm m m m m^2 m m^3 m^3 KN KN KPa m KN KN KN KNm KNm coefficients m m m rad rad rad KNm KN KN KNm KNm

0 0 0 01 4 4 4 80 4000 260 1736.29961 0 65989.7016 4120356.33 1.53080805 50 306.16161 303.941939 2.21967168 1105.24341 58.170706 -6.706E-09 5.7899E-05 4.0475E-07 5.8303E-05 2.8842E-05 1.9241E-07 2.9034E-05 1.4576E-05 240.23102 -0.855823 0.85582301 193.986548 22.22136932 4 8 8 80 4000 260 1736.29961 0 65989.7016 4054366.63 1.77131367 49.805 352.881109 343.000438 9.88067105 2286.66959 254.074399 3.6455E-06 0.00022988 1.4625E-06 0.00023134 5.704E-05 3.2728E-07 5.7368E-05 4.3259E-05 701.555942 -4.7355026 4.73550261 441.980243 119.264513 4 12 12 80 4000 260 1736.29961 0 65989.7016 3988376.93 1.92915587 49.61 382.82169 359.565272 23.2564177 3319.06405 585.717186 0 0.00051336 2.9528E-06 0.00051632 8.4595E-05 4.0951E-07 8.5004E-05 7.1244E-05 1136.58794 -10.868622 10.8686222 531.354861 264.2566954 4 16 16 80 4000 260 1736.29961 0 65989.7016 3922387.22 2.04960518 49.415 405.12496 362.991964 42.1329958 4148.47959 1037.1199 0 0.00090578 4.6757E-06 0.00091045 0.00011151 4.4458E-07 0.00011195 9.8535E-05 1545.96224 -18.551547 18.5515469 494.707917 432.8694285 4 20 20 80 4000 260 1736.29961 0 65989.7016 3856397.52 2.14818816 49.22 422.935284 356.851646 66.0836382 4758.02195 1586.00732 0.00140455 6.4544E-06 0.001411 0.00013777 4.3836E-07 0.00013821 0.00012514 1930.31581 -27.145066 27.1450661 361.934215 603.2236916 4 24 24 80 4000 260 1736.29961 0 65989.7016 3790407.82 2.232246 49.025 437.743441 343.190858 94.5525833 5147.86287 2206.22694 0.0020071 8.1358E-06 0.00201523 0.0001634 3.9702E-07 0.00016379 0.00015106 2290.28476 -36.071985 36.071985 160.319933 755.7939717 4 28 28 80 4000 260 1736.29961 0 65989.7016 3724418.12 2.30587688 48.83 450.383872 323.488216 126.895656 5328.04121 2868.94527 0.00271085 9.5922E-06 0.00272045 0.00018837 3.2694E-07 0.0001887 0.0001763 2626.50285 -44.814705 44.8147049 -85.361343 873.3121978 4 32 32 80 4000 260 1736.29961 0 65989.7016 3658428.42 2.37161914 48.635 461.374787 298.970862 162.403925 5315.03754 3543.35836 0.00351324 1.0722E-05 0.00352396 0.00021271 2.3476E-07 0.00021295 0.00020088 2939.60046 -52.912808 52.9128082 -352.75205 940.6721469 4 36 36 80 4000 260 1736.29961 0 65989.7016 3592438.72 2.43116199 48.44 471.061948 270.742855 200.319093 5129.86461 4197.16196 0.00441168 1.145E-05 0.00442313 0.0002364 1.2724E-07 0.00023653 0.00022479 3230.20381 -59.960658 59.9606582 -621.81423 944.834615

10 4 40 40 80 4000 260 1736.29961 0 65989.7016 3526449.02 2.48569051 48.245 479.688554 239.844277 239.844277 4796.88554 4796.88554 0.0054036 1.1729E-05 0.00541533 0.00025945 1.1342E-08 0.00025946 0.00024805 3498.93438 -65.60502 65.6050197 -874.7336 874.73359511 4 44 44 80 4000 260 1736.29961 0 65989.7016 3460459.31 2.53607039 48.05 487.432729 207.280768 280.151961 4343.02561 5308.14242 0.00648642 1.1539E-05 0.00649796 0.00028185 -1.059E-07 0.00028175 0.00027066 3746.4084 -69.542706 69.5427059 -1095.8245 721.18361612 4 48 48 80 4000 260 1736.29961 0 65989.7016 3394469.61 2.5829547 47.855 494.429189 174.039075 320.390114 3797.21617 5695.82426 0.00765757 1.089E-05 0.00766846 0.00030361 -2.172E-07 0.0003034 0.00029263 3973.23643 -71.518256 71.5182558 -1271.4357 476.78837213 4 52 52 80 4000 260 1736.29961 0 65989.7016 3328479.91 2.62684912 47.66 500.782515 141.095474 359.687042 3189.98462 5924.25716 0.00891448 9.8189E-06 0.0089243 0.00032473 -3.153E-07 0.00032442 0.00031396 4180.02307 -71.321644 71.3216437 -1389.8577 135.8507514 4 56 56 80 4000 260 1736.29961 0 65989.7016 3262490.21 2.66815374 47.465 506.57567 109.420345 397.155325 2553.14138 5957.32988 0.01025456 8.3945E-06 0.01026296 0.0003452 -3.928E-07 0.00034481 0.00033467 4367.36659 -68.786024 68.7860238 -1441.231 -305.7156615 4 60 60 80 4000 260 1736.29961 0 65989.7016 3196500.51 2.707191 47.27 511.875675 79.9805741 431.8951 1919.53378 5758.60134 0.01167525 6.7136E-06 0.01168197 0.00036503 -4.423E-07 0.00036459 0.00035475 4535.85872 -63.785513 63.7855132 -1417.4558 -850.4735116 4 64 64 80 4000 260 1736.29961 0 65989.7016 3130510.81 2.74422478 47.075 516.737526 53.7407027 462.996823 1322.84807 5291.39227 0.01317397 4.9039E-06 0.01317887 0.00038422 -4.56E-07 0.00038376 0.00037423 4686.08438 -56.233013 56.2330126 -1312.1036 -1499.54717 4 68 68 80 4000 260 1736.29961 0 65989.7016 3064521.1 2.779474 46.88 521.206965 31.6633231 489.543642 797.446656 4518.86439 0.01474814 3.1234E-06 0.01475126 0.00040276 -4.264E-07 0.00040233 0.0003931 4818.62154 -46.078068 46.0780685 -1120.3295 -2252.705618 4 72 72 80 4000 260 1736.29961 0 65989.7016 2998531.4 2.81312243 46.685 525.322483 14.7090295 510.613453 378.232188 3404.08969 0.01639519 1.5608E-06 0.01639675 0.00042066 -3.457E-07 0.00042031 0.00041137 4934.04095 -33.304776 33.3047764 -838.78696 -3108.445819 4 76 76 80 4000 260 1736.29961 0 65989.7016 2932541.7 2.84532593 46.49 529.116811 3.83609688 525.280714 100.532194 1910.11169 0.01811254 4.3599E-07 0.01811297 0.00043791 -2.062E-07 0.0004377 0.00042906 5032.90605 -17.929728 17.9297278 -465.54381 -4064.071620 4 80 80 80 4000 260 1736.29961 0 65989.7016 2866552 2.87621793 46.295 532.618037 0 532.618037 0 0 0.01989762 0 0.01989762 0.00045452 0 0.00045452 0.00044616 5115.77278 0 0 0 -5115.772821 4 84 4 80 3372.1 235.25 1378.78567 0 53870.9031 2800562.3 2.90591358 46.1 535.850464 531.965549 3.88491587 1934.42018 101.811588 -5.329E-09 0.02175636 6.2301E-07 0.02175698 0.00047476 2.9522E-07 0.00047506 0.00046484 5207.26888 -18.550895 18.5508954 4204.86962 481.67237222 4 88 8 80 3372.1 235.25 1378.78567 0 53870.9031 2746691.4 2.93451301 45.905 538.835279 523.747891 15.0873878 3491.65261 387.961401 2.5624E-06 0.02369505 2.2382E-06 0.02369729 0.0004945 4.9776E-07 0.00049499 0.00048508 5329.42939 -35.973648 35.9736484 3357.54051 906.00299623 4 92 12 80 3372.1 235.25 1378.78567 0 53870.9031 2692820.49 2.96210386 45.71 541.59107 508.689413 32.9016575 4695.59458 828.634337 0.00045452 0.02571165 4.495E-06 0.02571615 0.00051372 6.1771E-07 0.00051433 0.00050471 5436.41446 -51.985713 51.9857132 2541.52376 1263.9663624 4 96 16 80 3372.1 235.25 1378.78567 0 53870.9031 2638949.59 2.98876333 45.515 544.134251 487.544289 56.5899621 5571.93473 1392.98368 0.01989762 0.02780411 7.0833E-06 0.02781119 0.00053243 6.652E-07 0.00053309 0.00052376 5528.71822 -66.344619 66.3446187 1769.18983 1548.041125 4 100 20 80 3372.1 235.25 1378.78567 0 53870.9031 2585078.69 3.01455976 45.32 546.479393 461.091988 85.3874052 6147.89318 2049.29773 0.02997038 9.7336E-06 0.02998011 0.00055062 6.5044E-07 0.00055127 0.00054223 5606.82664 -78.846 78.8459996 1051.27999 1752.1333226 4 104 24 80 3372.1 235.25 1378.78567 0 53870.9031 2531207.78 3.039554 45.125 548.639498 430.133366 118.506131 6452.00049 2765.14307 0.03220841 1.2217E-05 0.03222063 0.00056831 5.8364E-07 0.00056889 0.00056013 5671.21737 -89.321674 89.3216735 396.985216 1871.5017327 4 108 28 80 3372.1 235.25 1378.78567 0 53870.9031 2477336.88 3.06380047 44.93 550.62622 395.487282 155.138937 6513.90818 3507.48902 0.03451617 1.4347E-05 0.03453051 0.00058548 4.751E-07 0.00058596 0.00057747 5722.35972 -97.637763 97.6377628 -185.97669 1902.6846128 4 112 32 80 3372.1 235.25 1378.78567 0 53870.9031 2423465.98 3.08734801 44.735 552.450053 357.987634 194.462419 6364.22461 4242.81641 0.03689159 1.5976E-05 0.03690757 0.00060215 3.3513E-07 0.00060248 0.00059426 5760.71456 -103.69286 103.692862 -691.28575 1843.4286629 4 116 36 80 3372.1 235.25 1378.78567 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story story height total height int position int height floor area perimeter conc vol steel vol weight axial force seis W W*H^ lat force F bot F top M bot M top disp disp I disp II total disp rot I rot II total rot drift P moment P F bot P F top P M bot P M topm m m m m^2 m m^3 m^3 KN KN KN KN*m^2 KN KN KN KNm KNm coefficients m m m rad rad rad KNm KN KN KNm KNm

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220 60 80 2744.2 210.5 1004.4907 0 41387.9561 1143712.85 34801.8761 1684410803 3345.16812 522.682519 2822.4856 12544.3805 37633.1414 0.72516744 7.01E-05 0.72523754 0.00575298 -4.535E-06 0.00574845 0.00572154 26175.2064 -368.08884 368.08884 -8179.752 -4907.851256 4 224 64 80 2744.2 210.5 1004.4907 0 41387.9561 1102324.9 34801.8761 1746218935 3467.91644 360.66331 3107.25313 8877.86609 35511.4643 0.74828404 5.145E-05 0.74833549 0.00580483 -4.722E-06 0.00580011 0.00577449 25461.4543 -305.53745 305.537452 -7129.2072 -8147.665457 4 228 68 80 2744.2 210.5 1004.4907 0 41387.9561 1060936.94 34801.8761 1809140727 3592.87644 218.267244 3374.6092 5497.10095 31150.2387 0.77160218 3.293E-05 0.77163511 0.00585374 -4.455E-06 0.00584929 0.0058249 24719.4225 -236.37948 236.379477 -5747.2657 -11556.3358 4 232 72 80 2744.2 210.5 1004.4907 0 41387.9561 1019548.98 34801.8761 1873176179 3720.04812 104.161347 3615.88677 2678.43465 24105.9118 0.79511007 1.6538E-05 0.79512661 0.00589971 -3.643E-06 0.00589607 0.00587287 23950.7345 -161.66746 161.667458 -4071.6249 -15088.96359 4 236 76 80 2744.2 210.5 1004.4907 0 41387.9561 978161.027 34801.8761 1938325291 3849.43148 27.9083782 3821.5231 731.391982 13896.4477 0.81879595 4.6429E-06 0.81880059 0.00594274 -2.19E-06 0.00594055 0.0059185 23156.9675 -82.496697 82.4966966 -2142.0195 -18699.25160 4 240 80 80 2744.2 210.5 1004.4907 0 41387.9561 936773.071 34801.8761 2004588063 3981.02653 0 3981.02653 0 0 0.84264804 0 0.84264804 0.00598282 0 0.00598282 0.00596186 22339.649 0 0 0 -22339.64961 4 244 4 80 2116.3 185.75 619.573655 0 28674.5103 895385.115 23595.3903 1404775158 2789.82364 2769.59742 20.2262214 10071.2633 530.066492 -2.916E-08 0.8667017 8.8519E-06 0.86671055 0.00604354 4.2057E-06 0.00604775 0.00601563 21545.2135 -76.754823 76.7548229 17397.7599 1992.9322462 4 248 8 80 2116.3 185.75 619.573655 0 28674.5103 866710.604 23595.3903 1451210886 2882.04302 2801.34581 80.6972045 18675.6388 2075.07097 7.7655E-06 0.89099266 3.1962E-05 0.89102462 0.00610147 7.1484E-06 0.00610862 0.00607852 21073.2595 -142.2445 142.244502 13276.1535 3582.4541263 4 252 12 80 2116.3 185.75 619.573655 0 28674.5103 838036.094 23595.3903 1498401667 2975.7619 2794.98436 180.777535 25799.8557 4552.91571 0.00598282 0.91550972 6.4514E-05 0.91557423 0.0061566 8.9473E-06 0.00616554 0.0061374 20573.4617 -196.73373 196.733728 9618.09335 4783.3298564 4 256 16 80 2116.3 185.75 619.573655 0 28674.5103 809361.584 23595.3903 1546347500 3070.98028 2751.59833 319.381949 31446.8381 7861.70952 0.84264804 0.94024169 0.00010218 0.94034386 0.00620892 9.7256E-06 0.00621865 0.00619241 20047.5897 -240.57108 240.571077 6415.22871 5613.3251265 4 260 20 80 2116.3 185.75 619.573655 0 28674.5103 780687.073 23595.3903 1595048386 3167.69817 2672.74533 494.952839 35636.6044 11878.8681 0.96517737 0.00014113 0.96531849 0.00625845 9.6104E-06 0.00626806 0.00624366 19497.3699 -274.18176 274.181764 3655.75685 6092.9280966 4 264 24 80 2116.3 185.75 619.573655 0 28674.5103 752012.563 23595.3903 1644504324 3265.91555 2560.47779 705.43776 38407.1669 16460.2144 0.99030556 0.00017805 0.99048361 0.00630518 8.7329E-06 0.00631391 0.00629128 18924.4831 -298.06061 298.06061 1324.71382 6245.0794467 4 268 28 80 2116.3 185.75 619.573655 0 28674.5103 723338.053 23595.3903 1694715314 3365.63244 2417.3655 948.266941 39815.4318 21439.0787 1.01561508 0.00021015 1.01582524 0.00634911 7.2284E-06 0.00635634 0.00633541 18330.563 -312.76523 312.765232 -595.7433 6094.9122168 4 272 32 80 2116.3 185.75 619.573655 0 28674.5103 694663.542 23595.3903 1745681357 3466.84883 2246.51804 1220.33079 39938.0986 26625.399 1.04109472 0.00023522 1.04132995 0.00639024 5.2362E-06 0.00639548 0.00637618 17717.1934 -318.90948 318.90948 -2126.0632 5669.5018769 4 276 36 80 2116.3 185.75 619.573655 0 28674.5103 665989.032 23595.3903 1797402453 3569.56473 2051.60733 1517.9574 38872.5599 31804.8217 1.0667333 0.00025159 1.06698488 0.00642858 2.9E-06 0.00643148 0.00641373 17085.9062 -317.15713 317.157133 -3289.0369 4997.6275570 4 280 40 80 2116.3 185.75 619.573655 0 28674.5103 637314.522 23595.3903 1849878601 3673.78012 1836.89006 1836.89006 36737.8012 36737.8012 1.09251961 0.00025816 1.09277777 0.00646411 3.6776E-07 0.00646448 0.00644822 16438.1794 -308.21586 308.215863 -4109.5448 4109.5448471 4 284 44 80 2116.3 185.75 619.573655 0 28674.5103 608640.011 23595.3903 1903109802 3779.49502 1607.23026 2172.26476 33675.3006 41158.7008 1.11844245 0.00025447 1.11869692 0.00649685 -2.208E-06 0.00649464 0.00647979 15775.4345 -292.8315 292.831503 -4614.3146 3036.7711472 4 288 48 80 2116.3 185.75 619.573655 0 28674.5103 579965.501 23595.3903 1957096055 3886.70942 1368.12172 2518.5877 29849.9283 44774.8925 1.14449064 0.00024065 1.14473129 0.00652678 -4.671E-06 0.00652211 0.00650859 15099.0345 -271.78262 271.782621 -4831.691 1811.8841473 4 292 52 80 2116.3 185.75 619.573655 0 28674.5103 551290.991 23595.3903 2011837360 3995.42332 1125.71052 2869.7128 25450.8466 47265.8579 1.17065298 0.00021746 1.17087044 0.00655392 -6.86E-06 0.00654706 0.00653479 14410.281 -245.87542 245.87542 -4791.4184 468.33413474 4 296 56 80 2116.3 185.75 619.573655 0 28674.5103 522616.48 23595.3903 2067333718 4105.63672 886.817533 3218.81919 20692.4091 48282.2879 1.19691827 0.00018635 1.19710462 0.00657826 -8.609E-06 0.00656965 0.00655854 13710.4125 -215.939 215.938997 -4524.4361 -959.7288775 4 300 60 80 2116.3 185.75 619.573655 0 28674.5103 493941.97 23595.3903 2123585129 4217.34963 658.96088 3558.38875 15815.0611 47445.1833 1.22327532 0.0001494 1.22342472 0.0065998 -9.748E-06 0.00659005 0.00658002 13000.6012 -182.82095 182.820954 -4062.6879 -2437.612776 4 304 64 80 2116.3 185.75 619.573655 0 28674.5103 465267.46 23595.3903 2180591592 4330.56204 450.378452 3880.18359 11086.2388 44344.9553 1.24971292 0.00010941 1.24982233 0.00661854 -1.01E-05 0.00660844 0.0065994 12281.9509 -147.38341 147.383411 -3438.9463 -3930.224377 4 308 68 80 2116.3 185.75 619.573655 0 28674.5103 436592.949 23595.3903 2238353107 4445.27395 270.050392 4175.22356 6801.26914 38540.5251 1.27621989 6.9871E-05 1.27628977 0.00663448 -9.491E-06 0.00662499 0.00661686 11555.4947 -110.49942 110.499418 -2686.6525 -5402.193878 4 312 72 80 2116.3 185.75 619.573655 0 28674.5103 407918.439 23595.3903 2296869675 4561.48536 127.72159 4433.76377 3284.26946 29558.4251 1.30278504 3.5012E-05 1.30282005 0.00664762 -7.731E-06 0.00663989 0.00663257 10822.1917 -73.049794 73.0497937 -1839.7726 -6817.980779 4 316 76 80 2116.3 185.75 619.573655 0 28674.5103 379243.929 23595.3903 2356141296 4679.19627 33.924173 4645.2721 889.047292 16891.8986 1.32939715 9.8078E-06 1.32940696 0.00665797 -4.632E-06 0.00665334 0.00664673 10082.9249 -35.92042 35.9204201 -932.67056 -8141.961980 4 320 80 80 2116.3 185.75 619.573655 0 28674.5103 350569.419 23595.3903 2416167969 4798.40669 0 4798.40669 0 0 1.35604505 0 1.35604505 0.00666551 0 0.00666551 0.00665952 9338.49866 0 0 0 -9338.498781 4 324 4 80 1488.4 161 240.817023 0 16094.7454 321894.908 12522.5854 1314570926 2610.68188 2591.75443 18.9274436 9424.56158 496.029557 -1.605E-08 1.38274346 2.0163E-05 1.38276362 0.00668344 9.5732E-06 0.00669301 0.00667964 8600.57245 -30.639539 30.6395393 6944.96225 795.55295182 4 328 8 80 1488.4 161 240.817023 0 16094.7454 305800.163 12522.5854 1347229829 2675.54107 2600.62592 74.9151499 17337.5061 1926.38957 2.3365E-06 1.40951047 7.2709E-05 1.40958318 0.00669982 1.6239E-05 0.00671606 0.00670489 8201.42662 -55.35963 55.3596297 5166.89877 1394.2425383 4 332 12 80 1488.4 161 240.817023 0 16094.7454 289705.417 12522.5854 1380289454 2741.19608 2574.66841 166.527662 23766.17 4194.02999 0.00666551 1.43633994 0.00014657 1.43648651 0.00671466 2.0281E-05 0.00673494 0.00672583 7794.03983 -74.530506 74.5305059 3643.71362 1812.1142684 4 336 16 80 1488.4 161 240.817023 0 16094.7454 273610.672 12522.5854 1413749802 2807.6469 2515.65162 291.995278 28750.3043 7187.57607 1.35604505 1.46322568 0.00023185 1.46345754 0.00672796 2.1994E-05 0.00674995 0.00674276 7379.56016 -88.554722 88.554722 2361.45925 2066.2768585 4 340 20 80 1488.4 161 240.817023 0 16094.7454 257515.927 12522.5854 1447610873 2874.89355 2425.69143 449.202117 32342.5524 10780.8508 1.49016155 0.00031982 1.49048137 0.00673972 2.1678E-05 0.0067614 0.00675596 6959.06857 -97.861902 97.8619017 1304.82536 2174.7089386 4 344 24 80 1488.4 161 240.817023 0 16094.7454 241421.181 12522.5854 1481872667 2942.93601 2307.26183 635.674178 34608.9275 14832.3975 1.51714138 0.00040298 1.51754435 0.00674994 1.9638E-05 0.00676958 0.00676575 6533.57665 -102.90383 102.903832 457.350366 2156.0802987 4 348 28 80 1488.4 161 240.817023 0 16094.7454 225326.436 12522.5854 1516535183 3011.77429 2163.20688 848.567407 35629.2899 19185.0022 1.544159 0.00047505 1.54463405 0.00675862 1.6189E-05 0.00677481 0.00677242 6104.02445 -104.14992 104.149917 -198.38079 2029.5881388 4 352 32 80 1488.4 161 240.817023 0 16094.7454 209231.69 12522.5854 1551598423 3081.40839 1996.75264 1084.65575 35497.8247 23665.2164 1.57120826 0.00053104 1.5717393 0.00676576 1.1653E-05 0.00677741 0.00677631 5671.27816 -102.08301 102.083007 -680.55338 1814.8090189 4 356 36 80 1488.4 161 240.817023 0 16094.7454 193136.945 12522.5854 1587062385 3151.83831 1811.51907 1340.31924 34323.5192 28082.8793 1.598283 0.00056726 1.59885026 0.00677136 6.3595E-06 0.00677771 0.00677774 5236.12784 -97.195623 97.1956231 -1007.9546 1531.5673990 4 360 40 80 1488.4 161 240.817023 0 16094.7454 177042.2 12522.5854 1622927069 3223.06405 1611.53202 1611.53202 32230.6405 32230.6405 1.62537705 0.00058135 1.6259584 0.00677541 6.4482E-07 0.00677606 0.00677704 4799.28507 -89.986595 89.9865951 -1199.8213 1199.8212791 4 364 44 80 1488.4 161 240.817023 0 16094.7454 160947.454 12522.5854 1659192476 3295.0856 1401.23515 1893.85045 29359.2127 35883.4822 1.65248425 0.00057232 1.65305657 0.00677793 -5.147E-06 0.00677278 0.00677454 4361.38059 -80.958127 80.9581272 -1275.7038 839.56576492 4 368 48 80 1488.4 161 240.817023 0 16094.7454 144852.709 12522.5854 1695858607 3367.90297 1185.50185 2182.40113 25865.4948 38798.2422 1.67959844 0.00054055 1.68013899 0.00677891 -1.066E-05 0.00676824 0.00677061 3922.9619 -70.613314 70.6133142 -1255.3478 470.75542893 4 372 52 80 1488.4 161 240.817023 0 16094.7454 128757.963 12522.5854 1732925459 3441.51616 969.647179 2471.86898 21922.458 40713.1362 1.70671346 0.00048786 1.70720132 0.00677834 -1.554E-05 0.0067628 0.00676558 3484.49083 -59.454125 59.4541247 -1158.5932 113.24595294 4 376 56 80 1488.4 161 240.817023 0 16094.7454 112663.218 12522.5854 1770393035 3515.92517 759.439837 2756.48534 17720.2629 41347.28 1.73382314 0.00041754 1.73424068 0.00677624 -1.942E-05 0.00675682 0.00675984 3046.34106 -47.979872 47.9798717 -1005.2925 -213.2438795 4 380 60 80 1488.4 161 240.817023 0 16094.7454 96568.4725 12522.5854 1808261333 3591.13 561.114063 3030.01594 13466.7375 40400.2125 1.76092133 0.00033433 1.76125566 0.0067726 -2.192E-05 0.00675068 0.00675375 2608.79565 -36.686189 36.6861889 -815.24864 -489.1491896 4 384 64 80 1488.4 161 240.817023 0 16094.7454 80473.727 12522.5854 1846530354 3667.13065 381.381587 3285.74906 9387.85446 37551.4178 1.78800186 0.00024453 1.78824639 0.00676741 -2.265E-05 0.00674476 0.00674768 2172.04449 -26.064534 26.0645338 -608.17246 -695.0542497 4 388 68 80 1488.4 161 240.817023 0 16094.7454 64378.9816 12522.5854 1885200098 3743.92711 227.443572 3516.48354 5728.20848 32459.8481 1.81505857 0.00015597 1.81521453 0.00676069 -2.124E-05 0.00673945 0.00674204 1736.1817 -16.602238 16.6022375 -403.66225 -811.6649498 4 392 72 80 1488.4 161 240.817023 0 16094.7454 48284.2362 12522.5854 1924270564 3821.51939 107.002543 3714.51685 2751.49396 24763.4457 1.8420853 7.8057E-05 1.84216335 0.00675242 -1.726E-05 0.00673516 0.0067372 1301.2031 -8.783121 8.78312095 -221.20453 -819.7579699 4 396 76 80 1488.4 161 240.817023 0 16094.7454 32189.4908 12522.5854 1963741754 3899.90749 28.2743293 3871.63317 740.982424 14078.6661 1.86907588 2.1839E-05 1.86909772 0.00674261 -1.032E-05 0.00673229 0.00673359 867.00354 -3.0887001 3.08870011 -80.197827 -700.10536

100 4 400 80 80 1488.4 161 240.817023 0 16094.7454 16094.7454 12522.5854 2003613666 3979.09141 0 3979.09141 0 0 1.89602416 0 1.89602416 0.00673127 0 0.00673127 0.00673161 433.374213 0 0 0 -433.37421

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Stress Factorsstories gravity core 1 core 2 core 3 column column A column B column C column D outrigger belt

81 to 100 5185.99496 508593.75 6781250 0.00366343 542500 0.0489066 0.06202286 0.06201328 0.06202286 0 061 to 80 5670.35091 508593.75 6781250 0.0014257 542500 0.07582326 0.10049282 0.10048335 0.10049282 0 041 to 60 6756.971 508593.75 6781250 0.00087673 542500 0.09600157 0.12800771 0.12799864 0.12800771 0 021 to 40 8014.91554 508593.75 6781250 0.00063646 542500 0.11197989 0.14990615 0.14989787 0.14990615 0 01 to 20 9389.36555 508593.75 6781250 0.00050474 542500 0.12545486 0.16834456 0.16833716 0.16834456 0 0

Wind Displacements Wind Moment Reactionstory horizontal rotation vertical A vertical B vertical C vertical D story sum bot100 0.30553586 0.00105017 0.01160755 0 0 0 81 69019.279480 0.22107105 0.00104872 0.01059798 0 0 0 61 73081.532460 0.13984295 0.00095597 0.00886057 0 0 0 41 75061.428840 0.06993034 0.00076219 0.0063923 0 0 0 21 73319.756420 0.01989762 0.00045452 0.00329004 0 0 0 1 59737.131

base 0 0 0 0 0 0

Wind Core/Column Stress Gravity Plus Wind Core/Column Stressstory core column A column B column C column D core column A column B column C column D

81 521.656135 573.202603 32.3546065 32.3496073 32.3546065 5707.6511 5759.19757 5218.34957 5218.34457 5218.3495761 1262.43057 1038.2696 126.86521 126.853256 126.86521 6932.78147 6708.62051 5797.21612 5797.20416 5797.2161241 1983.21043 1529.4251 253.866226 253.848245 253.866226 8740.18142 8286.39609 7010.83722 7010.81924 7010.8372221 2826.89143 1999.53265 423.7684 423.745 423.7684 10841.807 10014.4482 8438.68394 8438.66054 8438.683941 3985.51212 2284.84862 670.939304 670.909775 670.939304 13374.8777 11674.2142 10060.3049 10060.2753 10060.3049

max 13374.8777 11674.2142 10060.3049 10060.2753 10060.3049 11674.2142

Wind Outrigger Stress Wind Belt Stressstory outrig B outrig D belt AB belt BC belt AD belt DE100 0 0 0 0 0 080 0 0 0 0 0 060 0 0 0 0 0 040 0 0 0 0 0 020 0 0 0 0 0 0

max 0 0 0 0 0 0 0 0

Wind Diag Stressstory Vertical StrainHorizontal StrainSTRESS Wind + Grav Diagonal Stresses100 0.01862685 0.07114229 3895980.66 3897487.680 0.01573998 0.06841611 3652374.2 3654021.8960 0.0118815 0.05888539 3071283.05 3073246.4840 0.00725786 0.04214113 2143916.01 2146244.9820 0.00237221 0.01675919 830302.91 833031.262

max 3897487.6

Seismic Displacements Seismic Moment Reactionstory horizontal rotation vertical A vertical B vertical C vertical D story sum bot100 1.89602416 0.00673127 0.07316596 0 0 0 81 410854.00180 1.35604505 0.00666551 0.06645574 0 0 0 61 462945.62960 0.84264804 0.00598282 0.05510068 0 0 0 41 341482.94540 0.4106056 0.00462206 0.03933276 0 0 0 21 154963.56120 0.11303739 0.00262882 0.02003899 0 0 0 1 19112.4217

base 0 0 0 0 0 0

Seismic Core/Column Stress Gravity Plus Seismic Core/Column Stressstory core column A column B column C column D core column A column B column C column D

81 4040.26687 3837.88877 250.588915 250.550196 250.588915 9226.26183 9023.88373 5436.58388 5436.54516 5436.5838861 9085.53901 6849.0175 913.031452 912.945424 913.031452 14755.8899 12519.3684 6583.38236 6583.29633 6583.3823641 13517.9865 9851.84584 1730.4065 1730.28394 1730.4065 20274.9575 16608.8168 8487.37749 8487.25493 8487.3774921 17446.4833 12420.5224 2615.33509 2615.19067 2615.33509 25461.3989 20435.438 10630.2506 10630.1062 10630.25061 21846.397 13611.8902 3677.72219 3677.56033 3677.72219 31235.7625 23001.2558 13067.0877 13066.9259 13067.0877

max 31235.7625 23001.2558 13067.0877 13066.9259 13067.0877 23001.2558

Seismic Outrigger Stress Seismic Belt Stressstory outrig B outrig D belt AB belt BC belt AD belt DE100 0 0 0 0 0 080 0 0 0 0 0 060 0 0 0 0 0 040 0 0 0 0 0 020 0 0 0 0 0 0

max 0 0 0 0 0 0 0 0

Seismic Diagonal Stress Wing + Seismic Diagonal Stressstory Vertical StrainHorizontal StrainSTRESS Diag A100 0.11712002 0.29395426 17840623.9 17842130.980 0.09832673 0.30185134 17367728.5 17369376.260 0.07356061 0.27091819 14950380.2 14952343.640 0.04450489 0.19695873 10479521.1 10481850.120 0.01444866 0.07832436 4026349.14 4029077.49

max 17840623.9 max 17842130.9

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