StructuraDepth Braced Frame - engr.psu.edu

H y a t t C e n t e r C h i c a g o , I l l i n o i s ( 7 1 S o u t h W a c k e r D r i v e ) S t r u c t u r a l R e d e s i g n

Patrick Hopple − Structural Option The Pennsylvania State University Dr. Hanagan − Spring 2005 Senior Thesis − 18 − Department of Architectural Engineering

6.0 Structural Depth

Introduction

Solutions presented in this section of the report are geared as a response to the outlined problems and design goals as stated in previous sections. The structural redesigns presented herein have been analyzed with many simplifying assumptions to lessen the complexity of the design process. The goal of the structural redesign are to replace the reinforced concrete core structure with an efficient structural system that meets required inter-story drift and deflection criteria. Structural schemes to be investigated include a braced frame core, a braced core with upper level outriggers and hat truss, and finally a braced core with multiple outriggers and belt trusses. Suitable systems will be compared to the original shear wall system and conclusions will be made based upon the performance of each system.

Braced Frame Design

Introduction

The first proposed structural redesign consists of replacing the shear walls in the core with braced frames as seen in Figures 6.0a, b, respectively. A braced frame was chosen to be evaluated due to the high stiffness a braced frame can provide to a building compared to the overall weight of the structural system. Initial sizes

will be calculated by classical analysis methods then input into the finite element structural analysis program ETABS for further design checks and optimization. Results of the analysis and performance of the braced frame system will be checked against code required strength criteria and recommended drift limits.

Figure 6.0b: Braced Frame Core Layout

Figure 6.0a: Shear Wall Core Layout



Methodology

A braced frame system is an efficient means of resisting lateral loads on a building because the horizontal shear forces are resisted by diagonals or V-bracing between beams and columns in a bay. The addition of a diagonal or chevron brace to bays within the frame transforms the system into a vertical truss, eliminating bending from columns and beams all together. High stiffness is achieved because the horizontal story shear is now being absorbed by the web members (braces) and not by the columns. The braces resist lateral forces by developing internal axial forces and relatively small bending moments. Since forces are resisted by almost purely axial forces in frame members, a highly efficient system results due to the complete the cross section of steel resisting loads by axial deformations, instead of deformations caused by bending of members.

To understand the behavior of a braced frame system, the frame may be

considered as a cantilevered vertical truss resisting lateral loads primarily through the axial stiffness of columns and braces. The frame columns act as the chords of the truss and primarily resist the overturning moment caused by lateral loads placed on the truss. Resistance comes in the form of axial deformations with tension on the windward side of the truss and compression on the leeward column side. The horizontal shear force is mainly absorbed in the braces, acting like web members, through axial tension or compression in the brace. The horizontal girders between columns act axially, if the truss is fully symmetric and triangulated. Bending can occur in the girder if a diagonal or brace is eccentrically connected to it. Mainly since wind loads are reversible, the braces in a braced frame system can undergo both compression and tension depending upon the direction of the load. Therefore, most often the braces and diagonals are designed for the more stringent case of buckling of the brace caused by compression. The behavior and deformation characteristics of a braced frame due to lateral load can be seen in Figure 6.1.

Figure 6.1: Braced Frame Deflection and Framing Behavior



Columns of a braced frame in a tall building would accumulate great axial forces

from both gravity and lateral loads imparted to the structure. In a tall braced frame a large percentage of the frame drift is caused by flexural deformation, also known as “chord drift” with a smaller percentage of the total drift caused by axial deformation of the braces, called “shear deformation”. To control deflections, care must be taken to proportion column members for the increased load caused by wind along with gravity loads accumulated from floors above. This results very large column sizes much in excess of what is required to resist gravity loads alone.

Assumptions and Design Goals

To effectively evaluate the validity of a braced frame solution many factors and limiting assumptions must be made. Assumptions made in the design of the braced frame system and the goals which are to be accomplished are as follows: Assumptions:

1. Bracing shall be configured to maximize space for architectural requirements including openings for doors, building systems and spaces.

2. Concentric braced frames shall be used when possible to provide for greater stiffness than eccentric braced frames.

3. Calculated ASCE 7-02 wind loads control the strength of N-S frames. See Appendix A.

4. Calculated ASCE 7-02 wind and seismic load control the E-W frame as shown in Appendix A.

5. Compression bracing controls the design of the braced frame system. 6. Limiting slenderness ratios for braces: Tension KL/r <= 300 Compression <=200. 7. P-Delta effects are accounted for in deflection and strength design.

Design Goals:

1. Initially sizing truss members using moment area method for columns and a classical work method similar to an implementation of virtual work presented in AISC Design Guide 5: Low-and Medium-Rise Steel Buildings for input into ETABS for analysis.

2. Design an efficient and least weight alternative to a reinforced core.

3. Reduce inter-story and total drift to H/480 in N-S direction and H/1000 in E-W.

4. Minimize impact on interior spaces and layouts.

5. Find an optimal braced frame solution for use in further problem solutions.

6. Use chevron bracing when possible with the apex pointing up, also called an “inverted-V” brace.



Design Process

The design of the braced frame starts with initially sizing members based on gravity and lateral loads for input into the computer analysis program ETABS for final optimization. It is very important to understand the flow of forces and the behavior of a structure before utilizing the computing power of a structural analysis program. Without an advanced understanding of a structure and the behavior of the system, design output by a computer can possibly be incorrect and could lead to serious design flaws if not checked thoroughly.

By sizing members according to gravity and lateral loads imparted on the structure, columns, braces and beams can be approximated through the use of classical work methods of analysis. Floor framing members and design was not expected to change dramatically due to this study focused directly on the lateral system of the Hyatt Center. Therefore, simple hand calculations (Appendix B) were used to check the composite beam capacities in a typical bay then incorporated into ETABS for final analysis and confirmation.

The floor system consisted of approximately 42 foot spans from the core to the spandrels with radial beam spacing of 10 feet. The floor design consisted of a 5 ½” composite deck with W18x50 as most floor members, decreasing in weight as the spans lessened towards the east and west sides of the building. Spandrel beam designs are controlled by deflection issues arising from the cladding system and therefore are mostly W27x84 as the main members with W24x76 spandrels at each corner bay. The typical floor seen in Figures 6.2a, b below is repeated throughout the building and used as the floor plate design during the lateral system study to minimize complexity in loads and calculations.

Figure 6.2a: Composite Floor Framing



Lateral Frame Analysis – Moment-Area

Initial member sizes were approximated by two methods: moment-area method to account for column deformations or “chord drift” and a classical work method adopted from AISC Design Guide 5 which is a braced frame optimization technique.

The Moment-Area method, presented in Appendix B, was used to calculate the

approximate column areas required to resist overturning moments caused by ASCE 7-02 wind loads calculated previously. The moment-area method is useful in tall frames to predict the axial forces in the columns and acts much like the cantilever method. The overturning moments cause larger axial forces and deformations on the columns which are farther from the center line of the frame. Therefore, larger braced frames like BF#3 and BF#4 will acquire more loads than the smaller frames like BF#1 or BF#2 in the N-S direction.

First, the structure is split into five – 10-story increments and overturning

moments, M1 through M5, labeled in Figure 6.3 and Table 6.0 below, are found using the controlling wind loads. The N-S direction was chosen to be analyzed due to the slender aspect ratio of the frames in this direction, therefore, drift would be quite difficult to control in this direction. Areas under the M/EI diagram were found using EI as an unknown value using equation (6-0).

( )⎟⎟⎠

⎞⎜⎜⎝

⎛ += +

oi

iiii EI

hMMA

21 (6-0)

Figure 6.2b: Composite Floor Framing - Sides



Next the centroid of the areas was then found by equation (6-1) and deflections,

assuming EI was an unknown, were then found through equation (6-2). A tall building acts as a flexible cantilevered truss resisting overturning moments primarily though axial loads in the columns of a frame. The approximate moment of inertia for the entire structure can then be found to equal the sum of the areas of a column multiplied by the distance from the center line squared as seen in equation (6-3). This is an equivalent moment of inertia and is an approximate procedure to determine loads applied to a structure in finding initial member sizes.

The final drift is known to be H/480 in the N-S direction and values were

substituted into the deflection equation (6-2) leaving only the required moment of inertia at each level as the unknown. Applying equation (6-3) and assuming all columns areas are equal leaves just the summation of the distances squared for the columns. Required areas for columns are each level were then found and summarized in Table 6.0 below.

( )⎟⎟⎠

⎞⎜⎜⎝

⎛++

=+

+

1

123 ii

iiii MM

MMhX (6-1)

∑=

=

−+−=∆1

1)()(

i

jjijiiici XHAXhA (6-2)

∑= )( 2iioi dAI (6-3)

Figure 6.3: Moment-Area Method



Overturning Moment (kip-ft)

Area/Column (in2)

M6= 0 M5= 11057 A5 151.74 M4= 424897 A4 253.81 M3= 900652 A3 342.22 M2= 1440634 A2 399.62 M1= 2071539 A1 438.91

The required column areas for each increment and each braced frame can be seen in Table 6.0 above. Column areas for each floor between increments were found by linear extrapolation assuming a 2-story column size. The N-S BF #3 & BF #4 were the heaviest loaded frames in the building, therefore, sample calculations were completed adding gravity loads and load factors to find the initial column sizes.

Lateral Frame Analysis – Classical Work Method

Another method to calculate initial member sizing was used from AISC Design Guide 5. This is an optimization method for an entire braced frame using virtual work and multiplying initial member sizes by a correction factor which accounts for required deflection limits. This method can be found complete in Appendix B.

Many assumptions were made to utilize this method, the inherent inaccuracies

between the actual braced frame geometry and the model geometry were assumed to be negligible in finding preliminary member sizes. The model assumes Chevron bracing with the apex pointing upwards, however, this is not actual case in many bays of the frame due to openings required at the corners. Therefore, the calculations will approximate a drift which is much lower than the actual drift due to the apex geometry causing bending in the girders resulting in more drift due to bent actions.

The procedure to find optimal areas include first finding member forces due to

external (wind) forces; second finding member forces due to virtual loads at the point the deflection is to be optimized; third calculating areas due to strain with lambda=1.0; fourth computing the deflection by virtual loads with lambda=1.0; and finally factoring the areas by a correction factor which is a ratio of a target deflection and the actual calculated deflection. This method gives a fairly good approximation of member properties; however strength design will still need to be checked in order for design to be finalized. The approximate member sizes found for the columns are compared to the members found in the Moment-Area method in Table 6.1. The areas required for each method are very close to each other, resulting in an acceptable approximation in member sizes using both methods. The brace areas were increased at the upper floors due to small moments in the brace not accounted for in this approximate method.

Table 6.0: Moment-Area Required Column Areas (No Gravity)



TABLE 4: Optimum Areas Col. No. 23 24 25 26 27 28 29

MOMENT-AREA

Item COLAR GIRDAR BRACAR C.R. ACOL AGIRD ABRAC Area/Column (in2) 50 0.0 0.0 2.2 1.2 0.0 0.0 2.7 40 36.5 9.3 10.6 1.2 45.1 11.5 13.2 A5 151.74 30 104.3 12.9 14.8 1.2 129.1 16.0 18.4 A4 253.81 20 188.8 15.6 17.9 1.2 233.6 19.3 22.1 A3 342.22 10 276.7 17.4 20.0 1.2 342.4 21.6 24.8 A2 399.62 2 377.5 19.0 21.8 1.2 467.1 23.6 27.0 A1 438.91

Composite Column Analysis

The required column sizes found by the approximate methods of analysis are quite large compared to typical W14 column shapes. The largest member in AISC tables is a W14x808 with an area of 237 in2; therefore, built-up or composite columns must be designed to withstand the great amount of force from the numerous floors above as well at the chord action caused by wind loads on the frame. Composite columns must be designed before the initial framing sizes can be placed into ETABS for further analysis.

The design rules for composite columns are covered by both AISC-LRFD and in

the ACI building code, however each very slightly in how the analysis and design are completed. Both agencies provide methods for evaluating strength and the limiting effects of slenderness. Both apply to encased or concrete-filled sections like tubes or fabricated shells. The AISC method assumes the composite columns are mostly like typical steel design. Analytic expressions are used for strength, stiffness and slenderness effects which lead directly to values of axial-load capacity and beam-column capacity of composite columns. The ACI building code treats the section much like a bar reinforced-concrete column and require a strain-compatibility analysis to be performed and does not permit column designs without accounting for a minimum eccentricity. Since the structural redesign is in steel and the sections will be a

standard box shape, the AISC-LRFD method of composite column design will be utilized.

Table 6.1: Member Area Comparison (No Gravity Loads)

Figure 6.4: Typical Box Column



AISC-LRFD specifies a strict limit of at least 4% of the gross cross-section must be

composed of structural steel. If less than 4% is not steel, the section is treated as a concrete column and ACI design specifications apply.

Composite box columns are originally used on the Hyatt Center due to large

unbraced story heights at the lower lobby levels and the massive loads accumulated from stories above. Since this type of column was originally used, the box shape was varied and sizes were increased to meet architectural layouts and resist the large axial loads.

Advantages of composite columns use as compared to regular w-shapes or built-

up structural shapes are realized in large unbraced lengths and large axial loads. This condition exists mainly in the lower lobby and corridor spaces of a high-rise since architects and owners would prefer vast open spaces to allow circulation and visual appearance to onlookers from street level. The tendency for a regular w-shape to buckle under large axial loads would increase as the unbraced length (KL) is increased. This causes regular columns to lose axial strength over longer story heights. A composite column, however, introduces concrete to help in resisting axial loads over larger unbraced lengths.

Concrete-filled columns with 8ksi compressive strength were chosen, therefore,

the increased resistance to buckling caused by the stiffness and confinement of the concrete in the box section caused more axial load to be absorbed with less tendency to buckle like its counterpart. Axial load capacity of the column will diminish as the unbraced length increases; however, the reduction in load is significantly smaller than a regular w-shape. Encased w-shape composite columns are another type of composite column which was not investigated due to the immense axial loads imparted on the columns. Here the encased concrete adds the stiffness and resistance to buckling, therefore, larger axial loads can exist over longer unbraced length compared with a regular w-shape column.

The axial strength design process for the composite columns followed AISC-

LRFD Specification Chapter I – Composite Columns. The design axial strength of composite columns is determined with similar equations used in steel design of columns except the formulas are entered with modified Fym, Em and rm. The modified properties account for the effects of concrete added to the bare steel column. The axial design strength is computed with equation (6-4) and the modified properties are calculated using equations (6-5) through (6-10) below.

)85.0( crgncnc FAPandP ==ΦΦ (6-4)



m

my

m

mycr

myc

cr

EF

rKLc

where

Fc

F

cIf

FF

cIf

πλ

λ

λ

λλ

=

⎟⎠⎞

⎜⎝⎛=

>

=

≤

2

877.0:5.1

)658.0(

:5.12

(6-5)

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

s

cc

s

ryrymy A

Afc

AAFcFF '21 (6-6)

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

s

ccm A

AEcEE 3 (6-7)

The coefficients of c1, c2 and c3 in equations (6-6) and (6-7) above account for the stresses and strains caused by creep and shrinkage of concrete. These are found experimentally based upon the encasement or confinement of the concrete. Table 6-2 summarizes the coefficients based upon the composite column type.

Filled Column Coefficients: Encased Column Coefficients:

c1= 1.0 0.7 c2= 0.85 0.6 c3= 0.4 0.2

First original composite box column properties and strength capacities were found. The bare steel capacities calculated were enough to satisfy the gravity load requirements for the exterior column lines; however the columns of the braced frames need to be filled with 8ksi high-strength concrete to increase capacity to account for axial deformations by wind loads. Table 6.3 below summarizes the bare steel column design strengths and Table 6.4 summarizes the 8ksi filled composite axial strength capacities of the typical columns used in the redesign (KL=13.5 feet).

Appendix C further summarizes the design calculations and strength values of 4ksi and 8ksi filled composite box columns over increasing unbraced lengths (KL). Axial force transfer into the concrete is accomplished by mechanical (shear studs) connectors as per AISC-LRFD Chapter I4. The number of shear studs required is labeled in Appendix C as per equation (6-8). )/1(' nysuu PFAVV −= (6-8)

Table 6.2: Numerical Coefficients for Design of Composite Columns



Mark As Es Fy

(ksi) rx λc Fcr (ksi) ΦcPn (kips)

BX24X665 195.75 29000 50 8.93 0.240 48.81 8121 BX36X815 239.75 29000 50 14.00 0.153 49.51 10090 BX36X926 272.00 29000 50 13.90 0.154 49.51 11446 BX36X1034 303.75 29000 50 13.81 0.155 49.50 12780 BX36X1140 335.00 29000 50 13.71 0.156 49.49 14093 BX36X1245 365.75 29000 50 13.62 0.157 49.49 15384 BX36X1450 425.75 29000 50 13.44 0.159 49.47 17903 BX36X1650 483.75 29000 50 13.25 0.162 49.46 20336 BX36X1750 512.00 29000 50 13.17 0.163 49.45 21520 BX36X1840 539.75 29000 42 13.08 0.150 41.61 19088 BX42X2075 608.00 29000 50 15.60 0.137 49.61 25637 BX42X2190 641.75 29000 42 15.51 0.127 41.72 22757 BX48X2260 663.75 29000 50 18.13 0.118 49.71 28045

Axi

al D

esig

n St

reng

th o

f A57

2 G

rade

50

(KL=

13.5

ft)

BX48X2400 704.00 29000 50 18.04 0.119 49.71 29744

Mark As Ac %As Es Ec Em

(ksi) Fmy (ksi) λc

Fcr (ksi)

ΦcPn (kips)

BX24X665 195.75 380.25 0.34 29000 5154 33004.4 63.21 0.275 61.24 10190 BX36X815 239.75 1056.25 0.18 29000 5154 38081.9 79.96 0.194 78.71 16040 BX36X926 272.00 1024 0.21 29000 5154 36760.7 75.60 0.191 74.46 17214 BX36X1034 303.75 992.25 0.23 29000 5154 35734 72.21 0.189 71.15 18369 BX36X1140 335.00 961 0.26 29000 5154 34913.6 69.51 0.187 68.50 19505 BX36X1245 365.75 930.25 0.28 29000 5154 34243.1 67.30 0.185 66.33 20622 BX36X1450 425.75 870.25 0.33 29000 5154 33213.7 63.90 0.184 63.00 22800 BX36X1650 483.75 812.25 0.37 29000 5154 32461.3 61.42 0.183 60.57 24904 BX36X1750 512.00 784 0.40 29000 5154 32156.6 60.41 0.182 59.58 25928 BX36X1840 539.75 756.25 0.42 29000 5154 31888.3 51.53 0.170 50.91 23358 BX42X2075 608.00 1156 0.34 29000 5154 32919.5 62.93 0.157 62.28 32188 BX42X2190 641.75 1122.25 0.36 29000 5154 32604.9 53.89 0.146 53.41 29135 BX48X2260 663.75 1640.25 0.29 29000 5154 34094.2 66.80 0.139 66.27 37387

A57

2 G

race

50

(50k

si) &

f'c

= 80

00ps

i

BX48X2400 704.00 1600 0.31 29000 5154 33685.1 65.45 0.138 64.93 38856

Table 6.3: Bare Steel Axial Design Strengths (KL=13.5’)

Table 6.4: 8ksi Composite Axial Design Strengths (KL=13.5’)



ETABS Frame Analysis

ETABS was chosen as the structural analysis software due to its proven use in the design of some of the worlds most complex and tall building structure and the ease of object modeling of structures. The floor plan and story heights were constructed in ETABS floor beam properties and initial member sizes were placed into the program. Lateral loads were then added in the form of ASCE 7-02 wind and seismic for strength design of members and ASCE 7-98 wind tunnel analysis data and loads for serviceability checks of the structure. The braced frame core was constructed to allow for required openings in the core walls for elevators and spaces. This caused inconsistent bracing configurations in many N-S braces as seen below in Figure 6.5; E-W bracing can be seen in Figure 6.6.

Figure 6.5: N-S Braced Frames: (left to right) #1, #2, #3, #4, #5, #6



The N-W frames are primarily concentrically braced frames because braces are able to accommodate single door openings in the walls. The E-W frames, however, had to accommodate double doors for elevator lobby access in many areas. Therefore, the E-W frames consist of a mixture of concentric and eccentrically braced bays to allow for larger openings.

Overall, the member forces were compared and designed to meet equation (H1-1a) or (H1-1b); members under combined forces. Members not meeting these requirements were increased until member stresses were below unity. Due to the immense size of the structure, only a description of the members in BF #4 will be discussed. The resulting member sizes are similar to BF #4, for economy.

Figure 6.5: E-W Braced Frames: (left to right) BF North, BF South



The typical bracing members consist of W14x90 at the upper levels and W14x665

at lower levels in the concentrically braced frames. Composite box columns were filled with 8ksi concrete to level 20 of the structure to provide extra stiffness to control column deformations caused by wind. The E-W eccentric braces were also W14’s that increased linearly down the core structure due to very high shear forces near the base of the structure. Figure 6.6 shows the 3-dimensional geometry of the braced frame structure modeled in ETABS. Figure 6.8 shows the axial forces in members for BF #4 using load combination of (a) 1.2D+1.0L+1.3W and (b) 1.2D+1.6L. Figure 6-9 shows the governing support reactions for BF #4 for the load combination 1.2D+1.0L+1.6W. A net tension, or uplift, force of 5775 kips on the foundation is the controlling uplift force on the deep foundations; therefore, the deep foundation system is still required for the braced core configuration.

Figure 6.6: Braced Frame Core Structure

Figure 6.7: Axial Forces in BF #4 due to 1.2D+1.0L+1.3W (Left) and 1.2D+1.6L (Right)



The resulting total drift summary can be seen in Table 6-3 below. The drift was

limited to H/480 in the N-S direction; however the overall drift after optimization was not acceptable. Second-order direct P-Delta analysis was incorporated into the drift calculations in Table 6.3. ETABS calculates 2nd-order effects through an exact P-Delta analysis using the stiffness matrix. P-Delta effects are especially important in tall high-rise structures to ensure lateral stability and resist overturning due to excessive deflections.

Braced Frame Drifts No P-Delta Including P-Delta Effects

Load UX UY RZ UX UY RZ WINDY 0.2222 37.8955 -0.00019 0.2435 40.0504 -0.00021

TUNNELNS 0.1351 22.7687 -0.00012 0.1475 24.0347 -0.00014 EQY 0.3631 28.4712 0.0045 0.3977 30.0232 0.00474 N

-S

H/480 17.0825 17.0825 WINDX 9.2732 0.1009 0.00041 9.6435 0.1103 0.00046

TUNNELEW 3.1706 0.0319 0.00016 3.2926 0.0348 0.00018 EQX 19.9015 0.2045 -0.00097 20.6395 0.2229 -0.00099 E-

W

H/1000 8.1996 8.1996

A 2,381,800 kip-ft overturning moment results from calculated ASCE 7-02 wind loads in the N-S direction and an 875,000 kip-ft overturning moment in the E-W direction. The dead load of the structure alone is enough to resist the effects of overturning and the capacity of deep rock caisson foundation provide sufficient resistance to a maximum upward tension of 5750 kips in the windward bracing columns.

Results

For the Hyatt Center, the 6 concentrically braced frames in the N-S and the 2 eccentrically braced frames, designed for strength using ASCE 7-02 wind loads and drift checked with the wind tunnel analysis data, were found to be excessively flexible. As seen in Table 6.3 above, the E-W braced frames meet the allowable drift limit H/1000 set by the structural engineer on the project when check against wind tunnel analysis data. The N-S braced frames, however, exceeded the allowable drift limit quite considerably and alternative means to reduce the drift in this direction should be taken to either stiffen the frame or engage the exterior columns in helping to resist the overturning moments. The aspect ratio of the height to core width is a very slender 14:1. However, by widening the effective width of the vertical truss, a more efficient and less slender (5:1) lateral system results that can possible bring the drift limits closer to the allowable.

Table 6.3: Braced Frame Total Drift (inches)

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