An Ex­per­i­men­tal Study to Es­ti­mate Loss of Pre­stress and De­ter­min­ing Fun­da­men­tal Nat­u­ral Fre­quency of Pre­stressed Con­crete Bridge

NBM&CW - - CONTENTS - Ra­jeev Goel

In­tro­duc­tion

Pre­stressed Con­crete (PSC) is de­fined as con­crete in which there have been in­tro­duced in­ter­nal stresses [1] of such mag­ni­tudes and dis­tri­bu­tion that the stresses re­sult­ing from given ex­ter­nal load­ing are coun­ter­acted to a de­sired de­gree. Pre-stressed con­crete (PSC) struc­tures are ad­van­ta­geous in terms of de­lay­ing cracks, sav­ing ma­te­ri­als, re­duc­ing de­flec­tion etc.

How­ever, there is sub­stan­tial dif­fer­ence be­tween the de­sired and the ac­tual pre­stress­ing forces in ex­ist­ing PSC struc­tures. Hence, this dif­fer­ence leads to se­vere and crit­i­cal ser­vice­abil­ity and safety prob­lems. This dif­fer­ence in pre­stress­ing force is due to losses in pre­stress­ing force over a pe­riod of time. It is known that the loss of the pre­stress force in ten­don oc­curs due to elas­tic short­en­ing and bend­ing of con­crete, creep and shrink­age of con­crete, steel re­lax­ation, an­chor­age slip, and fric­tional loss be­tween ten­don and its sur­round­ing ma­te­ri­als. Also, the loss of the pre­stress­ing force un­ex­pect­edly oc­curs due to dam­age or break­age of pre­stress­ing strands. If this loss in the pre­stress is de­vi­at­ing from the es­ti­mated loss in the de­sign, the struc­ture will not be­have in a man­ner as en­vis­aged dur­ing the de­sign. There­fore, it is very im­por­tant to es­ti­mate the pre­stress-loss by con­sid­er­ing the fact that a pre­stressed con­crete mem­ber should keep ef­fec­tive force at each sig­nif­i­cant level of load­ing, to­gether with ap­pro­pri­ate ma­te­rial prop­er­ties for that time dur­ing the ser­vice life of the struc­ture.

To have trou­ble free ser­vice from pre-stressed con­crete struc­tures, lot of con­sid­er­a­tions are re­quired at the time of con­struc­tion. In the old ex­ist­ing bridges, dura­bil­ity as­pect was usu­ally ig­nored. Be­cause of this, many times PSC struc­tures de­velop de­fects [2] dur­ing their ser­vice life. The most com­mon prob­lems are cor­ro­sion of re­in­forc­ing steel and pre-stress­ing ca­bles, cracks de­vel­op­ment, de­flec­tion, shrink­age of con­crete, creep of con­crete, etc. These de­fects may lead to loss of pre­stress force. It is im­por­tant to note that there is no di­rect method to mea­sure loss of

Pre­stressed Con­crete (PSC) struc­tures es­pe­cially bridges are be­ing largely used all over the world due to their mul­ti­far­i­ous ad­van­tages in terms of struc­tural be­hav­iour, econ­omy as well as aes­thet­i­cal as­pects. How­ever, many PSC struc­tures de­te­ri­o­rate with time due to sev­eral fac­tors which may lead to cer­tain loss in their ini­tial ap­plied pre­stress. This loss may af­fect the struc­ture’s be­hav­iour and its ser­vice life ad­versely and need to be checked. Such loss of pre­stress re­sults in degra­da­tion of stiff­ness of the struc­ture. A pre­cise de­ter­mi­na­tion of pre­stress losses in pre­stressed con­crete mem­bers is a com­pli­cated prob­lem be­cause the rate of loss due to one fac­tor, such as re­lax­ation of ten­dons, is con­tin­u­ally be­ing al­tered by changes in stress due to other fac­tors, such as creep of con­crete, fa­tigue, etc. It has been known that any change in the stiff­ness of the struc­ture will change its nat­u­ral fre­quency also. Hence, it may be pos­si­ble to as­cer­tain the loss by mea­sure­ment of nat­u­ral fre­quency at reg­u­lar in­ter­vals. In this study, an ef­fort has been made to know the nat­u­ral fre­quency of a PSC struc­ture by Vi­bra­tion Method and de­ter­min­ing the ex­ist­ing pre­stress­ing force to as­cer­tain the loss of pre­stress.

pre-stress in old ex­ist­ing struc­tures, where ini­tial de­sign data are not avail­able.

Sev­eral re­searchers tried non­de­struc­tive eval­u­a­tion meth­ods such as vi­bra­tion test [3] to es­ti­mate pre­stress loss in the PSC bridges. Based on the var­i­ous re­searches, fol­low­ing is in­ferred [4]:

♦ Loss of the pre­stress force in the struc­ture re­sults in the change in struc­tural stiff­ness.

♦ Loss of the pre­stress force changes

vi­bra­tion char­ac­ter­is­tics of the struc­ture.

♦ The change in struc­tural stiff­ness can be es­ti­mated by mon­i­tor­ing changes in vi­bra­tion char­ac­ter­is­tics of the struc­ture.

Due to these, the­o­ret­i­cal and ex­per­i­men­tal ap­proach by us­ing Rayleigh Method i.e. as­sum­ing con­ser­va­tive sys­tem of en­ergy, cor­re­lat­ing pre­stress­ing force and nat­u­ral fre­quency is adopted for as­sess­ment in this study.

Ad­van­tages over RCC:

1. Crack­ing is highly re­duced or elim­i­nated.

2. Ap­ply­ing the pre­stress­ing forces de­vi­at­ing from the neu­tral axis in­duces mo­ments which op­pose those caused by ex­ter­nally ap­plied loads, thus sig­nif­i­cantly re­duc­ing the de­flec­tion.

3. Smaller cross-sec­tion is re­quired com­pared to RCC for the same im­posed loads.

4. Smaller foun­da­tions due to re­duc­tion in self weight

Dis­ad­van­tages over RCC:

1. The need for ex­pe­ri­enced & ex­pert builders & en­gi­neers.

2. Ini­tial cost of re­quired equip­ment is very high.

3. Pre­stressed sec­tions are brit­tle sec­tions and are less fire re­sis­tant.

Pre­stress Losses:

Pre-stress loss is noth­ing but the re­duc­tion of ini­tial ap­plied pre­stress force in the ca­ble with re­spect to time. In other words, loss in pre­stress is the dif­fer­ence be­tween ini­tial pre­stress and the ef­fec­tive pre­stress that re­mains in a mem­ber at a par­tic­u­lar in­stant of time. Fig.ure-1 shows var­i­ous losses oc­curred in the pre­stress­ing force im­me­di­ately and over a pe­riod of time [4]. The present study is con­cerned with losses oc­curred over a pe­riod of time in Post­ten­sioned sys­tems of pre­stress­ing.

Also, the var­i­ous types of losses in pre­stressed sys­tems can be cat­e­go­rized as per the oc­cur­rence of ten­sion­ing of ten­dons car­ried out be­fore or af­ter cast­ing of con­crete i.e. Pre-ten­sion­ing or Post­ten­sion­ing sys­tems of pre­stress­ing as tab­u­lated in Ta­ble-1.

In the present study, an at­tempt has been made to find the re­la­tion be­tween nat­u­ral fre­quency and pre­stress­ing force of a struc­ture for de­ter­min­ing the present pre­stress­ing force and con­se­quently loss of pre­stress [5]. The­o­ret­i­cal study is car­ried out to gen­er­al­ize a re­la­tion be­tween pre­stress­ing force (P) and fun­da­men­tal nat­u­ral fre­quency (ω1) of the struc­ture. The eval­u­a­tion of pre­stress­ing force in terms of nat­u­ral fre­quency is uti­lized be­cause it is fea­si­ble to ex­tract the nat­u­ral fre­quency of an ex­ist­ing as well as new struc­ture with the help of in­stru­men­ta­tion and other tech­niques.

So, by an­a­lyz­ing a math­e­mat­i­cal in­ter­re­la­tion­ship be­tween first fun­da­men­tal nat­u­ral fre­quency (ω1) and pre­stress­ing force (P) for a par­tic­u­lar type of struc­ture, it is pos­si­ble to es­ti­mate the ex­ist­ing force in PSC struc­ture if its fre­quency is known. The present study is done in ac­cor­dance with a study con­ducted by Wang et al [6] and by us­ing Rayleigh Method. The the­o­ret­i­cal ap­proach used in the re­ferred pa­per is based on Rayleigh’s method for get­ting an ap­prox­i­mate value of nat­u­ral fre­quency of a beam. Ex­act so­lu­tions of the model anal­y­sis prob­lems are usu­ally too cum­ber­some to ob­tain. In such sit­u­a­tions, ap­prox­i­mate meth­ods can pro­vide suf­fi­ciently ac­cu­rate re­sults to serve the pur­pose. Rayleigh’s method can be used to es­ti­mate the low­est (or fun­da­men­tal) fre­quency of a self-ad­joint (con­ser­va­tive) con­tin­u­ous sys­tem.

De­tails of Spec­i­men:

Test model re­quired for the study is avail­able at Dy­namic Heavy Test­ing lab­o­ra­tory of CSIR-CRRI at Ghazi­abad. The bridge model was con­structed in the year 2007. The su­per­struc­ture for 10 m ef­fec­tive span bridge con­sists of two lon­gi­tu­di­nal PSC gird­ers with 0.2m thick cast-in-situ RCC slab above the gird­ers. The PSC gird­ers are sim­ply sup­ported on end sup­ports. The con­crete grade adopted for the PSC girder is M45 and for the cast-in-situ RCC slab is M30 [7]. The pre­stress­ing in each PSC girder is done us­ing two ca­bles con­sist­ing of 12T13. The ca­bles are pro­vided with 75 mm in­ner di­am­e­ter (ID) and 81mm outer di­am­e­ter (OD) of Cor­ru­gated HDPE sheath­ing. The cor­rect cross sec­tion of PSC girder and plan show­ing lo­ca­tions of ac­celerom­e­ters on top of com­pos­ite bridge model shown in Fig. 2&3. Firstly, an ef­fort has been made to ex­tract the present pre­stress­ing force in the ca­bles of this bridge from the em­bed­ded load cells. Then, the nat­u­ral fre­quency of the bridge has been eval­u­ated us­ing vi­bra­tion based ex­per­i­men­tal study.

Struc­tural De­tail:

Fol­low­ing are the de­tail of the test model em­ployed for study:

Ef­fec­tive span of girder (L) i.e. centre to centre of sup­ports/bear­ings = 10.00 m Mo­ment of In­er­tial of com­pos­ite Sec­tion (I): 4810871.50 cm4

Se­lected 7 ply 12.7 mm Φ (Low re­lax­ation class-II strand, con­firm­ing IS 14268 : 1995)

Each 12 T13 ca­ble con­sists of 12 Nos. 12.7 mm Φ low re­lax­ation strands

The prop­er­ties of pre­stress ca­bles as given by the man­u­fac­turer are as fol­lows: ○ Area of each 12T13 ca­ble: 1184.40 mm2

○ Ul­ti­mate ten­sile strength: 1860.00 MPa ○ Break­ing Load of the ca­ble: 2204.00 kN ○ An­chor­age slip at stress­ing end: 6mm As per IRC:112-2011, Mod­u­lus of elas­tic­ity of con­crete (Ec ):

○ E = E = 5000 √ f MPa c con­crete ck

● Ec (M-30) = 0.27386x105 MPa

● Ec (M-45) = 0.33541x105 MPa

○ Ecj (j days) = 5000 √ fcj MPa

Mass per unit length of the beam (ρ): 1.70 ton/m

Es = 2.00 x 105 MPa

The cross sec­tional de­tails of the com­pos­ite girder show­ing ten­don lo­ca­tion are as shown in Fig.-2 and the plan show­ing lo­ca­tion of sen­sors on the com­pos­ite girder is shown in Fig.-3.

Ex­per­i­men­tal Study

In this ex­per­i­men­tal study, the pre-stress­ing force present in all the four ca­bles is mea­sured us­ing the Load Cells. The change in stress level can be known by pe­ri­od­i­cal mea­sure­ment of the same. The force in pre-stress­ing steel can be mea­sured by us­ing Vi­brat­ing Wire (VW) Load Cells or Vi­brat­ing Wire (VW) Strain Gauges. To achieve the ob­jec­tive of the study, ex­per­i­men­tal as well as the­o­ret­i­cal stud­ies have been car­ried out. In the ex­per­i­men­tal study, the pre­stress­ing force present in the ca­ble is found out by de­riv­ing read­ing from the load cell, in­stru­mented at the time of con­struc­tion. This has been done by de­ploy­ing read out unit (GK-403) for find­ing fre­quency and then cal­cu­lat­ing the load us­ing equa­tion. The nat­u­ral fre­quency of first mode of beam is ob­tained us­ing FFT an­a­lyzer af­ter vi­bra­tion study as shown in Fig.-4. While in the the­o­ret­i­cal study, a re­la­tion­ship be­tween first nat­u­ral fre­quency of beam and pre­stress­ing force in ca­bles of the beam has been es­tab­lished us­ing Rayleigh‟s method. Fi­nally a com­par­i­son be­tween mea­sured and cal­cu­lated fre­quency is done for the fea­si­bil­ity of the adopted method­ol­ogy.

In­stru­men­ta­tion of the Struc­ture and Method adopted:

Twelve ac­celerom­e­ters (PCB Piezotron­ics model T333B50), OROS FFT An­a­lyzer, and an im­pact hammer are used to know the nat­u­ral fre­quency of the beam. The FFT or Fast Fourier Trans­form an­a­lyzer is one of a use­ful tool in vi­bra­tional anal­y­sis. The FFT anal­y­sis uses the Fast Fourier Trans­for­ma­tion al­go­rithm in which a con­tin­u­ous time do­main gets con­verted to con­tin­u­ous fre­quency do­main in­clud­ing mag­ni­tude as well as phase in­for­ma­tion. Ac­celerom­e­ter is an electro­mechan­i­cal de­vice that mea­sures the ac­cel­er­a­tion forces. These forces could be static, like the con­stant force of grav­ity, or they could be dy­namic – due to mov­ing or vi­brat­ing the ac­celerom­e­ter. For ob­tain­ing the nat­u­ral

fre­quency of the post-ten­sioned beam, the adopted pro­ce­dure and set-up is shown in the Fig.-4, where the com­po­nents of data ac­qui­si­tion sys­tem has been separately shown and the func­tions of each can be clearly un­der­stood.

The fol­low­ing steps have been used for the vi­bra­tion study of the full scale com­pos­ite bridge girder:

● The beam was cleaned and lo­ca­tion for ac­celerom­e­ters marked.

● Grease is ap­plied at the sur­face where sen­sors have to be placed in or­der to make per­fect con­tact

● Twelve ac­celerom­e­ters were fixed as per the de­tail be­low (re­fer Fig.3.4):

○ 3 num­bers at Quar­ter span (to­wards roller end)

○ 3 num­bers at Mid span

○ 3 num­bers at Quar­ter span

○ 3 num­bers at sup­port over rocker

● The con­nec­tions were made be­tween ac­celerom­e­ters, an­a­lyzer and dis­player.

● Con­fig­u­ra­tion set­ting has to be done for each and ev­ery ac­celerom­e­ter be­fore in­stal­la­tion of the same.

● The Girder was then sub­jected to ham­mer­ing ef­fect us­ing the hammer.

● At sup­ports, both quar­ters and mid span, ham­mer­ing ef­fect had been given on the top of the slab so that en­tire bridge may be cov­ered.

● The Fre­quency vs Ac­cel­er­a­tion graphs were ob­tained us­ing the dis­player.

● The Fre­quency of the struc­ture is then found out from the graph.

The­o­ret­i­cal Anal­y­sis of Com­pos­ite Bridge girder:

The­o­ret­i­cal study is car­ried out to gen­er­al­ize a re­la­tion be­tween pre­stress­ing force (P) and fun­da­men­tal nat­u­ral fre­quency (ω1) of the struc­ture. So, by an­a­lyz­ing a math­e­mat­i­cal in­ter-re­la­tion be­tween first fun­da­men­tal nat­u­ral fre­quency (ω1) and pre­stress­ing force (P), it is pos­si­ble to es­ti­mate the ex­ist­ing force in PSC struc­ture if fre­quency is known [8]. The the­o­ret­i­cal ap­proach used in the re­ferred pa­per is based on Rayleigh’s method for get­ting an ap­prox­i­mate value of nat­u­ral fre­quency of a beam. Ex­act so­lu­tions of the modal anal­y­sis prob­lem are usu­ally too cum­ber­some to ob­tain [9]. In such sit­u­a­tions, ap­prox­i­mate meth­ods can pro­vide suf­fi­ciently ac­cu­rate re­sults to serve the pur­pose. Rayleigh’s method can be used to es­ti­mate the low­est (or fun­da­men­tal) fre­quency of a sys­tem. In this study, sim­ply sup­ported beam with par­a­bolic ten­don pro­file has been an­a­lyzed us­ing the math­e­mat­i­cal ap­proach as shown in Fig.-5. The same math­e­mat­i­cal ap­proach is uti­lized to an­a­lyze the sin­gle span PSC com­pos­ite girder, on which ex­per­i­men­tal stud­ies have been car­ried out. This method is used to de­ter­mine the ap­prox­i­mate value of fun­da­men­tal nat­u­ral fre­quency. This method is based on the prin­ci­ple that if the sys­tem is con­ser­va­tive, the max­i­mum ki­netic en­ergy (Tmax) is equal to the max­i­mum po­ten­tial en­ergy (Vmax). By equat­ing both Tmax and Vmax, the fun­da­men­tal nat­u­ral fre­quency ω1 can be ob­tained.

Nat­u­ral fre­quen­cies of bridges have cer­tain sen­si­tiv­ity to pre­stress­ing force [10], so the iden­ti­fi­ca­tion of ef­fec­tive pre­stress­ing force based on bridge’s nat­u­ral fre­quen­cies is an ef­fec­tive method. The be­hav­iour of pre­stressed beam can be de­scribed as a com­bi­na­tion of two sub-sys­tems: a com­pres­sive con­crete beam and a ten­sioned ca­ble. The dy­namic equi­lib­rium equa­tions of the two sub sys­tems are es­tab­lished us­ing Rayleigh Method of struc­tural vi­bra­tion anal­y­sis. Based on the cou­pling anal­y­sis and pro­cess­ing of the vi­bra­tion equa­tion of sub sys­tems, a cal­cu­la­tion method of nat­u­ral fre­quency of beam is de­rived and fun­da­men­tal fre­quency can be cal­cu­lated.

This method is used to de­ter­mine the ap­prox­i­mate value of fun­da­men­tal nat­u­ral fre­quency.

The ki­netic en­ergy of Pre­stressed Con­crete Beam is ex­pressed as: (1)

Where, ρ(x) mass per unit length, y is the har­monic mov­ing equa­tion as­sumed as: y = w(x) cosωt. w(x) is as­sumed as ver­ti­cal de­formed shape func­tion of the beam. Then the max­i­mum ki­netic en­ergy (Tmax) can be ex­pressed as:

Where M is the bend­ing mo­ment ex­pressed as: Where, ω1 = Fun­da­men­tal Nat­u­ral Fre­quency

E = Mod­u­lus of Elas­tic­ity

I = Mo­ment of In­er­tial

K = where g0 is unit weight of the beam

Re­sults

(2)

By ig­nor­ing work done by shear forces, the po­ten­tial en­ergy of the de­formed beam can be ex­pressed as: (3) (4)

(5) By sub­sti­tut­ing M and dθ from equa­tions (4) and (5) in (3), we get, the max­i­mum value of V as: (6) By putting Tmax = Vmax, the fun­da­men­tal nat­u­ral fre­quency ‘ω1’ can be ob­tained as:

(7) In this case of con­sid­ered spec­i­men for vi­bra­tion study, the ap­prox­i­mate fun­da­men­tal nat­u­ral fre­quency can be ob­tained as:

P = Pre­stress­ing force

L = Ef­fec­tive Span of Girder e1 & e2 = Ec­cen­tric­ity above and be­low neu­tral axis ρ(x) = Weight of beam per run­ning unit

By putting the val­ues of EI, K, ρ, P, L, C1, C2, e1 & e2 in equa­tion we get, ω12 = 35007.13

First Nat­u­ral Fre­quency ‘f’ of struc­ture = ω1 /2π = 29.93 Hz

Mea­sure­ment through read out unit has been car­ried out to find the val­ues of the fre­quency from load cells and then con­vert­ing it into pre­stress­ing force us­ing the equa­tion as per cal­i­bra­tion cer­tifi­cate of load cells:

Force (ton-f) = gauge fac­tor x (zero read­ing-cur­rent read­ing) / 1000

The data ob­tained from load cells are tab­u­lated in the Ta­ble-2 as be­low:

The re­sults for ex­ist­ing and ini­tial pre­stress­ing force in ten­dons are given in Ta­ble -3, loss of pre­stress along with per­cent­age loss is cal­cu­lated and tab­u­lated in Ta­ble -4 as be­low.

Based on the ini­tial ap­plied pre­stress­ing force in ten­dons and the cal­cu­lated ex­ist­ing pre­stress­ing force, loss of pre­stress can be worked out dur­ing last 10 years as given be­low in Ta­ble -4:

The loss ob­served is quite uni­form through­out. The slight vari­a­tion could be due to the ap­pli­ca­tion of suc­ces­sive pre­stress­ing in all the ca­bles. So, there might be some loss of pre­stress oc­curred in the ca­bles at the time of ap­pli­ca­tion of pre­stress. Spec­trum of the ver­ti­cal vi­bra­tion (Fre­quency vs Ac­cel­er­a­tion) has also been pro­cessed out and some of the re­sults have been shown in Graph-1 and 2. From the spec­trum, re­sults of es­ti­ma­tion of first fre­quency of vi­bra­tion for the span from this ex­per­i­men­tal study are found to be in the range of 24.00 Hz to 26.00 Hz. From the spec­trum of the ver­ti­cal vi­bra­tion, it is ob­served that the nat­u­ral fre­quen­cies for each lo­ca­tion are dif­fer­ent. It could be due to the rea­son of lo­cal stiff­ness be­cause global ex­ci­ta­tion is prob­a­bly can not achieved, so the ef­fect of lo­cal stiff­ness of gird­ers or low stiff­ness of the slab has made it of vari­able fre­quency. The the­o­ret­i­cal and ex­per­i­men­tal val­ues of fun­da­men­tal fre­quency of struc­ture are given in Ta­ble-5.

Re­sults of es­ti­ma­tion of first fre­quency of vi­bra­tion for the span from this ex­per­i­men­tal and the­o­ret­i­cal study are given in Ta­ble.6. From the graphs, it is found that the min­i­mum fre­quency mea­sured in vi­bra­tion study is 24.00 Hz.

The­o­ret­i­cal and ex­per­i­men­tal re­sults:

From the graphs, it is ob­served that the nat­u­ral fre­quen­cies for each lo­ca­tion are dif­fer­ent. It could be due to the lo­cal stiff­ness be­cause global ex­ci­ta­tion is prob­a­bly could not achieved, so the ef­fect of lo­cal stiff­ness of gird­ers or low stiff­ness of the slab has made it vari­able fre­quency. From the the­o­ret­i­cal value of nat­u­ral fre­quency, the pre­stress­ing force P1 in the ca­bles has de­ter­mined and re­spec­tive val­ues for P2, P3 and P4 have cal­cu­lated by us­ing Ta­ble.3. The val­ues for P1, P2, P3 and P4 are tab­u­lated in Ta­ble.7.

Dis­cus­sion

Test re­sults ob­tained from the­o­ret­i­cal as well as ex­per­i­men­tal stud­ies, it can be seen that the method used for es­ti­mat­ing the nat­u­ral fre­quency and pre­stress­ing force is quite sat­is­fy­ing and could be ap­pli­ca­ble for dif­fer­ent PSC struc­tures. How­ever the re­sult shows a vari­a­tion of about 21% with re­spect to ex­per­i­men­tal re­sults. This vari­a­tion could be due to the fol­low­ing rea­sons:

The ma­te­rial prop­erty of con­crete changes with time, be­cause of which cer­tain pa­ram­e­ters which depends on the ma­te­rial prop­erty of con­crete like flex­ure rigid­ity will also get changed to some ex­tent. Since these are be­ing uti­lized in the an­a­lyt­i­cal study, their vari­a­tion could have af­fected the fi­nal re­sult of es­ti­mated nat­u­ral fre­quency. Fix­ity of the sup­port bear­ings may get changed over a pe­riod of time due to var­i­ous rea­sons, which in turn changes the bend­ing mo­ment of the beam. Since, in the an­a­lyt­i­cal study, sup­ports are as­sumed to be per­fectly hinged and per­fectly roller, so ac­tual bend­ing mo­ments might be dif­fer­ent than the bend­ing mo­ments com­puted as­sum­ing to be per­fectly be­hav­ing sup­ports. Spalling of the con­crete has been ob­served in the beam at few lo­ca­tions. Thereby, the cross-sec­tion of the gird­ers also gets al­tered from the de­signed girder sec­tion.

In the the­o­ret­i­cal anal­y­sis of beam, the value of mod­u­lus of elas­tic­ity is es­ti­mated on the ba­sis of M30 and M45 grade of con­crete (which was used in con­struc­tion), dis­re­gard­ing the fact that af­ter cer­tain pe­riod of time the con­crete gained some strength.

The bridge has un­der­gone fa­tigue test­ing of more than 1.4 mil­lion cy­cles due to which dis­tress might have oc­curred.

Con­clu­sions

The fol­low­ing con­clu­sions have been de­rived from this study:

Forces in all the pre­stress­ing strands are found to be less than the ini­tial force ap­plied to these strands about 10 years ago.

The Fun­da­men­tal fre­quency of sin­gle span pre­stressed con­crete com­pos­ite girder has been de­ter­mined us­ing vi­bra­tion based dam­age de­tec­tion tech­nique and the fun­da­men­tal fre­quency of struc­ture ob­tained is in the range of 24.00 Hz to 30.00 Hz.

The­o­ret­i­cal study has also been car­ried out to de­ter­mine the nat­u­ral fre­quency of the Struc­ture and the fre­quency ob­tained as 31.63 Hz. The the­o­ret­i­cally es­ti­mated nat­u­ral fre­quency of the span is found to be more than the fre­quen­cies ob­tained from ex­per­i­men­tal study. This vari­a­tion is be­tween 15-20%, which could be due to change in bound­ary con­di­tions, ma­te­rial prop­er­ties, sec­tional prop­er­ties, sup­port con­di­tion, etc. over a pe­riod of time.

With the pas­sage of time, in fu­ture, the pre­stress will fur­ther re­duce and cor­re­spond­ingly the fun­da­men­tal fre­quency will also vary. Thus by keep­ing con­tin­u­ous or reg­u­lar mon­i­tor­ing, the re­la­tion be­tween pre­stress­ing force and fun­da­men­tal fre­quency can be es­tab­lished which can be used as an ef­fec­tive non de­struc­tive tech­nique of de­ter­min­ing pre­stress level in a PSC struc­ture.

Ac­knowl­edge­ment:

The au­thors are thank­ful to Di­rec­tor, CSIRCen­tral Road Re­search In­sti­tute, for pro­vid­ing the op­por­tu­nity to carry out the work re­ported here.

Ref­er­ences:

1. Halvonik, J., Dol­nak, J., and Bor­zovic, V., “Longterm losses of pre­stress in Pre-cast mem­bers cast from HPC.” Con­crete and Con­crete struc­tures con­fer­ence, El­se­vier, vol. 81-86, (2013).

2. Caw­ley, P., and Adams, R. D., “The lo­ca­tion of de­fects in struc­tures from mea­sure­ments of nat­u­ral fre­quency”, Jour­nal of Strain Anal­y­sis, 80(8), 49-57 (1979)23. Clough, R.W., and Pen­zien, J., Dy­namic of Struc­tures, McGraw Hill. In­stru­men­ta­tion Tech­niques to Mon­i­tor Loss of Pre­stress and Cor­ro­sion of Steel in Pre-Stressed Con­crete. Bridge and struc­ture Re­port No.-34, RDSO, 21 June 2001.

3. Kim J. T., Ryu Y.S., and Yun C.B., “vi­bra­tion-based method to de­tect pre­stress-loss in beam-type bridges.” Smart Struc­tures and Ma­te­ri­als, SPIE, vol. 5057 (2003).

4. Kim J.T., Na, W.B., Ryu, Y.S., Park, J.H., Lee, J.M., and Lee S.Y., “vi­bra­tion based dam­age mon­i­tor­ing al­go­rithms for pre­stress-loss in PSC girder Bridges” Sen­sors and Smart struc­ture tech­nolo­gies for civil, me­chan­i­cal and aero­space sys­tem, SPIE vol. 6932. (2008).

5. IS: 456:2000, In­dian Stan­dard Code of Prac­tice for Plain and Re­in­forced Con­crete, Bu­reau of In­dian Stan­dards, New Delhi, (2002).

6. Wang. T.H., Huang, R., and Wang, T.W., “The Vari­a­tion of Flex­u­ral Rigid­ity for Post-Ten­sioned Pre­stressed Con­crete Beams.” Jour­nal of Ma­rine Sci­ence and Tech­nol­ogy, Vol. 21, No. 3, pp. 300-308 (2013).

7. Li, H., Lv, Z., and Liu, J., “as­sess­ment of pre­stress force in Bridges us­ing struc­tural dy­namic re­sponses un­der mov­ing ve­hi­cles.” Math­e­mat­i­cal prob­lems in en­gi­neer­ing, vol. 2013, (2013).

8. Jain, S.K., Murty, C.V.R., and Kamle, S., “Ex­per­i­men­tal Study on Nat­u­ral Fre­quency of Pre­stressed Con­crete Beams.” RDSO (2003).

9. Sai­idi, M., Dou­glas, B., and Feng, S., “Pre­stress force ef­fect on vi­bra­tion fre­quency of con­crete bridges”, Jour­nal of Struc­tural En­gi­neer­ing,, ASCE, 120(7), 2233-2241 (1994).

10. Yaot­ing, Z., and Ruige, L., “Nat­u­ral Fre­quency of full pre-stressed con­crete beam.” Trans­ac­tion of Tian­jan Univer­sity, ISSN 1006-4982, vol. 13, No. 5, (Oc­to­ber 2007).

Fig­ure 1: Types of Pre­stress Losses

Fig­ure 2: Cross-sec­tion of Com­pos­ite PSC Girder

Fig­ure 3: Plan sow­ing lo­ca­tion of Ac­celerom­e­ters on top of RCC Slab of Bridge Model

Fig­ure 4: Nat­u­ral fre­quency mea­sure­ment scheme

Photo 1: In­stal­la­tion of ac­celerom­e­ters for vi­bra­tion study

Fig­ure 5: Sim­ply sup­ported beam with par­a­bolic duct pro­file

Graph-1: Spec­trum of the ver­ti­cal vi­bra­tion in the centre of quar­ter span (24 Hz)

Graph-2: Spec­trum of the ver­ti­cal vi­bra­tion at D/s quar­ter span (24 Hz)

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