4.1 Design of Members

Transcription

1 restressed Conrete Strutures Dr. Amlan K Sengupta and ro. Devdas Menon 4.1 Design o Members This setion overs the ollowing topis Calulation o Demand Design o Setions or Axial Tension Introdution The design o prestressed onrete members an be done by the limit states method as given in Setion 4 o IS: First, the ore demand in a member under the design loads is determined rom a strutural analysis. A preliminary size o the member is assumed or analysis. Next, the member is designed to meet the demand. I neessary, another yle o analysis and design is perormed. The ollowing material explains the alulation o the demand in a member under the design loads Calulation o Demand In the limit states method, the design loads are alulated rom the harateristis loads by multiplying them with load ators (γ ). Several types o loads are onsidered to at together under the seleted load ombinations. The load ators are inluded in the load ombinations as weightage ators. The demand in a member or a partiular type o load is obtained rom the analysis o the struture subjeted to the harateristi value o the load. The demands or the several load types are then ombined under the load ombinations, based on the priniple o superposition. Charateristis Loads For dead loads, a harateristi load is deined as the value whih has a 95% probability o not being exeeded during the lie o the struture. This onept assumes a normal distribution o the values o a partiular dead load. In the ollowing igure, the

2 restressed Conrete Strutures Dr. Amlan K Sengupta and ro. Devdas Menon shaded area above the harateristi value represents 5% probability o exeedane o the load in the design lie o the struture. Frequeny 5% probability o exeedene Mean Charateristi value Values o load Figure Idealised normal distribution or a dead load For live load, wind load and earthquake load, a harateristi load is deined based on an extreme value distribution. For example, the harateristi wind load is deined as the value whih has a 98% probability o not being exeeded during a year. Frequeny % probability o exeedene Charateristi value Annual maximum mean wind speed Figure 4-1. Extreme value distribution The harateristis loads an be obtained rom IS: (Code o ratie or Design Loads or Buildings and Strutures) and IS: (Criteria or Earthquake Resistant Design o Strutures) as ollows.

3 restressed Conrete Strutures Dr. Amlan K Sengupta and ro. Devdas Menon Table Codes overing inormation o loads Type o load Code Dead load (DL) IS: art 1 Live (imposed) load (LL) IS: art Wind load (WL) IS: art 3 Snow Load (SL) IS: art 4 Earthquake load (EL) IS: art 1 For speial loads, there are some guidelines in IS: , art 5. In addition, speialised literature may be reerred to or these loads. The speial loads are listed below. Temperature Hydrostati Soil pressure Fatigue Aidental load Impat and ollision Explosions Fire For speial situations, the loads are determined rom testing o prototype speimens. Dynami load tests, wind tunnel tests, shake table tests are some types o tests to determine the loads on a struture. Finite element analysis is used to determine the stresses due to onentrated ores and dynami loads. Load Fators and Load Combinations The load ators and the ombinations o the various types o loads are given in Table 5 o IS: The ollowing are the ombinations or the ultimate ondition. 1.5 (DL + LL) 1. (DL + LL ± WL) 1. (DL + LL ± EL) 1.5 (DL ± EL)

4 restressed Conrete Strutures Dr. Amlan K Sengupta and ro. Devdas Menon 1.5 (DL ± WL) 0.9 DL ± 1.5 EL The load ombinations or servie onditions are as ollows. DL + LL DL (LL ± EL) DL ± EL DL ± WL Analysis o Strutures Regarding analysis o strutures, IS: reommends the same proedure as stated in IS: A struture an be analysed by the linear elasti theory to alulate the internal ores in a member subjeted to a partiular type o load. Design o Members There an be more than one way to design a member. In design, the number o unknown quantities is larger than the number o available equations. Hene, some quantities need to be assumed at the beginning. These quantities are subsequently heked. The member an be designed either or the servie loads or, or the ultimate loads. The proedure given here is one o the possible proedures. The design is based on satisying the allowable stresses under servie loads and at transer. Initially, a lumpsum estimate o the losses is onsidered under servie loads. Ater the irst round o design, detailed omputations are done to hek the onditions o allowable stresses. reise values o the losses are omputed at this stage. The setion is then analysed or the ultimate apaity. The apaity should be greater than the demand under ultimate loads to satisy the limit state o ollapse.

5 restressed Conrete Strutures Dr. Amlan K Sengupta and ro. Devdas Menon 4.1. Design o Setions or Axial Tension Introdution restressed members under axial loads only, are unommon. Members suh as hangers and ties are subjeted to axial tension. Members suh as piles may have bending moment along with axial ompression or tension. Design o restressing Fore First, a preliminary dimension o the member is seleted based on the arhitetural requirement. The prestressing ore at transer ( 0 ) should be suh that the ompressive stress in onrete is limited to the allowable value. At servie, the designed prestressing ore ( e ) should be suh that the tensile stress in onrete should be within the allowable value. The amount o prestressing steel (A p ) is determined rom the designed prestressing ore based on the allowable stress in steel. At transer, in absene o non-prestressed reinorement, the stress in onrete ( ) is given as ollows. 0 =- A (4-1.1) Here, A = net area o onrete 0 = prestress at transer ater short-term losses. In presene o non-prestressed reinorement, the stress in the onrete ( ) an be alulated as ollows. 0 =- A + (E s /E )A s (4-1.) Here, A s = area o non-prestressed reinorement E s = modulus o elastiity o steel E = modulus o elastiity o onrete. At servie, the stress in onrete ( ) an be alulated as ollows. e =- ± A A t (4-1.3)

6 restressed Conrete Strutures Dr. Amlan K Sengupta and ro. Devdas Menon Here, A t = transormed area o setion = external axial ore e = eetive prestress. The external axial ore is onsidered positive i it is tension and negative i it is ompression. In the above expression, non-prestressed reinorement is not onsidered. I there is non-prestressed reinorement, A is to be substituted by (A + (E s /E ) A s ) and A t is to be alulated inluding A s. Analysis o Ultimate Strength The ultimate tensile strength o a setion ( ur ) is alulated as per Clause.3, IS: The ultimate strength should be greater than the demand due to atored loads. In absene o non-prestressed reinorement, the ultimate tensile strength o a setion ( ur ) is given as ollows. ur = 0.87pk Ap (4-1.4) In presene o non-prestressed reinorement, ur = 0.87y A s pk Ap (4-1.5) In the previous equations, y = harateristi yield stress or non-prestressed reinorement with mild steel bars = harateristi 0.% proo stress or non-prestressed reinorement with high yield strength deormed bars. pk = harateristi tensile strength o prestressing tendons. The ollowing example shows the design o a post-tensioned hanger or tension.

7 restressed Conrete Strutures Dr. Amlan K Sengupta and ro. Devdas Menon Example Design a post-tensioned hanger to arry an axial tension o DL = 300 kn (dead load inluding sel-weight) and LL = 130 kn. The dimension o the hanger is mm. Design the setion without onsidering non-prestressed reinorement. Tension is not allowed under servie loads. The grade o onrete is M 35. The age at transer is 8 days. Assume 15% long term losses in the prestress. The ollowing properties o the prestressing strands are available rom tests. Type o prestressing tendon : 7 wire strand Nominal diameter = 1.8 mm Nominal area = 99.3 mm Tensile strength pk = 1860 N/mm Modulus o elastiity = 195 kn/mm. Solution reliminary alulations at transer A A = = 6,500 mm Allowable stress or M35 onrete under diret ompression at transer,all = i = =14.3N/mm Maximum prestressing ore at transer = 0 max A = ,500 = 89,500 N

8 restressed Conrete Strutures Dr. Amlan K Sengupta and ro. Devdas Menon reliminary alulations at servie A t A = = 6,500 mm Stress in onrete e =- + A A t Allowable stress at servie Considering 15% loss t,all =0 N/mm = e Substituting the values =- + A A reliminary alulations at servie (ontinued ) Solving, 0.85 = Allowable prestress in tendon = 0.85 =506kN p0 =0.8 pk = =1488N/mm Required area o tendon A p 506,000 = 1488 = 340 mm Selet 4 strands with A p = = 397. mm restress at transer = N 0 =591kN

9 restressed Conrete Strutures Dr. Amlan K Sengupta and ro. Devdas Menon Final alulations at transer A = 6, = 6103 mm Stress in onrete 0 =- A 591,000 =- 6,103 =-9.5 N/mm <,all OK Final alulations at servie E p =195 kn/mm E = 5, = 9,580 N/mm A t 195 = 6, =64,70 mm Stress in onrete e =- + A A t ,000 ( ) 10 =- + 6,103 64,70 =-1.4 N/mm 3 No tensile stress in onrete. OK. Final alulations or ultimate strength =0.87 A ur pk p = N = kn

10 restressed Conrete Strutures Dr. Amlan K Sengupta and ro. Devdas Menon Demand under atored loads u = 1.5( ) = kn ur u OK Designed ross-setion (4) 7-wire strands with 0 = 591 kn Nominal non-prestressed reinorement is provided or resisting thermal and shrinkage raks.