SAFE DESIGN OF SLABS, BEAMS AND FOUNDATIONIS REINFORCED AND POST-TENSIONED CONCRETE Pot-Tenioned Conrete Deign Manual ISO SAF120108M5-Rev2 Berkeley, California, USA Verion 12 Deember 2010
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Content Part I Pot-Tenioning Conrete Deign Theory and Methodology Chapter 1 Introdution 1.1 Overview 1-1 1.2 Pot Tenioning Sytem in SAFE 1-1 1.3 Definition of Term 1-2 1.4 Analyi and Deign Proedure 1-3 Chapter 2 The Tendon Objet in SAFE 2.1 Overview 2-1 2.2 Tendon Geometry 2-1 2.3 Tendon Diretization 2-2 2.4 Tendon Material Property 2-3 2.5 Tendon Property 2-3 2.6 Tendon Load 2-4 i
Pot-Tenioned Conrete Deign Chapter 3 Computing Pretre Loe 3.1 Overview 3-1 3.2 Computation of Short-Term Loe 3-3 3.2.1 Stre Lo Due to Frition (Curvature and Wobble) 3-3 3.2.2 Anhorage Set Slip Loe 3-4 3.2.3 Elati Shortening of Conrete 3-6 3.3 Computation of Long-Term Loe 3-6 Chapter 4 Load Due to Pot-Tenioning 4.1 Overview 4-1 4.2 Dead Load-Balaning 4-2 4.3 Primary Moment 4-3 4.4 Seondary (Hypertati) Moment 4-4 Chapter 5 Automated Tendon Layout 5.1 Overview 5-1 5.2 Adding Tendon to a SAFE Model 5-2 5.3 Proedure Ued in Automated Tendon Layout 5-4 ii
Content Part II Pot-Tenioning Conrete Deign Code Chapter 6 Deign for ACI 318-08 6.1 Notation 6-1 6.2 Deign Load Combination 6-5 6.2.1 Initial Servie Load Combination 6-5 6.2.2 Servie Load Combination 6-5 6.2.3 Long-Term Servie Load Combination 6-6 6.2.4 Strength Deign Load Combination 6-6 6.3 Limit on Material Strength 6-7 6.4 Strength Redution Fator 6-7 6.5 Deign Aumption for Pretreed Conrete 6-8 6.6 Servieability Requirement of Flexural Member 6-10 6.6.1 Servieability Chek at Initial Servie Load 6-10 6.6.2 Servieability Chek at Servie Load 6-10 6.6.3 Servieability Chek at Long-Term Servie Load 6-11 6.6.4 Servieability Chek of Pretreing Steel 6-11 6.7 Beam Deign 6-12 6.7.1 Deign Flexural Reinforement 6-12 6.7.2 Deign Beam Shear Reinforement 6-23 6.7.3 Deign Beam Torion Reinforement 6-26 6.8 Slab Deign 6-31 6.8.1 Deign for Flexure 6-31 6.8.2 Chek for Punhing Shear 6-33 6.8.3 Deign Punhing Shear Reinforement 6-37 Chapter 7 Deign for AS 3600-01 7.1 Notation 7-1 iii
Pot-Tenioned Conrete Deign 7.2 Deign Load Combination 7-4 7.2.1 Initial Servie Load Combination 7-5 7.2.2 Servie Load Combination 7-5 7.2.3 Ultimate Limit State Load Combination 7-5 7.3 Limit on Material Strength 7-6 7.4 Strength Redution Fator 7-7 7.5 Deign Aumption for Pretreed Conrete Struture 7-7 7.6 Servieability Requirement of Flexural Member 7-8 7.6.1 Servieability Chek at Initial Servie Load 7-8 7.6.2 Servieability Chek at Servie Load 7-9 7.7 Beam Deign 7-10 7.7.1 Deign Flexural Reinforement 7-10 7.7.2 Deign Beam Shear Reinforement 7-20 7.7.3 Deign Beam Torion Reinforement 7-23 7.8 Slab Deign 7-28 7.8.1 Deign for Flexure 7-28 7.8.2 Chek for Punhing Shear 7-30 7.8.3 Deign Punhing Shear Reinforement 7-32 Chapter 8 Deign for BS 8110-97 8.1 Notation 8-1 8.2 Deign Load Combination 8-4 8.2.1 Initial Servie Load Combination 8-4 8.2.2 Servie Load Combination 8-5 8.2.3 Ultimate Limit State Load Combination 8-5 8.3 Limit on Material Strength 8-6 8.4 Partial Safety Fator 8-6 8.5 Deign Aumption for Pretreed Conrete Struture 8-7 iv
Content 8.6 Servieability Requirement of Flexural Member 8-9 8.6.1 Servieability Chek at Initial Servie Load 8-9 8.6.2 Servieability Chek at Servie Load 8-9 8.7 Beam Deign 8-10 8.7.1 Deign Flexural Reinforement 8-11 8.7.2 Deign Beam Shear Reinforement 8-21 8.7.3 Deign Beam Torion Reinforement 8-24 8.8 Slab Deign 8-27 8.8.1 Deign for Flexure 8-27 8.8.2 Chek for Punhing Shear 8-30 8.8.3 Deign Punhing Shear Reinforement 8-33 Chapter 9 Deign for CSA A23.3-04 9.1 Notation 9-1 9.2 Deign Load Combination 9-4 9.2.1 Initial Servie Load Combination 9-5 9.2.2 Servie Load Combination 9-5 9.2.3 Long-Term Servie Load Combination 9-5 9.2.4 Strength Deign Load Combination 9-6 9.3 Limit on Material Strength 9-7 9.4 Strength Redution Fator 9-8 9.5 Deign Aumption for Pretreed Conrete 9-8 9.6 Servieability Requirement of Flexural Member 9-9 9.6.1 Servieability Chek at Initial Servie Load 9-9 9.6.2 Servieability Chek at Servie Load 9-10 9.6.3 Servieability Chek at Long-Term Servie Load 9-11 9.7 Beam Deign 9-11 9.7.1 Deign Flexural Reinforement 9-11 9.7.2 Deign Beam Shear Reinforement 9-21 v
Pot-Tenioned Conrete Deign 9.7.3 Deign Beam Torion Reinforement 9-28 9.8 Slab Deign 9-33 9.8.1 Deign for Flexure 9-33 9.8.2 Chek for Punhing Shear 9-35 9.8.3 Deign Punhing Shear Reinforement 9-38 Chapter 10 Deign for Euroode 2-2004 10.1 Notation 10-2 10.2 Deign Load Combination 10-5 10.2.1 Initial Servie Load Combination 10-6 10.2.2 Servie Load Combination 10-6 10.2.3 Ultimate Limit State Load Combination 10-6 10.3 Limit on Material Strength 10-9 10.4 Partial Safety Fator 10-10 10.5 Deign Aumption for Pretreed Conrete Struture 10-11 10.6 Servieability Requirement of Flexural Member 10-12 10.6.1 Servieability Chek at Initial Servie Load 10-12 10.6.2 Servieability Chek at Servie Load 10-13 10.7 Beam Deign 10-13 10.7.1 Deign Flexural Reinforement 10-14 10.7.2 Deign Beam Shear Reinforement 10-25 10.7.3 Deign Beam Torion Reinforement 10-28 10.8 Slab Deign 10-33 10.8.1 Deign for Flexure 10-33 10.8.2 Chek for Punhing Shear 10-35 10.8.3 Deign Punhing Shear Reinforement 10-37 10.9 Nationally Determined Parameter (NDP) 10-40 Chapter 11 Deign for Hong Kong CP-04 11.1 Notation 11-1 vi
Content 11.2 Deign Load Combination 11-4 11.2.1 Initial Servie Load Combination 11-4 11.2.2 Servie Load Combination 11-5 11.2.3 Ultimate Limit State Load Combination 11-5 11.3 Limit on Material Strength 11-5 11.4 Partial Safety Fator 11-6 11.5 Deign Aumption for Pretreed Conrete Struture 11-7 11.6 Servieability Requirement of Flexural Member 11-8 11.6.1 Servieability Chek at Initial Servie Load 11-8 11.6.2 Servieability Chek at Servie Load 11-9 11.7 Beam Deign 11-10 11.7.1 Deign Flexural Reinforement 11-10 11.7.2 Deign Beam Shear Reinforement 11-21 11.7.3 Deign Beam Torion Reinforement 11-24 11.8 Slab Deign 11-27 11.8.1 Deign for Flexure 11-28 11.8.2 Chek for Punhing Shear 11-30 11.8.3 Deign Punhing Shear Reinforement 11-33 Chapter 12 Deign for IS 1343-1980 12.1 Notation 12-1 12.2 Deign Load Combination 12-4 12.2.1 Initial Servie Load Combination 12-5 12.2.2 Servie Load Combination 12-5 12.2.3 Ultimate Limit State Load Combination 12-5 12.3 Limit on Material Strength 12-6 12.4 Partial Safety Fator 12-7 12.5 Deign Requirement of Pretreed Conrete Struture 12-7 12.5.1 Limit State of Collape 12-7 12.5.2 Limit State of Servieability 12-8 vii
Pot-Tenioned Conrete Deign 12.6 Maximum Compreion Chek 12-9 12.6.1 Maximum Compreive Stre at Tranfer 12-9 12.6.2 Maximum Compreive Stre Under Servie Condition 12-9 12.7 Beam Deign 12-10 12.7.1 Deign Flexural Reinforement 12-10 12.7.2 Deign Beam Shear Reinforement (Torion Exluded) 12-20 12.7.3 Deign Beam Shear Reinforement (Torion Inluded) 12.23 12.8 Slab Deign 12-25 12.8.1 Deign for Flexure 12-26 12.8.2 Chek for Punhing Shear 12-27 12.8.3 Deign Punhing Shear Reinforement 12-29 Chapter 13 Deign for NZ 3101:06 13.1 Notation 13-1 13.2 Deign Load Combination 13-5 13.2.1 Initial Servie Load Combination 13-5 13.2.2 Servie Load Combination 13-5 13.2.3 Long-Term Servie Load Combination 13-5 13.2.4 Ultimate Limit State Load Combination 13-6 13.3 Limit on Material Strength 13-6 13.4 Strength Redution Fator 13-7 13.5 Deign Aumption for Pretreed Conrete Struture 13-8 13.6 Servieability Requirement of Flexural Member 13-9 13.6.1 Servieability Chek at Initial Servie Load 13-9 13.6.2 Servieability Chek at Servie Load 13-10 13.6.3 Servieability Chek at Long-Term Servie Load 13-11 viii
Content 13.6.4 Servieability Chek of Pretreing Steel 13-11 13.7 Beam Deign 13-11 13.7.1 Deign Flexural Reinforement 13-12 13.7.2 Deign Beam Shear Reinforement 13-22 13.7.3 Deign Beam Torion Reinforement 13-24 13.8 Slab Deign 13-29 13.8.1 Deign for Flexure 13-29 13.8.2 Chek for Punhing Shear 13-31 13.8.3 Deign Punhing Shear Reinforement 13-33 Chapter 14 Deign for Singapore CP 65:99 14.1 Notation 14-1 14.2 Deign Load Combination 14-4 14.2.1 Initial Servie Load Combination 14-4 14.2.2 Servie Load Combination 14-5 14.2.3 Ultimate Limit State Load Combination 14-5 14.3 Limit on Material Strength 14-6 14.4 Partial Safety Fator 14-6 14.5 Deign Aumption for Pretreed Conrete Struture 14-7 14.6 Servieability Requirement of Flexural Member 14-8 14.6.1 Servieability Chek at Initial Servie Load 14-8 14.6.2 Servieability Chek at Servie Load 14-9 14.7 Beam Deign 14-10 14.7.1 Deign Flexural Reinforement 14-10 14.7.2 Deign Beam Shear Reinforement 14-21 14.7.3 Deign Beam Torion Reinforement 14-24 14.8 Slab Deign 14-28 14.8.1 Deign for Flexure 14-28 14.8.2 Chek for Punhing Shear 14-30 ix
Pot-Tenioned Conrete Deign Chapter 15 Deign for AS 3600-09 14.8.3 Deign Punhing Shear Reinforement 14-34 15.1 Notation 15-1 15.2 Deign Load Combination 15-4 15.2.1 Initial Servie Load Combination 15-5 15.2.2 Servie Load Combination 15-5 15.2.3 Ultimate Limit State Load Combination 15-5 15.3 Limit on Material Strength 15-6 154 Strength Redution Fator 15-7 15.5 Deign Aumption for Pretreed Conrete Struture 15-7 15.6 Servieability Requirement of Flexural Member 15-8 15.6.1 Servieability Chek at Initial Servie Load 15-8 15.6.2 Servieability Chek at Servie Load 15-9 15.7 Beam Deign 15-10 15.7.1 Deign Flexural Reinforement 15-10 15.7.2 Deign Beam Shear Reinforement 15-20 15.7.3 Deign Beam Torion Reinforement 15-23 15.8 Slab Deign 15-28 15.8.1 Deign for Flexure 15-28 15.8.2 Chek for Punhing Shear 15-31 15.8.3 Deign Punhing Shear Reinforement 15-33 Referene x
Chapter 1 Introdution 1.1 Overview Part I of thi manual deribe the methodology and deign algorithm performed by SAFE for the analyi and deign of pot-tenioned trutural lab and beam. It preent the method ued by SAFE to model tendon objet, pretre loe, pot-tenioning load, and the automation of tendon layout. There are two poible way to apply pretreing to onrete, namely, pottenioning and pre-tenioning. SAFE onider only the pot-tenioning of lab and beam. The pot-tenioning tendon may be bonded or unbonded. 1.2 Pot-Tenioning Sytem in SAFE In SAFE, tendon element are ued to provide the pot-tenioning. Tendon an be plaed anywhere and in any plan diretion (ee Chapter 5). Eah tendon onit of a peifi number of trand. Figure 1-1 provide a hemati of the apet involved in inluding pot-tenioning, from material definition through to detailed output. Overview 1-1
Pot-Tenioned Conrete Deign Tendon Material Tendon Propertie Tendon Load (Jaking fore) Lo Calulation Parameter Tendon Objet Draw Tendon Edit Tendon Auto Tendon Layout Fore due to Tendon Analyi Other load and option Strength and Capaity Deign Servieability Deign Output Strength Deign Output Detailing Output Figure 1-1 Shemati of pot-tenioning ytem and proe Speifi analyi and deign proedure ued in SAFE are intended to omply with the relevant deign ode, a preented in Part II of thi manual. 1.3 Definition of Term Term ued in thi manual, within the ontext of pretreed onrete, are a follow: 1-2 Definition of Term
Chapter 1 - Introdution Pretreed Conrete - Thi term refer to onrete that ha been preompreed, often before appliation of other load, and in thi manual refer to pot-tenioning only. Pot-Tenioning - A proedure in whih the teel tendon are tenioned after the onrete ha been at. Tendon Objet - Conit of a number of high-trength teel wire or trand enveloped by a dut, plaed anywhere in the lab or beam. Pot-Tenioning Load - The fore that the tendon exert on the truture. Thi inlude both the vertial load due to tendon profile and end fore due to anhorage of the tendon. The fore due to frition lo i uniformly ditributed along the length of the tendon. Self Weight - Weight of the truture due to gravity, omputed automatially by SAFE from objet dimenion and peified denity of material. 1.4 Analyi and Deign Proedure After a SAFE model ha been ompleted and all of the material property and etion property definition, model geometry (inluding tendon layout, profile, and jaking fore aignment), member aignment, and loading riteria have been peified, an analyi i ready to be performed. During the analyi phae, SAFE will alulate reation, member diplaement, beam fore, lab fore, and lab tree for all peified load pattern and ombination. SAFE then perform a deign in aordane with the peified deign ode and alulate the required amount of mild teel reinforement and arrie out the appropriate punhing hear hek. SAFE automate everal lab and mat deign tak. Speifially, it integrate lab deign moment aro deign trip and deign the required reinforement; it hek lab punhing hear around olumn upport and onentrated load; and it deign beam flexural, hear, and torion reinforement. The deign proedure are deribed in the hapter entitled "SAFE Deign Feature in the Key Feature and Terminology manual. The atual deign algorithm vary baed on the peifi deign ode hoen by the uer. Part II of thi manual deribe the algorithm ued for the variou ode. Analyi and Deign Proedure 1-3
Pot-Tenioned Conrete Deign It hould be noted that the deign of pot-tenioned reinfored onrete lab i a omplex ubjet and the deign ode over many apet of thi proe. SAFE i a tool to help the uer in thi proe. Only the apet of deign doumented in thi manual are automated by SAFE deign apabilitie. The uer mut hek the reult produed and addre other apet not overed by SAFE. 1-4 Analyi and Deign Proedure
Chapter 2 The Tendon Objet in SAFE 2.1 Overview Tendon are a peial type of objet that an be embedded in onrete element to repreent the effet of pot-tenioning. Thee tendon objet pa through lab and beam objet, attah to them, and impoe load upon them. The tendon are modeled a independent element. Any number of tendon may be defined. Eah tendon i drawn or defined a a type of line objet between two joint, i and j. The two joint mut not hare the ame loation in pae. The two end of the tendon are denoted end I and end J, repetively. The tendon may have an arbitrary urved or egmented hape in three dimenion between thoe point. 2.2 Tendon Geometry The vertial profile of a tendon an be defined or modified uing the form hown in Figure 2-1. Overview 2-1
Pot-Tenioned Conrete Deign Figure 2-1 Tendon Vertial Profile form, ue to define or modify the tendon profile If a vertial profile i not peified, SAFE will provide a default profile uing the maximum drape allowed by the learane ondition peified for the lab top and bottom. The automated tendon layout apabilitie alo automate the tendon profile, a deribed in Chapter 5. 2.3 Tendon Diretization A tendon may be a long objet with ompliated geometry, but internally, it will be diretized automatially into horter egment for the purpoe of analyi. The maximum length of thee diretization egment i peified a the maximum meh ize uing the Run menu > Meh Option ommand. Thee length an affet how the tendon load the truture and the auray of the analyi reult. It i reommended that horter length be ued for tendon with highly urved geometry or for tendon that pa through part of the truture with ompliated geometry or hange in propertie. If unure what value to ue, try everal different length to evaluate the effet on the reult. 2-2 Tendon Diretization
Chapter 2 - The Tendon Objet in SAFE 2.4 Tendon Material Property The material propertie for tendon are defined in term of the weight denity, modulu of elatiity (E), minimum yield tre (f y ), and minimum tenile tre (f u ). Ue the Define menu > Material ommand, Add New Material button, and the form hown in Figure 2-2 to peify the tendon material propertie. Multiple propertie an be peified if neeary. Figure 2-2 Material Property Data form 2.5 Tendon Property The tendon property ontain the trand area and tendon material type. Sine tendon an repreent ingle or multiple trand, the area of only a ingle trand hould be peified in the Tendon Property Data form, hown in Figure 2-3, whih i aeed uing the Define menu > Tendon Propertie ommand and the Add Property button. The number of trand i peified when aigning tendon propertie or editing a tendon (refer to the repetive Aign or Edit menu ommand). Tendon Material Property 2-3
Pot-Tenioned Conrete Deign 2.6 Tendon Load Figure 2-3 Tendon Property Data form After the tendon have been added to the SAFE model, tendon load an be peified. Load an be aigned to a ingle tendon or multiple tendon by firt eleting the tendon to be loaded, eleting the Aign menu > Load Data > Tendon Load ommand, and then modifying the data in the form hown in Figure 2-4. Figure 2-4 Tendon Load form 2-4 Tendon Load
Chapter 2 - The Tendon Objet in SAFE The load pattern name, jaking loation, and tendon jaking tre are defined in thi form. The tendon load (jaking tre) i the total load applied to one or both end of the tendon. The atual tendon fore will vary along the length of the tendon a governed by the fritional and other lo parameter. Tendon loe an be aigned to a ingle tendon or multiple tendon by firt eleting the tendon, eleting the Aign menu > Load Data > Tendon Loe ommand and then modifying the data in the form hown in Figure 2-5. Figure 2-5 Tendon Loe form Tendon Load 2-5
Chapter 3 Computing Pretre Loe 3.1 Overview The tendon load for a given load ae refer to the uer-defined jaking fore. The atual load that i applied to lab and beam will be le than the jaking fore beaue of pretre loe. The pretre loe are ategorized in SAFE into hort-term loe and long-term loe, a follow: Short-term or Streing loe - Thee are loe that our during and immediately after the pot-tenioning operation and are aued by frition between the tendon and the dut, elati hortening, and eating of anhor. Long-term loe - Thee type of loe happen over time and alo may be referred to a time-dependent loe and inlude reep, hrinkage, and teel relaxation. Uing the Aign menu > Load Data > Tendon Loe ommand diplay the form hown in Figure 3-1 and allow the pretre loe to be peified uing one of three method. Overview 3-1
Pot-Tenioned Conrete Deign Figure 3-1 Tendon Load form The firt two Lo Calulation Method on the form an be ued to peify the pretre loe a a fore perentage or fixed tre value for the Streing Loe and Long-Term Loe. The third option allow a more detailed alulation of the pretre loe baed on a number of input value for both Short- Term and Long-Term Loe. Fritional loe are omputed internally and expliitly by SAFE baed on the peified wobble and urvature oeffiient. All other loe are diretly input on thi form. Other fator, uh a hange in temperature and flexing of the truture under loading, do not ignifiantly lower the pretre level and are not onidered expliitly. Undertanding the tre ditribution along the length of a member with repet to hort-term or long-term effet i important for orretly analyzing the model and interpreting the reult. The pretre loe are evident in term of the tre ditribution along the length, a hown in Figure 3-2. The atual 3-2 Overview
Chapter 3 - Computing Pretre Loe variation in tre varie exponentially in aordane with Eqn 3.1 in the following etion. P g line TENDON P Figure 3-2 Pretre load variation along tendon length The jaking tre i ommonly peified a 0.80f pu, where f pu i the peified ultimate trength of the trand. Figure 3-2 how a repreentation of the tendon fore variation with the tendon jaked from the left end. If the tendon were to be jaked from the right end, Figure 3-2 would be revered. If the tendon were jaked from both end, the maximum initial pretre fore (jaking fore) would exit at eah end and would vary to a minimum value midway along the length of the tendon. The initial pretre fore are redued to the final pretre fore in aordane with the long-term loe peified and hown diagrammatially a the Final Pretre in Figure 3-2. 3.2 Computation of Short-Term Loe 3.2.1 Stre Lo Due to Frition (Curvature and Wobble) When "Baed on Detailed Calulation" i the Lo Calulation Method eleted, the fritional loe are alulated uing the urvature and wobble oef- Computation of Short-Term Loe 3-3
Pot-Tenioned Conrete Deign fiient peified by the uer. The fritional lo due to urvature i alulated in SAFE a: ( Kx) P(X) Pe 0, where (Eqn. 3.1) = urvature frition oeffiient = um of the tendon angular hange from the tendon jaking end to a ditane x K = wobble frition oeffiient (rad/unit length 2 ) P (X) = Pot-tenioning fore at a ditane x P 0 = Pot-tenioning fore at treing The pot-tenioning loe due to frition reult in a fore ditribution along the length of the tendon that i exponentially dereaing from the jaking point. In the empirial oeffiient, K i the umulative effet of the rigidity of the heathing, the diameter of the heathing, the paing of the heath upport (Figure 3-3), the tendon type, and the heath type, inluding the form of ontrution. Atual profile due to wobbling intended profile Sheath upport a = intended angle hange Figure 3-3 Wobble frition lo 3.2.2 Anhorage Set Slip Loe At the lat tage of the treing operation, the tendon uually are anhored with two-piee onial wedge. Anhoring operation normally reult in an additional pretre lo due to eating of the wedge, onidering that the trand retrat when it i releaed and pull the wedge into the anhoring devie. 3-4 Computation of Short-Term Loe
Chapter 3 - Computing Pretre Loe Calulation of the tre loe i typially performed in an iterative manner. A hown in Figure 3-4, the ditane refer to the extent of influene of an anhor et. Proedurally, anhor et i hoen firt (uually about 0.25 to 0.375 in or 6 to 8 mm), then the ditane i et, and finally the orreponding tre i omputed, with the aumption that the tree vary linearly from the jaking point. Jaking Fore, Pj Lok off Fore Fore dx Tendon Fore Pj Pa Px x a Anhor Set of Influene Figure 3-4 Anhor et influene ditane diagram The eating lo i then alulated uing the following equation: ( j x) dx SL a (Eqn. 3.2) E Computation of Short-Term Loe 3-5
Pot-Tenioned Conrete Deign The iteration proe top when the alulated eating lo i almot equal to the anhor et a ; then the maximum tre i alulated, a follow: max ( ) (Eqn. 3.3) j j x Further, the elongation hall be alulated a follow: a ( P P ) dx x AE a (Eqn. 3.4) where Δ a i the elongation aoiated with the aumed anhor et ditane a ; P x i the tendon fore at a ditane x from the jaking point; P a i the fore in the tendon under jaking tre at the aumed anhor et ditane a ; dx i the length of the element along the tendon; A i the ro-etional area of the tendon; and E i the modulu of elatiity of the tendon material. 3.2.3 Elati Shortening of Conrete Elati hortening refer to the hortening of the onrete a the pot-tenioning fore i applied. A the onrete horten, the tendon length alo horten, reulting in a lo of pretre. If equential jaking tep are ued, the firt tendon jaked and loked off will uffer the maximum amount of lo from elati hortening. Converely, there will be no lo beaue of elati hortening for the lat tendon in a equene or in a ingle tendon beaue the elati hortening will take plae before the tendon i loked into the anhoring devie. The uer-peified amount of pretre lo from elati hortening i applied uniformly over the entire length of the tendon. 3.3 Computation of Long-Term Loe The long-term pretre loe of a member inlude reep, hrinkage, and teel relaxation effet. Several method an be ued to determine the long-term tre loe; however, SAFE relie on the uer-defined value input in the Tendon Loe form hown in Figure 3-1. Lump um value input into SAFE hould reflet the appropriate ondition that exit for the truture being modeled. Creep, hrinkage, and 3-6 Computation of Long-Term Loe
Chapter 3 - Computing Pretre Loe teel relaxation effet are governed by material propertie and, in ome ae, other environmental ondition that need to be aounted for when peifying the long-term lo value. Eah tre lo i treated eparately and then ummed up, a follow: TL = CR + SH + RE (Eqn. 3.7) where TL i the total lo of tre; CR i the tre lo due to reep of the onrete; SH i the tre lo due to hrinkage of the onrete; and RE i the tre lo due to relaxation in the tendon teel. The um of thee loe i applied to the initial (jaking) load of the tendon, a repreented in Figure 3-2. All of the long-term loe are uniformly applied over the length of the tendon. Computation of Long-Term Loe 3-7
Chapter 4 Load Due to Pot-Tenioning 4.1 Overview SAFE doe not rely on an approximate equivalent loading method for alulating member repone ubjeted to pot-tenioning load. Intead, SAFE ue a finite element method that inlude the tendon effet a a load. When a paraboli drape i peified for the tendon, SAFE perform a numerial integration aro the finite element uing the atual paraboli hape funtion that define the tendon geometry. Thi approah i onidered to be more aurate, epeially when deeper member are being onidered. One of the onequene of applying a pot-tenioning load to a member i the introdution of eondary (hypertati) fore. Thee effet and load ae are diued in thi hapter. SAFE ue the dead load aning method a the primary proedure for the determination of tendon profile when they are requeted to be automated (ee Chapter 5). Thi hapter alo provide information regarding the approah ued to perform a load aned deign. Overview 4-1
Pot-Tenioned Conrete Deign 4.2 Dead Load-Balaning The dead load aning method i ued in SAFE to determine an initial tendon layout (inluding the profile, number of trand, and the jaking fore) when the automated tendon layout feature i ued. The bai onept of dead load aning i that the pretre bending tree, f Pe/ S, are equal but oppoite to the applied dead load bending tree, f M/ I. When the Self Load Balaning Ratio and the Preompreion Level in the Quik Tendon Layout form, hown in Figure 4-1, are peified, SAFE iterate the poition of the tendon a neeary to find the eentriity, e, that ane the peified dead load tree. Figure 4-1 Quik Tendon Layout form The tre diagram in Figure 4-2 illutrate the dead load aning onept. The peified preompreion limit tre i applied firt, (a). Then the dead load tree are omputed, (b), followed by iterating the tendon loation to ane the dead load tree, (), that finally reult in the preompreion tate hown in (d). The final tre ditribution i the reult of thi preompreion tre ombined with the tree reulting from the appliation of all remaining load and deign ombination. If the final tre ditribution ontain tenion tree that exeed the deign allowable limit, SAFE alulate the required amount of 4-2 Dead Load-Balaning
Chapter 4 - Load Due to Pot-Tenioning mild teel reinforement. Chapter 5 detail the tep ued by SAFE in the automation of the tendon layout. Figure 4-2 Preompreion and Load Balaning Stree 4.3 Primary Moment If a etion ut i made of a uniformly loaded beam, the ation at the ut etion will inlude the onentri fore P x, a primary moment M p, and a hear V x. The primary moment at thi etion i neeary to maintain equilibrium of the loading, whih an be expreed a: M p ( wdx) x PL a (Eqn. 4.1) where, w, i the intenity of loading at a ditane x, P L i the vertial omponent of tendon fore at the left anhorage, and a i the ditane to the ut etion meaured from the left anhorage. Similarly, a free-body diagram of the tendon would how the onentri fore P x and a hear V x at the ut etion, along with the loading w. In the ame Primary Moment 4-3
Pot-Tenioned Conrete Deign manner, the fore P x taking moment about the CGC line from an eentriity e or the ditane from the tendon entroid to the neutral axi of the member yield: P e' ( wdx x P a (Eqn. 4.2) x ) L The right-hand ide of Eqn. 4.1 and 4.2 are idential, therefore the primary moment an be defined a: M p Px e' (Eqn. 4.3) 4.4 Seondary (Hypertati) Moment The reation aued by the pot-tenioning fore in ontinuou lab or beam are often referred to a eondary (hypertati) reation. The two-pan beam hown in Figure 4-3 illutrate the reation and moment beaue of the eentri pot-tenioning fore. If the enter upport i eliminated for the two-pan beam hown in Figure 4-3, the appliation of the pot-tenioning would reult in a beam upward diplaement of. The appliation of the fore neeary to diplae the beam by the amount,, an be repreented a, R i. From Figure 4-3 (d) and (e), the hypertati reation in the amount R i /2 are produed at eah end of the beam and the hypertati moment M i produed over the enter upport. At any etion along the beam, the hypertati reation indue a hypertati moment M hyp and a hypertati hear V hyp. Hypertati analyi reult an be reviewed by defining a hypertati load ae uing the Define menu > Load Cae ommand to add a new load ae with a hypertati Load Cae Type, a hown in Figure 4-4. 4-4 Seondary (Hypertati) Moment
Chapter 4 - Load Due to Pot-Tenioning P g line TENDON P (a) Two-pan pot-tenioned beam Px Px (b) Tendon fore aue the beam to lift off the enter upport with a defletion Δ upward Px Px Ri/2 Ri/2 () Additional hypertati reation develop at the end due to appliation of the fore, R i, whih i needed to prevent the beam from lifting off the upport Ri Ri Ri/2 Ri/2 (d) Seondary (hypertati) reation R i in a theoretial, imply upported beam (e) Seondary (hypertati) moment diagram due to R i Figure 4-3 Seondary (hypertati) ation due to pot-tenioning Seondary (Hypertati) Moment 4-5
Pot-Tenioned Conrete Deign Figure 4-4 Hypertati Load Cae Data form In the deign proe, the eondary moment i aumed to be reited through a ompreion blok and a tenile fore uh that: C T (Eqn. 4.4) M e Tz Cz (Eqn. 4.7) where C i the total ompreion fore, T i the ombined tenion fore due to pot-tenioning tendon and mild reinforement, and Z i the lever arm of the etion, a illutrated in Figure 4-5. PL Conrete Compreion C Px Z T Tendon Fore R Ri Figure 4-5 Setion ation due to pot-tenioning and internal ditribution of hypertati fore Thu, the ombination of fore tipulated in mot deign ode for gravity ondition imply onider the addition of the hypertati effet to the ombination ued for non-pretreed onrete. 4-6 Seondary (Hypertati) Moment
Chapter 5 Automated Tendon Layout 5.1 Overview In the pat, the analyi and deign of pot-tenioned floor lab ha been diffiult beaue of the high degree of indeterminay of the truture, large number of deign requirement, and the need to provide an eonomial deign. Some analyi program rely on implified approximation in the analyi and the deign. SAFE eliminate the need for engineer to overimplify an analyi model and provide the tool to automate the tendon layout, profile, and jaking fore. Thi hapter deribe the variou method for adding tendon to a SAFE model and the methodology ued to automate the tendon input data. Not all of the method ued to add tendon to a SAFE model are uited for the automation a explained herein. The automation of tendon layout, profile, and jaking fore erve a a tarting point in the analyi and deign proe. If it i neeary to make further adjutment to the tendon layout, profile, or jaking fore, thee adjutment hould be made manually. SAFE doe not perform any reviion to the initial tendon automation. The parameter related to the tendon an be modified eaily, followed by re-analyzing and re-deigning the truture a neeary. Overview 5-1
Pot-Tenioned Conrete Deign 5.2 Adding Tendon to a SAFE Model Four method are available for adding tendon to a SAFE model: Template modeling If a SAFE model i initialized uing the File menu > New Model ommand and the appropriate initial model i eleted along with toggling the Add P/T option, pot-tenioning data an be defined. The Quik Tendon Layout form hown in Figure 5-1 allow peifiation of the tendon layout for the Layer A and B diretion, a well a the preompreion level and elf-load aning ratio. Tendon with the defined layout parameter are then inluded in the template model. Thi an be a quik and eay method to plae a large number of tendon into a SAFE model. The tendon profile atify the peified learane. Figure 5-1 Quik Tendon Layout form Figure 5-2 how two of everal tendon layout option uing banded and uniform tendon layout type. 5-2 Adding Tendon to a SAFE Model
Chapter 5 - Automated Tendon Layout Figure 5-2 Template model with tendon layout option Tendon Draw ommand Uing the Draw menu > Draw Tendon ommand, any number of point an be input to plae tendon into a SAFE model. Default tendon profile data i provided; however, it i expeted that it will be edited to provide the proper tendon profile and other tendon data a required to atify the deign requirement. Multiple tendon with the ame layout an be generated eaily uing the Edit menu > Repliate ommand. When thi option i ued, SAFE repliate the tendon profile of the oure tendon. Note: No automation of the tendon layout, profile, number of trand, or jaking fore i performed by SAFE when the Draw menu > Draw Tendon ommand i ued to plae tendon in a model. Add Tendon in Strip The Edit menu > Add/Edit Tendon > Add Tendon in Strip ommand an be ued to add tendon to an exiting SAFE model. The tendon layout, profile, number of trand, and jaking fore are all automated when tendon are added in thi manner, baed on the input in the Quik Tendon Layout form hown in Figure 5-3. The SAFE model an be further modified by adding additional tendon a neeary. Add Tendon in Beam The Edit menu > Add/Edit Tendon > Add Tendon in Beam ommand an be ued to add a ingle tendon to a beam, with a default profile. The tendon profile, number of trand, and jaking fore hould then be edited a required. Adding Tendon to a SAFE Model 5-3
Pot-Tenioned Conrete Deign Figure 5-3 Quik Tendon Layout form 5.3 Proedure Ued in Automated Tendon Layout The automated tendon layout (inluding profile, number of trand, and jaking fore) are generated baed on the deign trip definition. Automated tendon layout are developed only on tendon that have been added to deign trip. Eah trip i modeled a an equivalent ontinuou beam with the roetion derived from the lab objet lying within the trip width. The elf weight load are alulated to obtain the load to be ued in the load aning alulation. Only the load that are applied within the boundary area of a partiular trip are inluded in the determination of the automated tendon layout. A an example, if a olumn trip i defined a 60 inhe wide, only a tributary width of 60 inhe i ued to determine the load for ue in the elf load aning alulation to determine the tendon layout. A repreentative tendon i plaed in the equivalent beam, entered on the deign trip. The upport of the trip are derived from the interetion with perpendiular deign trip and by any olumn upport within the trip width. Note: SAFE doe not automatially onider the interetion of trip and beam to be point of upport for the trip. If it i deired to onider a partiular beam a a upport point for a trip, then a trip hould be defined at the beam loation. 5-4 Proedure Ued in Automated Tendon Layout
Chapter 5 - Automated Tendon Layout The upport loation are ued to determine the pan. For eah pan, the tendon profile i automated baed on the profile type peified for the tendon (parabola or revere parabola). An iterative proedure i then ued to determine the effetive jaking fore neeary to atify the range of dead load to be aned and the average preompreion tre required. The jaking fore i initially alulated to atify the minimum required elf load aning ratio and minimum preompreion level for the longet pan in the trip. The tendon profile in other pan are then adjuted o a not to exeed the maximum dead load aning ratio. A value of 60 to 80 perent i generally ued a the elf load aning ratio. Typially preompreion level generally range between 0.125 to 0.275 ki. Note: It i important to note that it i poible that an automated tendon layout annot atify the peified dead load aning ratio and preompreion level. In uh ae, SAFE generate a warning o that neeary manual adjutment to the tendon layout and profile an be made, or other modifiation to the SAFE model an be applied where required. Note: If the addition of partial tendon i ative, SAFE may add additional tendon in long pan or in exterior pan to atify the elf load aning and preompreion ontraint. After the total jaking fore and profile have been determined for the equivalent tendon, the atual number and paing of tendon i determined baed on the following riteria: For a banded tendon layout, the number of tendon i initially determined baed on the peified Tendon Property (material property and trand area), Preompreion Level, and Dead Load Balaning Ratio. The pretre loe are etimated uing the Fixed Stre Value from the Tendon Load aignment. If the number of tendon i too large to fit within the band width with a minimum paing of 12 in (300 mm), a larger tendon ize i automatially eleted by inreaing the number of trand. Similarly, if the paing of the tendon i too large (greater than 60 in or 1.5 m) or 16 time the lab thikne, a maller tendon i eleted, with fewer trand. For a uniform tendon layout, a imilar proedure a outlined above for the banded tendon layout i ued. Proedure Ued in Automated Tendon Layout 5-5
Chapter 6 Deign for ACI 318-08 Thi hapter deribe in detail the variou apet of the pot-tenioned onrete deign proedure that i ued by SAFE when the uer elet the Amerian ode ACI 318-08 [ACI 2008]. Variou notation ued in thi hapter are lited in Table 6-1. For referening to the pertinent etion of the ACI ode in thi hapter, a prefix ACI followed by the etion number i ued. The deign i baed on uer-peified load ombination. The program provide a et of default load ombination that hould atify the requirement for the deign of mot building type truture. Englih a well a SI and MKS metri unit an be ued for input. The ode i baed on inh-pound-eond unit. For impliity, all equation and deription preented in thi hapter orrepond to inh-pound-eond unit unle otherwie noted. 6.1 Notation The following table identifie the variou notation ued in thi hapter. Notation 6-1
Pot-Tenioned Conrete Deign Table 6-1 Lit of Symbol Ued in the ACI 318-08 Code A p Area enloed by the outide perimeter of the etion, in 2 A g Gro area of onrete, in 2 A l Total area of longitudinal reinforement to reit torion, in 2 A o A oh Area enloed by the hear flow path, q-in Area enloed by the enterline of the outermot loed tranvere torional reinforement, q-in A p Area of pretreing teel in flexural tenion zone, in 2 A Area of tenion reinforement, in 2 A' Area of ompreion reinforement, in 2 A (required) Area of teel required for tenion reinforement, in 2 A t / Area of loed hear reinforement per unit length of member for torion, q-in/in A v Area of hear reinforement, in 2 A v / a a b a max b b f b w b 0 b 1 b 2 b Area of hear reinforement per unit length of member, in 2 /in Depth of ompreion blok, in Depth of ompreion blok at aned ondition, in Maximum allowed depth of ompreion blok, in Width of member, in Effetive width of flange (T-beam etion), in Width of web (T-beam etion), in Perimeter of the punhing ritial etion, in Width of the punhing ritial etion in the diretion of bending, in Width of the punhing ritial etion perpendiular to the diretion of bending, in Depth to neutral axi, in Depth to neutral axi at aned ondition, in 6-2 Notation
Chapter 6 - Deign for ACI 318-08 Table 6-1 Lit of Symbol Ued in the ACI 318-08 Code d Ditane from ompreion fae to tenion reinforement, in d' Conrete over to enter of reinforing, in d e d d p E E f' f' i f pe f p f pu f py f t f y f y h h f 0 M n Effetive depth from ompreion fae to entroid of tenion reinforement, in Thikne of lab (T-beam etion), in Ditane from extreme ompreion fiber to entroid of pretreing teel, in Modulu of elatiity of onrete, pi Modulu of elatiity of reinforement, aumed a 29,000,000 pi (ACI 8.5.2) Speified ompreive trength of onrete, pi Speified ompreive trength of onrete at time of initial pretre, pi Compreive tre in onrete due to effetive pretre fore only (after allowane of all pretre loe), pi Stre in pretreing teel at nominal flexural trength, pi Speified tenile trength of pretreing teel, pi Speified yield trength of pretreing teel, pi Extreme fiber tre in tenion in the preompreed tenile zone uing gro etion propertie, pi Speified yield trength of flexural reinforement, pi Speified yield trength of hear reinforement, pi Overall depth of a etion, in Height of the flange, in Deign moment reitane of a etion with tendon only, N- mm Notation 6-3
Pot-Tenioned Conrete Deign Table 6-1 Lit of Symbol Ued in the ACI 318-08 Code M n M u N P u T u V V max V u V 1, max p,min f v Deign moment reitane of a etion with tendon and the neeary mild reinforement to reah the aned ondition, N-mm Fatored moment at etion, lb-in Tenion fore in onrete due to unfatored dead load plu live load, lb Fatored axial load at etion, lb Spaing of the hear reinforement along the length of the beam, in Fatored torional moment at etion, lb-in Shear fore reited by onrete, lb Maximum permitted total fatored hear fore at a etion, lb Fatored hear fore at a etion, lb Shear fore reited by teel, lb Fator for obtaining depth of ompreion blok in onrete Ratio of the maximum to the minimum dimenion of the punhing ritial etion Strain in onrete Maximum uable ompreion train allowed in extreme onrete fiber (0.003 in/in) Strain in pretreing teel Strain in reinforing teel Minimum tenile train allowed in teel reinforement at nominal trength for tenion ontrolled behavior (0.005 in/in) Strength redution fator Fration of unaned moment tranferred by flexure Fration of unaned moment tranferred by eentriity of hear 6-4 Notation
Chapter 6 - Deign for ACI 318-08 Table 6-1 Lit of Symbol Ued in the ACI 318-08 Code Shear trength redution fator for light-weight onrete Angle of ompreion diagonal, degree 6.2 Deign Load Combination The deign load ombination are the variou ombination of the load ae for whih the truture need to be deigned. For ACI 318-08, if a truture i ubjeted to dead (D), live (L), pattern live (PL), now (S), wind (W), and earthquake (E) load, and onidering that wind and earthquake fore are reverible, the load ombination in the following etion may need to be onidered (ACI 9.2.1). For pot-tenioned onrete deign, the uer an peify the pretreing load (PT) by providing the tendon profile or by uing the load aning option in the program. The default load ombination for pot-tenioning are defined in the following etion. 6.2.1 Initial Servie Load Combination The following load ombination i ued for heking the requirement at tranfer of pretre fore, in aordane with ACI 318-08 laue 18.4.1. The pretreing fore are onidered without any long-term loe for the initial ervie load ombination hek. 1.0D + 1.0PT (ACI 18.4.1) 6.2.2 Servie Load Combination The following load ombination are ued for heking the requirement of pretre for ervieability in aordane with ACI 318-08 laue 18.3.3, 18.4.2(b), and 18.9.3.2. It i aumed that all long-term loe have already ourred at the ervie tage. 1.0D + 1.0PT 1.0D + 1.0L + 1.0PT (ACI 18.4.2(b)) Deign Load Combination 6-5
Pot-Tenioned Conrete Deign 6.2.3 Long-Term Servie Load Combination The following load ombination are ued for heking the requirement of pretre in aordane with ACI 318-08 laue 18.4.2(a). The permanent load for thi load ombination i taken a 50 perent of the live load. It i aumed that all long-term loe have already ourred at the ervie tage. 1.0D + 1.0PT 1.0D + 0.5L + 1.0PT (ACI 18.4.2(b)) 6.2.4 Strength Deign Load Combination The following load ombination are ued for heking the requirement of pretre for trength in aordane with ACI 318-08, Chapter 9 and 18. The trength deign ombination required for hear deign of beam and punhing hear require the full PT fore (primary and eondary). Flexural deign require only the hypertati (eondary) fore. The hypertati (eondary) fore are automatially determined by SAFE by ubtrating out the primary PT moment when the flexural deign i arried out. 1.4D + 1.0PT * (ACI 9.2.1) 1.2D + 1.6L + 1.0PT * (ACI 9.2.1) 1.2D + 1.6(0.75 PL) + 1.0PT * (ACI 9.2.1, 13.7.6.3) 0.9D 1.6W +1.0PT * 1.2D + 1.0L 1.6W + 1.0PT * (ACI 9.2.1) 0.9D 1.0E + 1.0PT * 1.2D + 1.0L 1.0E + 1.0PT * (ACI 9.2.1) 1.2D + 1.6L + 0.5S + 1.0PT * 1.2D + 1.0L + 1.6S + 1.0PT * (ACI 9.2.1) 1.2D + 1.6S 0.8W + 1.0PT * 1.2D + 1.0L + 0.5S 1.6W + 1.0PT * (ACI 9.2.1) 1.2D + 1.0L + 0.2S 1.0E + 1.0PT * (ACI 9.2.1) * Replae PT by H for flexural deign only 6-6 Deign Load Combination
Chapter 6 - Deign for ACI 318-08 The IBC 2006 bai load ombination (Setion 1605.2.1) are the ame. Thee alo are the default deign load ombination in SAFE whenever the ACI 318-08 ode i ued. The uer hould ue other appropriate load ombination if roof live load i treated eparately, or if other type of load are preent. 6.3 Limit on Material Strength The onrete ompreive trength, f', hould not be le than 2500 pi (ACI 5.1.1). The upper limit of the reinforement yield trength, f y, i taken a 80 ki (ACI 9.4) and the upper limit of the reinforement hear trength, f yt, i taken a 60 ki (ACI 11.5.2). SAFE enfore the upper material trength limit for flexure and hear deign of beam and lab or for torion deign of beam. The input material trength are taken a the upper limit if they are defined in the material propertie a being greater than the limit. The uer i reponible for enuring that the minimum trength i atified. 6.4 Strength Redution Fator The trength redution fator,, are applied on the peified trength to obtain the deign trength provided by a member. The fator for flexure, hear, and torion are a follow: t = 0.90 for flexure (tenion ontrolled) (ACI 9.3.2.1) = 0.65 for flexure (ompreion ontrolled) (ACI 9.3.2.2(b)) = 0.75 for hear and torion. (ACI 9.3.2.3) The value of varie from ompreion-ontrolled to tenion-ontrolled baed on the maximum tenile train in the reinforement at the extreme edge, t (ACI 9.3.2.2). Setion are onidered ompreion-ontrolled when the tenile train in the extreme tenion reinforement i equal to or le than the ompreionontrolled train limit at the time the onrete in ompreion reahe it aumed train limit of.max, whih i 0.003. The ompreion-ontrolled train Limit on Material Strength 6-7
Pot-Tenioned Conrete Deign limit i the tenile train in the reinforement at the aned train ondition, whih i taken a the yield train of the reinforement, (f y /E) (ACI 10.3.3). Setion are tenion-ontrolled when the tenile train in the extreme tenion reinforement i equal to or greater than 0.005, jut a the onrete in ompreion reahe it aumed train limit of 0.003 (ACI 10.3.4). Setion with t between the two limit are onidered to be in a tranition region between ompreion-ontrolled and tenion-ontrolled etion (ACI 10.3.4). When the etion i tenion-ontrolled, t i ued. When the etion i ompreion-ontrolled, i ued. When the etion i in the tranition region, i linearly interpolated between the two value (ACI 9.3.2). The uer i allowed to overwrite thee value. However, aution i advied. 6.5 Deign Aumption for Pretreed Conrete Strength deign of pretreed member for flexure and axial load hall be baed on aumption given in ACI 10.2. The train in the reinforement and onrete hall be aumed diretly proportional to the ditane from the neutral axi (ACI 10.2.2). The maximum uable train at the extreme onrete ompreion fiber hall be aumed equal to 0.003 (ACI 10.2.3). The tenile trength of the onrete hall be negleted in axial and flexural alulation (ACI 10.2.5). The relationhip between the onrete ompreive tre ditribution and the onrete train hall be aumed to be retangular by an equivalent retangular onrete tre ditribution (ACI 10.2.7). The onrete tre of 0.85f' hall be aumed uniformly ditributed over an equivalent-ompreion zone bounded by edge of the ro-etion and a traight line loated parallel to the neutral axi at a ditane a = 1 from the fiber of maximum ompreive train (ACI 10.2.7.1). 6-8 Deign Aumption for Pretreed Conrete
Chapter 6 - Deign for ACI 318-08 The ditane from the fiber of maximum train to the neutral axi, hall be meaured in a diretion perpendiular to the neutral axi (ACI 10.2.7.2). Elati theory hall be ued with the following two aumption: The train hall vary linearly with depth through the entire load range (ACI 18.3.2.1). At raked etion, the onrete reit no tenion (ACI 18.3.2.1). Pretreed onrete member are invetigated at the following three tage (ACI 18.3.2): At tranfer of pretre fore At ervie loading At nominal trength The pretreed flexural member are laified a Cla U (unraked), Cla T (tranition), and Cla C (raked) baed on f t, the omputed extreme fiber tre in tenion in the preompreed tenile zone at ervie load (ACI 18.3.3). The preompreed tenile zone i that portion of a pretreed member where flexural tenion, alulated uing gro etion propertie, would our under unfatored dead and live load if the pretre fore wa not preent. Pretreed onrete i uually deigned o that the pretre fore introdue ompreion into thi zone, thu effetively reduing the magnitude of the tenile tre. For Cla U and Cla T flexural member, tree at ervie load are determined uing unraked etion propertie, while for Cla C flexural member, tree at ervie load are alulated baed on the raked etion (ACI 18.3.4). A pretreed two-way lab ytem i deigned a Cla U only with f t 6 f ' (ACI R18.3.3); otherwie, an over-treed (O/S) ondition i reported. Deign Aumption for Pretreed Conrete 6-9