Long term losses in pre-stressed concrete member as per IS 1343:2012 and IS 1343:1980

Transcription

1 Long term losses in pre-stressed concrete member as per IS 1343:2012 and IS 1343:1980 P Markandeya Raju and T Raghuram Sandeep In prestressed concrete structures, Creep and Shrinkage of concrete and Relaxation of prestressing steel are long term phenomena and cause gradual loss of compression in concrete and tension in prestressing steel Their inaccurate estimation leads to serviceability problems like excessive camber and cracking of concrete While revising IS 1343:1980, many modifications were incorporated in time dependent losses There is a need to understand the background of these changes before applying and this article is a beginning in this direction After discussing various parameters affecting Long term losses, the calculations involved and inferences on results were presented A typical example explaining calculation of losses based on both codes is also presented 1 Introduction Losses in prestressed concrete structures can be categorised as shown in Table 1 In properly designed and manufactured members, the loss of stress due to Creep, Shrinkage and Relaxation of steel account for major portion of the total loss So their magnitudes are vital in arriving at the residual prestress A reasonably accurate prediction of these losses is important to ensure satisfactory performance of structures in service If prestress losses are underestimated, the tensile strength of concrete can exceed under service loads, causing cracking and unexpected excessive deflection On the other hand, overestimating prestress losses can lead to excessive camber and an uneconomical design To determine with precision the extent of the losses from them is a challenging task The scientific model presented in [1] the new code (IS 1343:2012) provides an accurate mathematical model that is in line with Model Code 90 [2] (CEB MC-90) The objective of this paper is to discuss in detail, each parameter of long term loss as mentioned in the new code (IS 1343: 2012) and to explain them with a typical example based on assumed data The results are compared with those obtained based on old code [3] (IS 1343:1980) Table 1 Categorisation of losses Instantaneous Losses or Initial Losses of Prestress Time Dependent Losses or Final Losses of Prestress 1 Loss of prestress due to Elastic deformation of beam 1 Loss of prestress due to Bending of the beam 2 Loss of prestress due Anchorage slip 3 Loss of prestress due to Friction between tendon and duct (a) Curvature effect (b) Wave effect or Length effect 4 Losses of prestress due to Controlled prestressing force 5 Loss of prestress due to Elongation of the tendon 2 Loss of prestress due to Relaxation or creep of prestressing steel 3 Loss of prestress due to Shrinkage in the beam 4 Loss of prestress due to Temperature changes 48 The Indian Concrete Journal June 2017

2 2Creep in concrete Creep in concrete is associated with time, level of applied stress, density of concrete, cement content, water cement ratio, thickness of the elements and atmospheric conditions like humidity and temperature Creep is particularly important in prestressed concrete as the continued long term shortening of concrete in compression leads to reduction in prestressing force The creep strain is proportional to elastic strain at lower stress levels in concrete Hence most of the statutory codes express creep strain as a factor times elastic strain and the factor is called Creep co-efficient Several factors influence creep of concrete Some of the most important factors influencing creep are presented, with an emphasis on those factors that are most important for evaluating residual prestress 21 Age at loading The strength of concrete increases with time due to the hydration of the cement ie, creep decreases with age at loading Creep is inversely proportional to the degree of hydration, and hence the type of cement will influence the creep For instance, at the same age of loading, the use of slow-hardening cement will increase creep compared with the use of standard Portland cement At higher prestress levels, creep stress is not proportional to Elastic stress and the rate of change of creep with Elastic stress increases and the variation is non-linear as shown in Figure 1 In addition, other factors which influence the hydration of the cement, such as water/cement ratio, moisture conditions and temperature, will also affect the creep at a given age of loading Assuming a constant stress state in the concrete, the gain in strength with time reduces the creep since the stress-strength ratio will decrease The age at loading will also decrease the contribution from the drying creep on the total strains since most of the drying of the concrete would have already occurred without affecting the creep behaviour 22 Untensioned reinforcement The untensioned reinforcement in concrete has a restraining effect on the creep strain as some of the concrete stress will be transferred to reinforcement as the long-term strains due to creep and shrinkage develop They will reduce the prestress loss in the tendons but not the loss of stress in concrete Oh et al (1995) studied the effect of different reinforcement ratios on creep of high-strength concrete and observed that the reduction of creep strain in concrete with reinforcement ratios of 064% and 178% was 15% and 33% respectively [5,6] (Figure 2) 23 Size The main influence of size on creep is in drying state (after curing period) The size of the structure affects the drying rate and thus the drying creep rate Creep decreases as the volume to surface ratio increases A possible explanation for the size effect on creep is that since the drying is much slower for larger structures, the hydration in the inner parts of the structure will continue and thus relatively higher concrete strength is achieved, which reduces creep, when the drying process initiates [6] The Indian Concrete Journal June

3 24 Properties of concrete The properties of concrete that have significant influence on creep are those which affect the strength development in concrete ie, water-cement ratio and type and fineness of cement Considering the same age at loading and applied stress, the use of different types of cement will influence creep Slow-hardening cements will exhibit the largest creep strains and rapid- hardening cements, the lowest Another property worth mentioning is the fineness of cement which also influences the development of concrete strength The finer the cement, the higher the specific surface area and faster is the rate of development of strength Similarly the aggregate content of the concrete will have a restraining effect on the creep deformations since the aggregate does not undergo creep The most frequently used aggregates, such as granite and gneiss, have very low volume change and significantly high modulus of elasticity and thus higher restraining capacity than the cement paste This lowers the creep in concretes with higher aggregate content 25 Relative humidity Relative humidity is defined as the ratio of partial pressure of water vapour to the equilibrium or saturated vapour pressure A concrete member is said to be in moisture equilibrium if the moisture in the surrounding air is same as that in the member The ambient relative humidity that is in moisture equilibrium with the surrounding air will have very low influence on creep in concrete The higher the relative humidity, lesser the drying and hence resulting in lower creep values However, the moisture content of the concrete specimen will influence creep The lower the moisture content the lower the creep Results from several studies indicate that completely dry specimens exhibit significantly lower or no creep than those containing small amounts of moisture Further as temperature increases, equilibrium vapour pressure increases and hence relative humidity decreases In IS 1343:1980, ultimate creep coefficients are presented for different ages of loading These recommendations are only for structures where losses need not be evaluated at various stages They are not valid for evaluation of residual prestress or deflection or camber in structures at various stages of stressing/loading/measuring IS 1343:1980 has no mention of the effect of relative humidity and element thickness on loss of prestress Although IS 1343:2012 calculates creep coefficient for a given relative humidity and element thickness, accurate prediction of relative humidity on the day of loading during design calculations is not practically possible Further there is a need to incorporate the effect of untensioned reinforcement in the model for the determination of creep co-efficient Majority of the short comings of IS 1343:1980 are addressed in IS 1343:2012 with a scientific mathematical model that incorporates various parameters However, this model is valid only if stress in concrete does not exceed onethird of characteristic compressive strength of concrete and concrete should be of normal concrete ranging from M30 to M60 These models are not applicable for special concretes [1] 3 Shrinkage in concrete Concrete starts to lose moisture and undergoes a change in volume (due of chemical reaction between cement and water) towards the end of curing period This phenomenon, known as concrete shrinkage, starts to develop rapidly after the end of the curing period Excess water in concrete evaporates and cement matrix around aggregate contracts Shrinkage is basically divided into two components namely Autogenous shrinkage and drying shrinkage Autogenous shrinkage occurs during early hydration and is caused by the internal consumption of water during hydration as the hydration products occupy less volume than the unhydrated cement and water [7] Drying shrinkage is caused by loss of water from concrete to the atmosphere [7] Generally this loss of water is from the cement paste, but with a few types of aggregates (with high water absorption), the main loss of water contributing to the drying shrinkage of concrete is from aggregate Drying shrinkage is relatively slow and the stress it induces when restrained is partially relieved by tensile creep The rate of drying shrinkage is dependent upon the relative humidity of the surrounding air and the element geometry The drying shrinkage is partially reversible, ie upon rewetting; the swelling strains will be less than the preceding shrinkage strains [6] Similar to creep, shrinkage also depends on various factors that are presented below 31 Properties of concrete Generally, higher the water-cement ratio, greater is the shrinkage The water content in concrete has maximum influence on shrinkage as it is proportional to the amount of water that can leave the pore system of concrete The increase in cement content at constant water-cement ratio also increases shrinkage This is because, the hydrated cement occupies less volume than cement paste in concrete Another factor which influences the shrinkage is aggregate content Since the aggregate is minimally affected by moisture changes in concrete, it does not shrink and thus has a restraining effect on concrete 32 Untensioned reinforcement Similar to the effect of aggregate, untensioned reinforcement has a restraining effect on shrinkage of concrete In prestressed 50 The Indian Concrete Journal June 2017

4 concrete, shrinkage is unrestrained as untensioned steel is not considered for evaluating losses There may be a reduction in shrinkage loss if the effect of untensioned reinforcement is considered Oh et al (1995) studied the effect of different reinforcement ratios on shrinkage of concrete and observed that the reduction of shrinkage strain in concrete with reinforcement ratios of 064 % and 178% was 14% and 30% respectively [5,6] 33 Size The size of a concrete member mainly influences the drying rate and there by the rate of shrinkage significantly It also has an effect on the final shrinkage strain The influence of size on shrinkage of a concrete member is proportional to the volume to surface ratio, ie ratio of volume of member to the surface in contact with surrounding air The lower the ratio, faster is the development of shrinkage But the final shrinkage strain decreases with increase in volume to surface ratio, which means that final shrinkage strain is size dependent [6] 34 Relative humidity The moisture content of the concrete specimen if not in moisture equilibrium with ambient relative humidity will have influence on drying shrinkage The lower the moisture content the lower is the shrinkage because the rate of drying is faster IS 1343:1980 defines the values of ultimate shrinkage strain depending on age of loading alone and states that it has to be increased by 50% under dry atmospheric conditions for posttensioned members Whereas IS 1343:2012 has incorporated various parameters affecting shrinkage as discussed above However, the new model as per revised code does not factor in, the age of loading which is true to the practical situation 4 Relaxation of steel Under sustained loading of prestressing force, the strand steel gradually relaxes The resulting reduction in prestress is called Relaxation loss Relaxation loss increases with prestress and temperature The relaxation losses of lowrelaxation strands are considerably less than the loss in normal-relaxation strand Relaxation of a prestressing strand depends on the stress level in the strand However, because of other prestress losses, there is a continuous reduction of the strand stress, which causes a reduction in relaxation [6] To understand the process of calculation of long-term losses a typical example is considered for study 5 Example problem A post-tensioned concrete beam shown in Figure 3 is stressed on 7 th day Span of the beam = 200 m Diameter of strand = 95 mm Number of strands =10 Grade of concrete = M35 Curing period = 5 days Relative humidity (RH) = 80% Loss due elastic shortening = 5% Nominal cover to steel = 75 mm Live load =10 kn/m Age at which live load is subjected on the beam = 45 days The following are evaluated 1 Residual prestress on 28, 45, 70, 90, days when all strands are stressed on 7 th day (Single stage stressing) 2 Residual prestress on 28, 45, 70, 90, days when 5 strands are stressed on 7 th day and remaining 5 strands on 28 th day (Multistage stressing) 51 Creep As per Clause 625 of IS 1343:2012, creep loss is evaluated based on creep co-efficient method The final creep coefficient given in the Table of Clause 625 can also be arrived by equations given in the same clause and corresponding sub-clauses The final creep co-efficient given in the table corresponds to grade of concrete ranging from M30 to M60, subject to the condition that the compressive stress does The Indian Concrete Journal June

5 not exceed 036f ck These values can be used where the end results are not sensitive to precise values The creep co-efficient is given by RH = Relative humidity of the ambient environment in percentage h o = notional factor (Approximately the distance travelled by water molecule from the centre point of the cross-section to the surface of the concrete) it is given by = Creep strain at time t>t o = Initial strain at loading = = Initial time of loading The creep coefficient is given by = Area of cross-section (mm 2 ) = The perimeter of the member in contact with the atmosphere or exposed to drying (mm) where = = Notional creep co-efficient to which the creep coefficient reaches asymptotically with time (this value can be taken as value reached in 70 years) = a factor to allow for the effect of concrete strength on the notional creep coefficient = Co-efficient describing development with time The notional creep co-efficient = is given by = a factor to allow for the effect of concrete age at loading on the notional creep coefficient = a factor to allow for the effect of relative humidity on the notional creep coefficient = 228 (from 7 th day to infinity) Table 2 Notional creepco-efficient t, days ( (IS 1343:2012) (IS 1343:1980) Similarly the ultimate or notional creep co-efficients are evaluated for 28,45,70,90, 365 and infinity (70 years ie = 25550) days and presented in the Table 2 Creep co-efficient is directly proportional to creep loss The values from the table clearly indicate that the members which are stressed at the early age will have more loss due to creep and loss decreases with the increase in the age of loading Creep co-efficient as per IS 1343:1980 is given in Clause 5251 for age of loading on 7 th, 28 th and 365 th day Co-efficients for remaining days are interpolated and presented in Table 2 For this case study it can be observed that the old code underestimates the creep co-efficient values for age of 52 The Indian Concrete Journal June 2017

6 loading up to 45 days and over estimates after then The development of creep with time is given in Clause 6252 of IS 1343:2012 as follows [ where ] t = age of concrete in days at the moment considered, t o = age of concrete at loading in days, = coefficient depending on relative humidity (RH in percentage) and notional member size (h 0 in mm) RH = relative humidity expressed as percentage RH 0 = 100 (ie 100% of the relative humidity) RH = relative humidity expressed as percentage In the present case, member is stressed on 7 th day and losses are evaluated on 28 th day [ ] The co-efficient 038 is a fraction of the ultimate creep coefficient that has occurred from 7 th day to 28 th day ie creep co-efficient for 7 to 28 days is 038 x 228 =085 Similarly creep co-efficient for respective days are evaluated and presented in Table 3 Table 3 Creep co-efficient for various intervals ( (As per IS 1343:2012) t, days Stressed on 7 th day Stressed on 28 th day Creep co-efficient cannot be estimated in respective intervals with respect to IS 1343:1980 as there are no guidelines to arrive at creep co-efficient for evaluating residual prestressing force at various stages 52 Shrinkage As per IS 1343:2012 Clause 624 Total shrinkage strain is given by where = total shrinkage strain = drying shrinkage strain = autogeneous shrinkage strain Table mentioned in the Clause 6242 of IS 1343:2012 gives the values of autogeneous shrinkage strain with respect to grade of concrete These values have been multiplied by 10 6 and hence it has to be divided by 10 6 to get the actual values This strain is the ultimate strain or total autogeneous shrinkage strain that a member will experience it its life time Whereas the development of autogeneous shrinkage with time is given by equation mentioned in Clause 6244 which is as follows ( ) where, t = time in days = Total strain occurred at a given point of time = co-efficient describing autogeneous shrinkage with time = Autogeneous shrinkage strain that can occur in a member in its life time In the present case, for M35 grade concrete, the autogeneous shrinkage strain from the table in Clause 6242 is The autogeneous shrinkage strain is computed for different time intervals and presented in Table 4 The co-efficient gives the fraction of autogeneous shrinkage that has occurred upto t days For example co- The Indian Concrete Journal June

7 efficient for 7 days is 041 which indicates that 41% of the total autogeneous shrinkage ( ) has occurred upto 7 th day Remaining 59% will occur from 7 th day to th day The summation of column 3 in Table 4 gives the total percentage of autogeneous shrinkage strain that has occurred from 0 days to days which is always 100% ie factor 100, and summation of column 4 gives the total autogeneous shrinkage strain that occurred from 0 days to days ie Drying Shrinkage Drying shrinkage generally begins at the end of curing period Drying shrinkage is given by Clause 6243 of IS 1343:2012 as follows where, = Total drying shrinkage strain that a member will undergo in its life time ie for 70 years percentage (50 and 80) These values are given in the table of Clause 6243 of IS 1343:2012 IS 1343:2012 is not clear on source from which RH has to be considered Hence in general 50% can be considered for internal members of the building or structure which are not exposed to atmosphere and 80% for components which are exposed to atmosphere In the present case study M35 grade concrete and RH = 80% are considered From the table in Clause 642 for M35 grade of concrete, is obtained as after interpolation Drying shrinkage strain at infinity (70 years = days) is given by = = The development of drying shrinkage strain with time is given by Clause 6245 as follows = coefficient depending on notional size h o and the values of k h for corresponding h o are given in table of Clause 6243 of IS 1343:2012 where, h o = notion factor = mm From table of Clause 6243, after interpolation k h = 0987 = unrestrained drying shrinkage which depends on grade of concrete and relative humidity (RH) expressed in terms of = total drying shrinkage strain occurred at a given point of time t in days = co-efficient describing the drying shrinkage with time Table 4 Autogeneous shrinkage strain t, days CoeffDescribingautogeneous shrinkage Coeff of autogeneous strain with time ( (t )) shrinkage strain occurred as during the interval Autogeneous shrinkage strain occurred during the interval = Coeff of autogeneous shrinkage strain occurred during the interval X E ca ( ) (Up to 7th day) 1849 X 10-6 (On 7th day) X X X X X 10-6 Total X The Indian Concrete Journal June 2017

8 Table 5 Drying shrinkage strain t, days Coeffdescribing drying shrinkage strain with time ( ) Coeff Of drying shrinkage strain occurred during the interval Drying shrinkage strain occurred during the interval = Coeff Of autogeneous shrinkage strain occurred during the interval X 10-6 (On 7 th day) X X X X X 10-6 Total drying shrinkage strain X 10-6 It is given by the equation mentioned in Clause 6244 of IS 1343:2012 as follows ) = age of concrete at the beginning of drying shrinkage ie no of days curing has been done = 5 days (assumed in the present problem) Drying shrinkage strain on 7 th day is Similarly drying shrinkage strains are computed for different time intervals and presented in the Table 5 The co-efficient gives the fraction of drying shrinkage that has occurred upto t days For example, coefficient for 28 days is 029 which indicates that 29% of total drying shrinkage ( ) has occurred upto 28 days Remaining 71% will occur from 28 th day to th day The summation of column 4 in Table 5 gives the total percentage of drying strain that has occurred from 5 th day (Curing period) to th day which is always 100% ie factor 100, and summation column 5 gives the total drying shrinkage strain that has occurred during 5 th day to th day ie 100 Shrinkage strain as per IS 1343:1980 is given by Clause 5241 For post tensioned members ultimate shrinkage strain is given by where Table 6 Comparison of total shrinkage strain Period As per IS 1343:2012 Strain as per IS 1343:1980 Autogenous strain Drying strain Total Shrinkage Strain X X X X X X X X X X X X X X X10-6 Total strain 2651X X X X 10-6 t = age of concrete at transfer in days (7 th day) For member loaded on 7 th day This code is silent on estimation of shrinkage strain in respective intervals and has no special consideration for multi stage prestressing The autogeneous shrinkage strain and drying shrinkage strain are combined together to arrive at total shrinkage strain which are presented in Table 6 The Indian Concrete Journal June

9 53 Relaxation in steel Relaxation loss depends on the initial jacking force The maximum initial jacking force as per Clause 1951 of IS 1343:2012 is 76% of ultimate tensile strength of wire or bar or strand Assuming that the average stress to be 95% of 76% and considering 5% loss for elastic shortening, the average stress in the strand after anchorage will be as follows From Table 6 of IS 1343:2012, for low relaxation strands, loss is 25% For long-term relaxation losses, the values given in Table 6 of IS 1343:2012 should be multiplied by 3 The revised code has no mention of time limit for which the long term relaxation losses have to be evaluatedhowever it is understood that the long term relaxation loss (multiplying values of Table 6 of IS 1343:2012 by 3) have to be considered while evaluated losses at infinity The loss 25% is the total loss due to relaxation ie at 1000 hours at 20 ± 2 C Code did not specify any values for calculating losses up to 1000 hours and temperature greater than 20 C to evaluate relaxation loss in intervals In other words the break up for total loss (25%) for different intervals upto 1000 hours is not available in the revised code IRC 112:2011 considers the values up to 1000 hours and above and for the early age relaxation in case of initial temperatures higher than 40 C, asin case of steam curing [8, 9] From Table 4 of IS 1343:1980 for the initial stress of 07f p, relaxation loss is 70 MPa 54 Residual prestressing force for single stage stressing When all the strands are stressed in single stage, the total prestressing force in the beam is calculated as follows Ultimate tensile strength of strand is 1023 kn from Table 1 of IS 14268:1995 Maximum force allowed is only 76% Assuming the average stress to be 92% of 76% and considering 5% loss for elastic shortening, the average prestressing force in the strand after anchorage will be as follows Self-weight of the beam Bending moment due to self-weight of beam is Bending tensile at the soffit of the beam at mid span due to self-weight is Bending compressive stress or net stress in concrete at the level of steel is From Table 3, Creep co-efficient on 28 th day is 085 Loss of prestressing force due to creep from 7 th day to 28 th day is Where m = modular ratio, expressed as ratio of modulus of elasticity of steel to concrete f c = Stress in concrete at the level of steel A s = Total area of prestressing steel = mm 2 Total shrinkage strain in the period 7-28 days is obtained from Table 6 as = Loss due to relaxation of steel is 25 % ie 541 Residual prestressing force on 28 th day Strands stressed on 7 th day will have a prestressing force of 716 kn located at 0075 m from the bottom of girder Bending stress in the beam at mid span due to prestressing is Residual prestressing force on 28 th day 56 The Indian Concrete Journal June 2017

10 542 Residual prestressing force on 45 th day Strands stressed on 7 th day will have a residual prestressing force of kn on 28 th day with a loss % of 6043 in the period 7-28 days Bending stress in the beam at mid span due to prestressing is 543 Residual prestressing force on 70 th day Strands stressed on 7 th day will have a residual prestress force of kn on 45 th day with a loss % of 1050 in the period days Bending stress or net stress in the beam at mid span is Bending compressive stress or net stress in concrete at the level of steel up to 45 th day ie just before the beam is subjected to live load From Table 3, Creep co-efficient on 45 th and 70 th day are 101 and 116 respectively From Table 3, Creep co-efficients on 28 th and 45 th day are 085 and 101 respectively Total shrinkage strain in the period days is obtained from Table 6 as 3807) 10-6 Total shrinkage strain in the period days is obtained from Table 6 as 4004 x 10-6 Residual prestressing force on 70 th day = Residual prestressing force on 45 th day y 544 Residual prestressing force on 90 th day Strands stressed on 7 th day will have a residual prestressing force of kn on 70 th day with a loss % of 0783 in the period days Bending stress in the beam at mid span due to prestressing is Live load of 10 kn/m is subjected on the beam on 45 th day Bending moment due to this live load is Bending tensile stress at the soffit of the beam at mid span the due to live load is From Table 3, Creep co-efficient on 70 th and 90 th day are 116 and 125 respectively Total shrinkage strain in the period days is obtained from Table 6 as 2062 x 10-6 Bending compressive stress or net stress on 45 th day after the application of live load is Residual prestressing force on 90 th day = The Indian Concrete Journal June

11 545 Residual prestressing force at infinity (25550 days) Strands stressed on 7 th day will have a residual prestressing force of kn on 90 th day with a loss % of 0432 in the period days Bending stress or net stress in the beam at mid span is Table 7 Comparison of total long term loss Type of loss As per IS 1343:2012 (kn) As per IS 1343:1980 (kn) Creep Shrinkage Relaxation Total loss Relaxation loss for initial stress of 07 f p is 70 MPa Total relaxation loss is From Table 3, Creep co-efficient on 90 th and th day are 125 and 228 respectively Total shrinkage strain in the period 90 - from Table 6 as days is obtained Total loss evaluated from both the codes is presented in Table 7 55 Residual prestressing force for multi stage stressing In the present problem strands are stressed in two stages In first stage, 5 strands are stressed on 7 th day and in second stage remaining 5 strands are stressed on 28 th day Total force on the beam due to prestressing at first stage is As per Clause of IS 1343:2012, for long term relaxation loss values given in Table 6 of code should be multiplied by 3 Loss between 90 days to infinity is 551 Residual prestressing force on 28 th day Strands stressed on 7 th day will have a prstressing force of 360 kn located at 0075 m from soffit of the beam Bending stress in the beam at mid span due to first stage stressing is Residual prestressing force on th day Tensile stress due to self-weight of beam 546 Losses as per IS 1343:1980 Creep co-efficient for a member loaded on 7 th Table 2 is 22 Total loss due to creep is day, from Bending compressive stress or net stress in concrete at the level of steel up to 28 th day Shrinkage strain for a member loaded on 7 th day is obtained from Table 6 as x 10-6 Total loss due to shrinkage is From Table 3, Creep co-efficient for 28 th day corresponding to strands stressed on 7 th day is 085 Creep loss Total shrinkage strain in the period 7-28 is obtained from Table 6 as The Indian Concrete Journal June 2017

12 Total shrinkage strain in the period days is obtained from Table 6 as Loss due to relaxation of steel is 25 % ie Residual prestressing force on 28 th day just before stressing second stage strands Residual prestressing force on 45 th day in first stage strands is Prestressing force in the beam due to second stage stressing is 360 kn Bending stress in the beam at the soffit of the beam due to second stage stressing is Loss in second stage strands from 28 th day to 45 th day 552 Residual prestressing force on 45 th day Strands stressed on 7 th day will have a residual prestressing force of kn on 28 th day with a loss of 4689% in the period 7-28 days Bending stress in the beam at mid span due to first stage stressing is Bending compressive stress or net stress in concrete at the level of steel up to 45 th day ie just before the beam is subjected to live load is Residual prestressing force on 45 th strands is day in second stage From Table 3, Creep co-efficients on 28 th day and 45 th day corresponding to strands stressed on 7 th day are 085 and 101 respectively Creep loss in first stage strands due to stressing of second stage strands ie strands which are stressed on 28 th day From Table 3, Creep co-efficient on 45 th day corresponding to strands stressed on 28 th day is Residual prestressing force on 70 th day Strands stressed on 7 th day will have a residual prestressing force of kn on 45 th day with a loss of 1815% in the period days Bending stress in the beam at mid span due to first stage stressing is Bending compressive stress in concrete at the level of steel up to 45 th day ie just before the beam is subjected to live load is From Table 3, Creep co-efficients on 45 th day and 70 th day corresponding to strands stressed on 7 th day are 101 and 116 respectively The Indian Concrete Journal June

13 Creep loss in first stage strands due to stressing of second stage strands ie strands which are stressed on 28 th day From Table 3, Creep co-efficients on 45 th day and 70 th day corresponding to strands stressed on 28 th day is 080 and 062 Bending compressive stress in concrete at the level of steel after beam is subjected to live load on 45 th day is Total shrinkage strain in the period days is obtained from Table 3 as Residual prestressing force on 70 th day in first stage strands is Loss in second stage strands from 45 th day to 70 th day Strands stressed on 28 th day will have a residual prestressing force of kn on 45 th day with a loss of 4067% in the period days Bending compressive stress in concrete at the level of steel after beam is subjected to live load on 45 th day is 554 Residual prestressing force on 90 th day Strands stressed on 7 th day will have a residual prestressing force of kn on 70 th day with a loss of 0788% in the period days Bending stress at mid span due to due to first stage stressing is Bending compressive stress or net stress in concrete at the level of steel up to 70 th day From Table 3, Creep co-efficients on 70 th day and 90 th day corresponding to strands stressed on 7 th day are 116 and 125 respectively Creep loss in first stage strands due to stressing of second stage strands ie strands which are stressed on 28 th day From Table 3, Creep co-efficients on 70 th day and 90 th day corresponding to strands stressed on 28 th day is 080 and 089 Bending compressive stress in concrete at the level of steel after beam is subjected to live load on 45 th day is Total shrinkage strain in the period days is obtained from Table 3 as Residual prestressing force on 70 th strands is day in second stage Residual prestressing force on 90 th day in first stage strands is Loss in second stage strands from 70 th day to 90 th day 60 The Indian Concrete Journal June 2017

14 Strands stressed on 28 th day will have a residual prestressing force of kn on 70 th day with a loss of 0614% in the period days Bending compressive stress in concrete at the level of steel after beam is subjected to live load on 45 th day is Total shrinkage strain in the period 90- from Table 6 as x 10-6 Shrinkage loss= days is obtained As per Clause of IS 1343:2012, for long term relaxation loss values given in Table 6 of code should be multiplied by 3 Loss between 90 - days is Residual prestressing force on 90 th strands is day in second stage Residual prestressing force at infinity in first stage strands is 555 Residual prestressing force at infinity (25550 days) Strands stressed on 7 th day will have a residual prestressing force of kn on 90 th day with a loss of 0437% in the period days Bending stress in the beam at mid span due to first stage stressing is Compressive stress or net stress in concrete at the level of steel up to 70 th day Loss in second stage strands from 90 th day to infinity days Strands stressed on 28 th day will have a residual prestressing force of kN on 90 th day with a loss of 0333% in the period days Bending compressive stress in concrete at the level of steel after beam is subjected to live load on 45 th day is From Table 3, Creep co-efficients on 90 th day and th day corresponding to strands stressed on 7 th day are 125 and 228 respectively Creep loss in first stage strands due to stressing of second stage strands ie strands which are stressed on 28 th day From Table 3, Creep co-efficients on 90 th day and th day corresponding to strands stressed on 28 th day is 089 and 125 Bending compressive stress in concrete at the level of steel after beam is subjected to live load on 45 th day is As per Clause of IS 1343:2012, for long term relaxation loss values given in Table 6 of code should be multiplied by 3 Loss between 90 - days is Residual prestressing force at infinity in second stage strands is The Indian Concrete Journal June

15 Residual prestressing force in the beam after all the losses is = = kN 6 Conclusions The calculations of long term losses play a major role in performance of prestressed concrete structures [10] The revised IS 1343 has incorporated many factors into the model for calculating long term losses A typical case study has been considered to elaborate the long term loss calculation procedure based on old and revised code The following general observationscan be drawn from this study With reference to Creep In IS: 1343:1980, ultimate creep coefficients were given for different ages of loading These recommendations are only for structures where losses need not be evaluated at various stages Creep co-efficient cannot be estimated in respective intervals with respect to IS 1343:1980 as there are no guidelines to arrive creep co-efficient for evaluating residual stresses at various stagesthey are not valid for evaluation of residual prestress or deflection or camber in structures at various stages of stressing/loading/measuring These short comings are addressed in new code with a scientific mathematical model that incorporates various parameters like member size, relative humidity, and age of loading However, this model is valid only if stress in concrete does not exceed one-third characteristic compressive strength of concrete and concrete should be of normal concrete ranging from M30 to M60 These models are not applicable for special concretes With reference to Shrinkage loss Shrinkage strain as per IS 1343:1980 is given by the Clause 5241 For post tensioned members ultimate shrinkage strain is given by the equation which is dependent on age of concrete at the time of transfer of prestress Shrinkage strain cannot be estimated in respective intervals and for multistage case with respect to IS 1343:1980 as there are no guidelines for evaluating residual stresses at various stages Whereas IS1343:2012 has incorporated various parameters affecting the shrinkage like Relative humidity, member size and grade of concrete and can obtain shrinkage loss for multistage prestressing IS 1343:2012 is not clear on source from which RH has to be considered With reference to Relaxation loss From Table 6 of IS 1343:2012 for low relaxation strands loss percentage is based on initial prestress For long-term relaxation losses, the values given in this table should be multiplied by 3 The %loss from this table is the total loss due to relaxation ie at 1000 hours at 20 ± 2 C Code is silent on losses up to 1000 hours and for temperature greater than 20 C and on evaluation of relaxation loss in intervals IRC 112:2011 code considers the values up to 1000 hours and above and for temperatures greater than 20 C As per Table 4 of IS 1343:1980, the relaxation loss is dependent on the initial prestress only With reference to the results from case study Although the variation of total loss as calculated for the case considered from both the codes is not significant, it may definitely vary with the problem statement References 1 Indian standard code of practice for prestressed concrete (second revision), IS 1343: 2012Bureau of Indian Standards, New Delhi 2 Comite euro-international du-beton, CEB-FIP model code Indian standard code of practice for prestressedconcrete, IS 1343: 1980Bureau of Indian Standards, New Delhi 4 Beeby AW and Narayanan R S, Designers guide to Eurocode 2: design of concrete structures, Thomas Telford Publication 5 Oh B H, Cha S W, Um J Y and Lim D H, Effects of reinforcement and humidity onthe creep and shrinkage behaviour of high-strength concrete members, Creep andshrinkage of Concrete, RILEM Symposium Proceedings of the Fifth International, 1995, pp Peter L, Assessment of long-term losses in prestressedconcrete structure, Thesis submitted to Lund University, for PhD, Lund University, American concrete institute guide for modelling and calculating shrinkage and creep in hardened concrete, ACI 2092R-08 8 Indian road congress code of practise for concrete bridges, IRC 112:2011 Indian Road Congress, New Delhi 9 Viswanathan T, Calculation of time dependent losses in prestressed concrete as per IRC : 112 and IRC :18, Journal of Indian Road Congress, April - June 2014, Vol 74, No 4, pp Gilbert RI, Time effects in concrete structures, Elsevier Science publishing company, New york, The Indian Concrete Journal June 2017

16 Dr P Markandeya Raju holds a BTech (Civil Engineering) from Nagarjuna University; ME (Structural Engineering) from Andhra University; PhD from JNTU, Hyderabad He is a Professor of Civil Engineering at MVGR College of Engineering (Autonomous), Vizianagaram, Andhra Pradesh and has 15 years of teaching experience He has more than 45 papers to his credit in various national and international conferences and journals His areas of interest are prestressed steel structures, computer applications in structural engineering and durability studies on special concretes T Raghuram Sandeep holds a BTech (Civil Engineering) from JNTU, Hyderabad and ME (Structural Engineering) from Andhra University, Visakhapatnam He is a Technical Officer at Civil Engineering Division of BARC, Visakhapatnam, Andhra Pradesh He published three technical papers in reputed International journals His research interests are partial prestressing, prestressing in concrete and steelconcrete composite structures The Indian Concrete Journal June