EXAMPLE OF TIME-DEPENDENT CONCRETE ANALYSIS IN SAP2000 v14

Transcription

1 5 m EXAMPLE OF TIME-DEPENDENT CONCRETE ANALYSIS IN SAP2 v14 This is an example of a ime-dependen concree analysis using he non-linear saged consrucion feaure of SAP2. A 5 m high concree column is buil wih a circular crosssecion wih a diameer of.35 m. The column is fixed a is base and free a he op. The concree has a characerisic compressive srengh f ck = 25 MPa and is made wih limesone aggregae and slowly hardening cemen. The curing period is 2 days. A an age of 56 days a verical load of 1 kn is applied a he op of he column, which remains consan hereafer. The relaive humidiy of he amosphere is 75%. The weigh of he column will be negleced in he analysis. Obain he verical displacemen a an age of 5 days, for he following siuaions: (a) Variaion of he elasic modulus wih ime and concree creep shall be aken ino accoun. (b) Concree shrinkage shall also be considered. Fig. 1 1 kn Ø.35 m In he soluion by hand calculaion he following resuls are obained: E ci = 2888 MPa E ci (56 d) = 3457 MPa h = 175 mm cs (5 d, 2 d) =.316 (5 d, 56 d) = 1.78,adjus = 52.3 days c (56 d) = 1.4 MPa (a) The oal srain afer 5 days including creep is cs (5 d, 56 d) =.983. Therefore, he verical displacemen a he op would be z c = 4.92 mm. (b) The addiional verical displacemen due o shrinkage would be z s = 1.58 mm and he oal verical displacemen a he op would be z c + z s = 6.5 mm. Using SAP2 (link o YouTube uorial) he following resuls are obained: (a) z op = 4.87 mm by defining = 56 days (i.e., wihou adjusmen). However, if he loading age is adjused (,adjus = 52 days), hen a value z op = 4.93 mm is achieved. (b) z op = 6.5 mm (wih,adjus = 52 days). The formulaion of Model Code 199 (CEB-FIP 9) for he ime-dependen properies of concree (elasic modulus, creep and shrinkage) is presened in he following secions. UNIVERSITY OF ALICANTE Dp. of Civil Engineering Dr. F. B. VARONA 1

2 MODULUS OF ELASTICITY ACCORDING TO CEB-FIP 9 The angen modulus of elasiciy a an age of 28 days can be esimaed as follows: E ci cm Ec fcm f 1 3 E c = 215 MPa f cm = f ck + 8 MPa f cm = 1 MPa Depending on he ype of aggregae used in he mix, he angen modulus of elasiciy should be calculaed muliplying E ci () wih coefficien E, given in Table 1. Table 1. Values of coefficien E Aggregae ype E Limesone.9 Dense limesone 1.2 Quarziic 1 Sandsone.7 Basal 1.2 The angen modulus of elasiciy a an age differen from 28 days may be esimaed as follows:.5 E E E ci E ci cc ci is he age of concree (days), provided ha seasonal variaions produce mean emperaures beween -2 C and +4 C cc exp s1 s is a coefficien which depends on he ype of cemen, according o Table 2. Table 2. Values of coefficien s Rapid hardening high Normal and rapid hardening Slowly hardening cemen srengh cemen cemen s =.2 s =.25 s =.38 UNIVERSITY OF ALICANTE Dp. of Civil Engineering Dr. F. B. VARONA 2

3 CONCRETE SHRINKAGE ACCORDING TO CEB-FIP 9 The oal shrinkage of concree can be esimaed as follows:, cs s cs s s cs is he noional shrinkage coefficien is he coefficien o describe he developmen of shrinkage wih ime s s is he age of concree (days) s is he age of concree a he beginning of shrinkage The noional shrinkage coefficien cs may be obained from: wih: and wih: cs s fcm RH s cm sc cm 6 f f f cm RH RH 1 RH sc is a coefficien which depends on he ype of cemen, according o Table 3 RH is he relaive humidiy of he ambien amosphere (%) RH = 1% Table 3. Values of coefficien sc Rapid hardening high Normal and rapid hardening Slowly hardening cemen srengh cemen cemen sc = 8 sc = 5 sc = 4 The developmen of shrinkage wih ime is given by: s ss 2 35 h h s.5 UNIVERSITY OF ALICANTE Dp. of Civil Engineering Dr. F. B. VARONA 3

4 2 h is he noional size of he concree member (mm), o be calculaed as h u A c is he cross-secional area u is he perimeer of he cross-secion in conac wih he ambien amosphere h = 1 mm Ac UNIVERSITY OF ALICANTE Dp. of Civil Engineering Dr. F. B. VARONA 4

5 CONCRETE CREEP ACCORDING TO CEB-FIP 9 If he service sresses of concree in compression do no exceed.4 f cm ( ), creep is assumed o be linearly relaed o sress. The sress dependen srain may be esimaed as follows: c, c c is he consan sress applied a ime ci 1, Eci Eci E is he angen modulus of elasiciy a he ime of loading E ci is he angen modulus of elasiciy a he age of 28 days, is he creep coefficien a an age due o a consan sress applied a ime The creep coefficien can be esimaed as follows:, c is he noional creep coefficien, which may be calculaed from: 1 1 RH RH h fcm h fcm c describes he developmen of creep wih ime and is given by: c H 18 RH h wih H RH h The age a loading may have o be adjused depending on he ype of cemen, as given by:, adjus days 2 UNIVERSITY OF ALICANTE Dp. of Civil Engineering Dr. F. B. VARONA 5

6 where he values of power are given in Table 4. Table 4. Values of power Rapid hardening high Normal and rapid hardening Slowly hardening cemen srengh cemen cemen = 1 = = 1 UNIVERSITY OF ALICANTE Dp. of Civil Engineering Dr. F. B. VARONA 6

7 TIME-DEPENDENT PROPERTIES OF CONCRETE IN SAP2 v14 The ime-dependen properies for concree in SAP2 can be defined by he user according o he formulaion of he Model Code 199 (CEB-FIP 9). Alhough he final draf of Model Code 21 (published in 212) updaed he formulaion for creep and shrinkage, some recen versions of SAP2, such as v17, also refer o CEB-FIP 9. Table 5 gives he values of he CEB-FIP 9 Parameers which mus be chosen by he user in SAP2 v14. Cemen ype coefficien Table 5. CEB-FIP Parameers in SAP2.2 Rapid hardening high srengh cemen.25 Normal and rapid hardening cemen.38 Slowly hardening cemen Relaive humidiy (%) equaions in CEB-FIP 9 are valid for 4% RH < 99% Noional size, h Shrinkage coefficien, sc Shrinkage sar age (days) 2 h u Ac 8 Rapid hardening high srengh cemen 5 Normal and rapid hardening cemen 4 Slowly hardening cemen s, does no need adjusmen due o cemen ype In more recen versions of SAP2 (e.g. v17) he noional size is no defined wih he maerials. Insead, i can be defined for each of he secions. This change is arguably more reasonable. The formulaion for creep in CEB-FIP 9 is associaed o he angen modulus of elasiciy of concree. Therefore, if ime dependen analysis is performed wih SAP2, he angen modulus of elasiciy (E ci, a an age of 28 days) should be defined in he maerial propery daa form. Oherwise, when only an elasic analysis of a concree srucure is carried ou, he secan modulus of elasiciy E c may be used insead (E c =.85 E ci ). UNIVERSITY OF ALICANTE Dp. of Civil Engineering Dr. F. B. VARONA 7