H y a t t C e n t e r Chicago, Illinois (71 South Wacker Drive) Structural Redesign

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1 6.0 Structural Depth Introducton Solutons presented n ths secton of the report are geared as a response to the outlned problems and desgn goals as stated n prevous sectons. The structural redesgns presented heren have been analyzed wth many smplfyng assumptons to lessen the complexty of the desgn process. The goal of the structural redesgn are to replace the renforced concrete core structure wth an effcent structural system that meets requred nter-story drft and deflecton crtera. Structural schemes to be nvestgated nclude a braced frame core, a braced core wth upper level outrggers and hat truss, and fnally a braced core wth multple outrggers and belt trusses. Sutable systems wll be compared to the orgnal shear wall system and conclusons wll be made based upon the performance of each system. Braced Frame Desgn Introducton The frst proposed structural redesgn conssts of replacng the shear walls n the core wth braced frames as seen n Fgures 6.0a, b, respectvely. A braced frame was chosen to be evaluated due to the hgh stffness a braced frame can provde to a buldng compared to the overall weght of the structural system. Intal szes wll be calculated by classcal analyss methods then nput nto the fnte element structural analyss program ETABS for further desgn checks and optmzaton. Results of the analyss and performance of the braced frame system wll be checked aganst code requred strength crtera and recommended drft lmts. Fgure 6.0a: Shear Wall Core Layout Fgure 6.0b: Braced Frame Core Layout Dr. Hanagan Sprng 2005 Senor Thess 18 Department of Archtectural Engneerng

2 Methodology A braced frame system s an effcent means of resstng lateral loads on a buldng because the horzontal shear forces are ressted by dagonals or V-bracng between beams and columns n a bay. The addton of a dagonal or chevron brace to bays wthn the frame transforms the system nto a vertcal truss, elmnatng bendng from columns and beams all together. Hgh stffness s acheved because the horzontal story shear s now beng absorbed by the web members (braces) and not by the columns. The braces resst lateral forces by developng nternal axal forces and relatvely small bendng moments. Snce forces are ressted by almost purely axal forces n frame members, a hghly effcent system results due to the complete the cross secton of steel resstng loads by axal deformatons, nstead of deformatons caused by bendng of members. To understand the behavor of a braced frame system, the frame may be consdered as a cantlevered vertcal truss resstng lateral loads prmarly through the axal stffness of columns and braces. The frame columns act as the chords of the truss and prmarly resst the overturnng moment caused by lateral loads placed on the truss. Resstance comes n the form of axal deformatons wth tenson on the wndward sde of the truss and compresson on the leeward column sde. The horzontal shear force s manly absorbed n the braces, actng lke web members, through axal tenson or compresson n the brace. The horzontal grders between columns act axally, f the truss s fully symmetrc and trangulated. Bendng can occur n the grder f a dagonal or brace s eccentrcally connected to t. Manly snce wnd loads are reversble, the braces n a braced frame system can undergo both compresson and tenson dependng upon the drecton of the load. Therefore, most often the braces and dagonals are desgned for the more strngent case of bucklng of the brace caused by compresson. The behavor and deformaton characterstcs of a braced frame due to lateral load can be seen n Fgure 6.1. Fgure 6.1: Braced Frame Deflecton and Framng Behavor Dr. Hanagan Sprng 2005 Senor Thess 19 Department of Archtectural Engneerng

3 Columns of a braced frame n a tall buldng would accumulate great axal forces from both gravty and lateral loads mparted to the structure. In a tall braced frame a large percentage of the frame drft s caused by flexural deformaton, also known as chord drft wth a smaller percentage of the total drft caused by axal deformaton of the braces, called shear deformaton. To control deflectons, care must be taken to proporton column members for the ncreased load caused by wnd along wth gravty loads accumulated from floors above. Ths results very large column szes much n excess of what s requred to resst gravty loads alone. Assumptons and Desgn Goals To effectvely evaluate the valdty of a braced frame soluton many factors and lmtng assumptons must be made. Assumptons made n the desgn of the braced frame system and the goals whch are to be accomplshed are as follows: Assumptons: 1. Bracng shall be confgured to maxmze space for archtectural requrements ncludng openngs for doors, buldng systems and spaces. 2. Concentrc braced frames shall be used when possble to provde for greater stffness than eccentrc braced frames. 3. Calculated ASCE 7-02 wnd loads control the strength of N-S frames. See Appendx A. 4. Calculated ASCE 7-02 wnd and sesmc load control the E-W frame as shown n Appendx A. 5. Compresson bracng controls the desgn of the braced frame system. 6. Lmtng slenderness ratos for braces: Tenson KL/r <= 300 Compresson <= P-Delta effects are accounted for n deflecton and strength desgn. Desgn Goals: 1. Intally szng truss members usng moment area method for columns and a classcal work method smlar to an mplementaton of vrtual work presented n AISC Desgn Gude 5: Low-and Medum-Rse Steel Buldngs for nput nto ETABS for analyss. 2. Desgn an effcent and least weght alternatve to a renforced core. 3. Reduce nter-story and total drft to H/480 n N-S drecton and H/1000 n E-W. 4. Mnmze mpact on nteror spaces and layouts. 5. Fnd an optmal braced frame soluton for use n further problem solutons. 6. Use chevron bracng when possble wth the apex pontng up, also called an nverted-v brace. Dr. Hanagan Sprng 2005 Senor Thess 20 Department of Archtectural Engneerng

4 Desgn Process The desgn of the braced frame starts wth ntally szng members based on gravty and lateral loads for nput nto the computer analyss program ETABS for fnal optmzaton. It s very mportant to understand the flow of forces and the behavor of a structure before utlzng the computng power of a structural analyss program. Wthout an advanced understandng of a structure and the behavor of the system, desgn output by a computer can possbly be ncorrect and could lead to serous desgn flaws f not checked thoroughly. By szng members accordng to gravty and lateral loads mparted on the structure, columns, braces and beams can be approxmated through the use of classcal work methods of analyss. Floor framng members and desgn was not expected to change dramatcally due to ths study focused drectly on the lateral system of the Hyatt Center. Therefore, smple hand calculatons (Appendx B) were used to check the composte beam capactes n a typcal bay then ncorporated nto ETABS for fnal analyss and confrmaton. The floor system conssted of approxmately 42 foot spans from the core to the spandrels wth radal beam spacng of 10 feet. The floor desgn conssted of a 5 ½ composte deck wth W18x50 as most floor members, decreasng n weght as the spans lessened towards the east and west sdes of the buldng. Spandrel beam desgns are controlled by deflecton ssues arsng from the claddng system and therefore are mostly W27x84 as the man members wth W24x76 spandrels at each corner bay. The typcal floor seen n Fgures 6.2a, b below s repeated throughout the buldng and used as the floor plate desgn durng the lateral system study to mnmze complexty n loads and calculatons. Fgure 6.2a: Composte Floor Framng Dr. Hanagan Sprng 2005 Senor Thess 21 Department of Archtectural Engneerng

5 Lateral Frame Analyss Moment-Area Fgure 6.2b: Composte Floor Framng - Sdes Intal member szes were approxmated by two methods: moment-area method to account for column deformatons or chord drft and a classcal work method adopted from AISC Desgn Gude 5 whch s a braced frame optmzaton technque. The Moment-Area method, presented n Appendx B, was used to calculate the approxmate column areas requred to resst overturnng moments caused by ASCE 7-02 wnd loads calculated prevously. The moment-area method s useful n tall frames to predct the axal forces n the columns and acts much lke the cantlever method. The overturnng moments cause larger axal forces and deformatons on the columns whch are farther from the center lne of the frame. Therefore, larger braced frames lke BF#3 and BF#4 wll acqure more loads than the smaller frames lke BF#1 or BF#2 n the N-S drecton. Frst, the structure s splt nto fve 10-story ncrements and overturnng moments, M1 through M5, labeled n Fgure 6.3 and Table 6.0 below, are found usng the controllng wnd loads. The N-S drecton was chosen to be analyzed due to the slender aspect rato of the frames n ths drecton, therefore, drft would be qute dffcult to control n ths drecton. Areas under the M/EI dagram were found usng EI as an unknown value usng equaton (6-0). ( M + M + 1 ) h A = (6-0) 2EI o Dr. Hanagan Sprng 2005 Senor Thess 22 Department of Archtectural Engneerng

6 Next the centrod of the areas was then found by equaton (6-1) and deflectons, assumng EI was an unknown, were then found through equaton (6-2). A tall buldng acts as a flexble cantlevered truss resstng overturnng moments prmarly though axal loads n the columns of a frame. The approxmate moment of nerta for the entre structure can then be found to equal the sum of the areas of a column multpled by the dstance from the center lne squared as seen n equaton (6-3). Ths s an equvalent moment of nerta and s an approxmate procedure to determne loads appled to a structure n fndng ntal member szes. The fnal drft s known to be H/480 n the N-S drecton and values were substtuted nto the deflecton equaton (6-2) leavng only the requred moment of nerta at each level as the unknown. Applyng equaton (6-3) and assumng all columns areas are equal leaves just the summaton of the dstances squared for the columns. Requred areas for columns are each level were then found and summarzed n Table 6.0 below. h ( M + 2M + 1 ) X = (6-1) 3 M + M + 1 c = = 1 j= 1 A ( h X ) + A ( H X ) (6-2) I = ( A d ) (6-3) o j 2 j Fgure 6.3: Moment-Area Method Dr. Hanagan Sprng 2005 Senor Thess 23 Department of Archtectural Engneerng

7 Overturnng Moment (kp-ft) Area/Column (n2) M6= 0 M5= A M4= A M3= A M2= A M1= A Table 6.0: Moment-Area Requred Column Areas (No Gravty) The requred column areas for each ncrement and each braced frame can be seen n Table 6.0 above. Column areas for each floor between ncrements were found by lnear extrapolaton assumng a 2-story column sze. The N-S BF #3 & BF #4 were the heavest loaded frames n the buldng, therefore, sample calculatons were completed addng gravty loads and load factors to fnd the ntal column szes. Lateral Frame Analyss Classcal Work Method Another method to calculate ntal member szng was used from AISC Desgn Gude 5. Ths s an optmzaton method for an entre braced frame usng vrtual work and multplyng ntal member szes by a correcton factor whch accounts for requred deflecton lmts. Ths method can be found complete n Appendx B. Many assumptons were made to utlze ths method, the nherent naccuraces between the actual braced frame geometry and the model geometry were assumed to be neglgble n fndng prelmnary member szes. The model assumes Chevron bracng wth the apex pontng upwards, however, ths s not actual case n many bays of the frame due to openngs requred at the corners. Therefore, the calculatons wll approxmate a drft whch s much lower than the actual drft due to the apex geometry causng bendng n the grders resultng n more drft due to bent actons. The procedure to fnd optmal areas nclude frst fndng member forces due to external (wnd) forces; second fndng member forces due to vrtual loads at the pont the deflecton s to be optmzed; thrd calculatng areas due to stran wth lambda=1.0; fourth computng the deflecton by vrtual loads wth lambda=1.0; and fnally factorng the areas by a correcton factor whch s a rato of a target deflecton and the actual calculated deflecton. Ths method gves a farly good approxmaton of member propertes; however strength desgn wll stll need to be checked n order for desgn to be fnalzed. The approxmate member szes found for the columns are compared to the members found n the Moment-Area method n Table 6.1. The areas requred for each method are very close to each other, resultng n an acceptable approxmaton n member szes usng both methods. The brace areas were ncreased at the upper floors due to small moments n the brace not accounted for n ths approxmate method. Dr. Hanagan Sprng 2005 Senor Thess 24 Department of Archtectural Engneerng

8 TABLE 4: Optmum Areas Col. No MOMENT-AREA Item COLAR GIRDAR BRACAR C.R. ACOL AGIRD ABRAC Area/Column (n2) A A A A A Table 6.1: Member Area Comparson (No Gravty Loads) Composte Column Analyss The requred column szes found by the approxmate methods of analyss are qute large compared to typcal W14 column shapes. The largest member n AISC tables s a W14x808 wth an area of 237 n 2 ; therefore, bult-up or composte columns must be desgned to wthstand the great amount of force from the numerous floors above as well at the chord acton caused by wnd loads on the frame. Composte columns must be desgned before the ntal framng szes can be placed nto ETABS for further analyss. The desgn rules for composte columns are covered by both AISC-LRFD and n the ACI buldng code, however each very slghtly n how the analyss and desgn are completed. Both agences provde methods for evaluatng strength and the lmtng effects of slenderness. Both apply to encased or concrete-flled sectons lke tubes or fabrcated shells. The AISC method assumes the composte columns are mostly lke typcal steel desgn. Analytc expressons are used for strength, stffness and slenderness effects whch lead drectly to values of axal-load capacty and beam-column capacty of composte columns. The ACI buldng code treats the secton much lke a bar renforced-concrete column and requre a stran-compatblty analyss to be performed and does not permt column desgns wthout accountng for a mnmum eccentrcty. Snce the structural redesgn s n steel and the sectons wll be a standard box shape, the AISC-LRFD method of Fgure 6.4: Typcal Box Column composte column desgn wll be utlzed. Dr. Hanagan Sprng 2005 Senor Thess 25 Department of Archtectural Engneerng

9 AISC-LRFD specfes a strct lmt of at least 4% of the gross cross-secton must be composed of structural steel. If less than 4% s not steel, the secton s treated as a concrete column and ACI desgn specfcatons apply. Composte box columns are orgnally used on the Hyatt Center due to large unbraced story heghts at the lower lobby levels and the massve loads accumulated from stores above. Snce ths type of column was orgnally used, the box shape was vared and szes were ncreased to meet archtectural layouts and resst the large axal loads. Advantages of composte columns use as compared to regular w-shapes or bultup structural shapes are realzed n large unbraced lengths and large axal loads. Ths condton exsts manly n the lower lobby and corrdor spaces of a hgh-rse snce archtects and owners would prefer vast open spaces to allow crculaton and vsual appearance to onlookers from street level. The tendency for a regular w-shape to buckle under large axal loads would ncrease as the unbraced length (KL) s ncreased. Ths causes regular columns to lose axal strength over longer story heghts. A composte column, however, ntroduces concrete to help n resstng axal loads over larger unbraced lengths. Concrete-flled columns wth 8ks compressve strength were chosen, therefore, the ncreased resstance to bucklng caused by the stffness and confnement of the concrete n the box secton caused more axal load to be absorbed wth less tendency to buckle lke ts counterpart. Axal load capacty of the column wll dmnsh as the unbraced length ncreases; however, the reducton n load s sgnfcantly smaller than a regular w-shape. Encased w-shape composte columns are another type of composte column whch was not nvestgated due to the mmense axal loads mparted on the columns. Here the encased concrete adds the stffness and resstance to bucklng, therefore, larger axal loads can exst over longer unbraced length compared wth a regular w-shape column. The axal strength desgn process for the composte columns followed AISC- LRFD Specfcaton Chapter I Composte Columns. The desgn axal strength of composte columns s determned wth smlar equatons used n steel desgn of columns except the formulas are entered wth modfed F ym, E m and r m. The modfed propertes account for the effects of concrete added to the bare steel column. The axal desgn strength s computed wth equaton (6-4) and the modfed propertes are calculated usng equatons (6-5) through (6-10) below. Φ P Φ = 0.85 and P = A F ) (6-4) c n ( c n g cr Dr. Hanagan Sprng 2005 Senor Thess 26 Department of Archtectural Engneerng

10 If λc 1.5 : F cr If λc > 1.5 : λc = = (0.658 KL r π m F E my m 2 λc ) F Fcr = F 2 λc where my my (6-5) F my = F y A r Ac + c + 1 Fyr c2 f ' c (6-6) As As Ac E = + m E c3 Ec (6-7) As The coeffcents of c1, c2 and c3 n equatons (6-6) and (6-7) above account for the stresses and strans caused by creep and shrnkage of concrete. These are found expermentally based upon the encasement or confnement of the concrete. Table 6-2 summarzes the coeffcents based upon the composte column type. Flled Column Coeffcents: Encased Column Coeffcents: c1= c2= c3= Table 6.2: Numercal Coeffcents for Desgn of Composte Columns Frst orgnal composte box column propertes and strength capactes were found. The bare steel capactes calculated were enough to satsfy the gravty load requrements for the exteror column lnes; however the columns of the braced frames need to be flled wth 8ks hgh-strength concrete to ncrease capacty to account for axal deformatons by wnd loads. Table 6.3 below summarzes the bare steel column desgn strengths and Table 6.4 summarzes the 8ks flled composte axal strength capactes of the typcal columns used n the redesgn (KL=13.5 feet). Appendx C further summarzes the desgn calculatons and strength values of 4ks and 8ks flled composte box columns over ncreasng unbraced lengths (KL). Axal force transfer nto the concrete s accomplshed by mechancal (shear studs) connectors as per AISC-LRFD Chapter I4. The number of shear studs requred s labeled n Appendx C as per equaton (6-8). V ' = V (1 A F / P ) (6-8) u u s y n Dr. Hanagan Sprng 2005 Senor Thess 27 Department of Archtectural Engneerng

11 Axal Desgn Strength of A572 Grade 50 (KL=13.5ft) Mark As Es Fy (ks) rx λc Fcr (ks) ΦcPn (kps) BX24X BX36X BX36X BX36X BX36X BX36X BX36X BX36X BX36X BX36X BX42X BX42X BX48X BX48X Table 6.3: Bare Steel Axal Desgn Strengths (KL=13.5 ) A572 Grace 50 (50ks) & f'c = 8000ps Mark As Ac %As Es Ec Em (ks) Fmy (ks) λc Fcr (ks) ΦcPn (kps) BX24X BX36X BX36X BX36X BX36X BX36X BX36X BX36X BX36X BX36X BX42X BX42X BX48X BX48X Table 6.4: 8ks Composte Axal Desgn Strengths (KL=13.5 ) Dr. Hanagan Sprng 2005 Senor Thess 28 Department of Archtectural Engneerng

12 ETABS Frame Analyss ETABS was chosen as the structural analyss software due to ts proven use n the desgn of some of the worlds most complex and tall buldng structure and the ease of object modelng of structures. The floor plan and story heghts were constructed n ETABS floor beam propertes and ntal member szes were placed nto the program. Lateral loads were then added n the form of ASCE 7-02 wnd and sesmc for strength desgn of members and ASCE 7-98 wnd tunnel analyss data and loads for servceablty checks of the structure. The braced frame core was constructed to allow for requred openngs n the core walls for elevators and spaces. Ths caused nconsstent bracng confguratons n many N-S braces as seen below n Fgure 6.5; E-W bracng can be seen n Fgure 6.6. Fgure 6.5: N-S Braced Frames: (left to rght) #1, #2, #3, #4, #5, #6 Dr. Hanagan Sprng 2005 Senor Thess 29 Department of Archtectural Engneerng

13 The N-W frames are prmarly concentrcally braced frames because braces are able to accommodate sngle door openngs n the walls. The E-W frames, however, had to accommodate double doors for elevator lobby access n many areas. Therefore, the E- W frames consst of a mxture of concentrc and eccentrcally braced bays to allow for larger openngs. Fgure 6.5: E-W Braced Frames: (left to rght) BF North, BF South Overall, the member forces were compared and desgned to meet equaton (H1-1a) or (H1-1b); members under combned forces. Members not meetng these requrements were ncreased untl member stresses were below unty. Due to the mmense sze of the structure, only a descrpton of the members n BF #4 wll be dscussed. The resultng member szes are smlar to BF #4, for economy. Dr. Hanagan Sprng 2005 Senor Thess 30 Department of Archtectural Engneerng

14 The typcal bracng members consst of W14x90 at the upper levels and W14x665 at lower levels n the concentrcally braced frames. Composte box columns were flled wth 8ks concrete to level 20 of the structure to provde extra stffness to control column deformatons caused by wnd. The E-W eccentrc braces were also W14 s that ncreased lnearly down the core structure due to very hgh shear forces near the base of the structure. Fgure 6.6 shows the 3-dmensonal geometry of the braced frame structure modeled n ETABS. Fgure 6.8 shows the axal forces n members for BF #4 usng load combnaton of (a) 1.2D+1.0L+1.3W and (b) 1.2D+1.6L. Fgure 6-9 shows the governng support reactons for BF #4 for the load combnaton 1.2D+1.0L+1.6W. A net tenson, or uplft, force of 5775 kps on the foundaton s the controllng uplft force on the deep foundatons; therefore, the deep foundaton system s stll requred for the braced core confguraton. Fgure 6.6: Braced Frame Core Structure Fgure 6.7: Axal Forces n BF #4 due to 1.2D+1.0L+1.3W (Left) and 1.2D+1.6L (Rght) Dr. Hanagan Sprng 2005 Senor Thess 31 Department of Archtectural Engneerng

15 The resultng total drft summary can be seen n Table 6-3 below. The drft was lmted to H/480 n the N-S drecton; however the overall drft after optmzaton was not acceptable. Second-order drect P-Delta analyss was ncorporated nto the drft calculatons n Table 6.3. ETABS calculates 2 nd -order effects through an exact P-Delta analyss usng the stffness matrx. P-Delta effects are especally mportant n tall hghrse structures to ensure lateral stablty and resst overturnng due to excessve deflectons. Braced Frame Drfts No P-Delta Includng P-Delta Effects Load UX UY RZ UX UY RZ N-S E-W WINDY TUNNELNS EQY H/ WINDX TUNNELEW EQX H/ A 2,381,800 kp-ft overturnng moment results from calculated ASCE 7-02 wnd loads n the N-S drecton and an 875,000 kp-ft overturnng moment n the E-W drecton. The dead load of the structure alone s enough to resst the effects of overturnng and the capacty of deep rock casson foundaton provde suffcent resstance to a maxmum upward tenson of 5750 kps n the wndward bracng columns. Results Table 6.3: Braced Frame Total Drft (nches) For the Hyatt Center, the 6 concentrcally braced frames n the N-S and the 2 eccentrcally braced frames, desgned for strength usng ASCE 7-02 wnd loads and drft checked wth the wnd tunnel analyss data, were found to be excessvely flexble. As seen n Table 6.3 above, the E-W braced frames meet the allowable drft lmt H/1000 set by the structural engneer on the project when check aganst wnd tunnel analyss data. The N-S braced frames, however, exceeded the allowable drft lmt qute consderably and alternatve means to reduce the drft n ths drecton should be taken to ether stffen the frame or engage the exteror columns n helpng to resst the overturnng moments. The aspect rato of the heght to core wdth s a very slender 14:1. However, by wdenng the effectve wdth of the vertcal truss, a more effcent and less slender (5:1) lateral system results that can possble brng the drft lmts closer to the allowable. Dr. Hanagan Sprng 2005 Senor Thess 32 Department of Archtectural Engneerng