Procedure 4 Large Structures Construction Stage Analysis)
7.4.8 Output Description for LC Creep&Shrinkage
7.4.8.2 Description of the Output Listing of LC 602
A detailed protocol of the creep, shrinkage and relaxation behaviour is given directly in the output listing of LC 602 because only 1 time step has been used. If more time steps had been used then this information were given in the output listings of the partial load cases generated automatically for each time step (e.g. creep with 3 time steps produces 3 partial load cases numbered 9001, 9002 und 9003).
In order to get this detailed information in the output listing it is further necessary to activate the option „Output of Creep and Shrinkage Coefficients“ in "RECALC – SPECIAL SETTINGS.
Loading case 602 - time interval from 100 to 1100 (for w2=0.5 => t = 600) Loading case 101 and 501 applied at time t = 0
Loading case 601 applied at time 50 Loading case 201 applied at time t = 100 Element 101 7 days in scaffolding Element 102 14 days in scaffolding
A/u 0.25000RH 75 ZT 2 T 20
lamda 1.5065h0 500HF 6750 Fcm 46
Hunit 100 h0' 5 FCM' 4.6
El 101 El 102 El 101 El 102 El 101 El 102 El 101 El 102 LC 601 LC 601 LC 201 LC 201 LC 602 LC 602
T/t0 7 14 57 64 107 114 607 614
1 2
7 0.0000
14 0.4510 0.0000
21 0.5542 0.3958
57 0.8043 0.6759 0.0000
64 0.8350 0.7059 0.3031 0.0000
107 0.9777 0.8412 0.5405 0.5062 0.0000
114 0.9960 0.8582 0.5611 0.5286 0.2686 0.0000
607 1.5089 1.3214 0.9967 0.9723 0.8662 0.8532 0.0000
614 1.5123 1.3244 0.9993 0.9749 0.8687 0.8557 0.1919 0.0000
1107 1.6759 1.4696 1.1183 1.0926 0.9834 0.9704 0.6190 0.6158
1114 1.6775 1.4710 1.1194 1.0937 0.9845 0.9715 0.6208 0.6177
2000 1.8092 1.5875 1.2125 1.1855 1.0714 1.0580 0.7375 0.7354
5000 1.9457 1.7077 1.3068 1.2780 1.1574 1.1432 0.8219 0.8200
delta 0.6982 0.6128 0.5778 0.5651
LC 101 and 501
tables are therfore described in detail. The 4th table contains the load integrals. These are always zero for C&S cases.
The internal forces are output in 2 separate tables, containing 1. the primary part of the internal forces and
2. the total internal forces due to creep and shrinkage
The „primary part“ means the internal forces due to internal redistribution at cross- section level (stress redistribution from concrete to steel - or vice versa in the relaxation case). The total forces contain additionally the redistribution forces due to external con- straints. Primary and total internal forces are identical in this example, because the sec- ondary part is zero (no external constraints exist).
Parameters for describing the system behaviour (modification of the left-hand side for considering the stress changes within the creep period)
LOAD CASE : 602
TIME INTERVAL 100.000 600.000 1100.000
ELEM CREEP SHRINKAGE RELAXATION E-MOD --- 101 0.6190307 -0.27385E-04 0.0000000 0.33659E+08 102 0.6176510 -0.27239E-04 0.0000000 0.33661E+08
TIME INTERVAL
1st value TA Start time of the creep period
2nd value TM Integration point in the time interval (mostly centre point) 3rd value TE End time of the creep period
ELEM Element number
CREEP Creep coefficient for stresses arising in the creep period due to creep and shrinkage (φ(tE) - φ(tM))
SHRINKAGE Shrinkage coefficient for the time interval TM to TE (only for information – not used in the solution algorithm)
RELAXATION Relaxation coefficient for the time interval TM to TE (actually not used)
E-MOD Modulus of elasticity at the end time of the creep period (not used for the static analysis, used in some creep laws for deter- mining the creep coefficient φ.
Hints:
The described C&S Action starts at TA=100, lasts for 1000 days and ends at TE=1100. The line „TIME INTERVAL“ shows the start time and the end time of the creep period as well as the fictitious application time of the stress redistributions due to creep and shrinkage.
Table 1: Parameters for the system behaviour
This time is specified via the ratio value w2. This value is by default set to 0.5 (centre of the interval). This setting has not been changed in the example, therefor TM = (TA+(TE- TA)*w2 = 100+(1100-100)*0,5 = 600.
The table below this header line contains the parameters (creep coefficient, shrinkage coef- ficient, relaxation coefficient and modulus of elasticity) for each element for the time in- terval from T=600 to T=1100 based on the curve for the load application time T=600.
Attention must be paid - when checking the relationships - to the fact, that the concrete age at time T=0 has to be considered for the evaluation of the creep formulas. I.e. the creep curves for t0 = 7 or 14, 107 or 114, 607 or 614 respectively are to be considered. The modulus of elasticity is given for the age t=1107 or 1114 respectively.
Parameters for building the load vector (right-hand side of the equation system)
LOAD CASE : 602
TIME INTERVAL 100.000 1100.000
TIME LC ELEM CREEP SHRINKAGE RELAXATION E-MOD --- 0.0 101 101 0.6981721 -0.76687E-04 0.0000000 0.14509E+07 0.0 501 101 0.6981721 -0.76687E-04 0.0000000 0.14509E+07 50.0 601 101 0.5778032 -0.76687E-04 0.0000000 0.14509E+07 100.0 201 101 0.9834273 -0.76687E-04 0.0000000 0.14509E+07 0.0 101 102 0.6128284 -0.75817E-04 0.0000000 0.13887E+07 0.0 501 102 0.6128284 -0.75817E-04 0.0000000 0.13887E+07 50.0 601 102 0.5651234 -0.75817E-04 0.0000000 0.13887E+07 100.0 201 102 0.9715044 -0.75817E-04 0.0000000 0.13887E+07
TIME INTERVAL
1st value TA Start time of the creep period 2nd value TE End time of the creep period
TIME Application time of the Load Case. This time is used to calculate the age of the concrete at loading application. Must creep laws define the development of the creep strains to be dependent on that age at the load application time. The creep curve related to that Load Case may then be determined using this age.
LC Load Case No. (of the creep inducing load)
ELEM Element no.
CREEP Creep coefficient for the considered time interval φ(tE) - φ(tA) SHRINKAGE Shrinkage strain for the time interval TA to TE. The shrinkage
strain is not load case dependent and considered only once for each element, although ist is printed in every line of the table.
RELAXATION Relaxation coefficient for the time interval T to T (actually not
Table 2: Parameters for building the load vector (right-hand side)
Hints:
The described C&S Load Case starts at TA =100 days, lasts 1000 days and ends at TE=1100. This is shown in the header line „TIME INTERVAL“. The table below contains for every element the creep inducing Load Cases with their load application times (on the global time axis of the constrution schedule). The next rows contain the related creep coef- ficients and shrinkage strains. It can be seen that the first C&S Load Case is applied at time 50 (because w2=0.5 and the duration of the Load Case ist 100 days). The Load Case 201 is applied at time 100. The last column contains the change of the elastic modulus in this time interval (E(t=1107)-E(t=107) or E(t=1114)-E(t=114) respectively).
ITERATION PROTOCOL
LOAD CASE : 602
RELAXATION FACTOR 1.000 ITERATION PROTOCOL
ITER PROZ[%] RSUM RMAX XMAX XVMAX --- 1 100.000% 4162.5388 2982.246820 0.0000 0.000000 2 0.000% 0.0000 0.000000 -0.0010 -0.000966 3 0.000% 0.0000 0.000000 -0.0010 0.000000
The iteration protocol shows the development of basic iteration parameters during the it- eration process. An iterative solution is required because the redistribution forces evolve again a priori unknown creep strains. Only internal redistribution occurs in the above ex- ample, only few iterations are therefore necessary. If there were considerable constraint internal forces, the number of required iterations would be much higher.
The following equation shows the implicit relationship requiring an iterative solution. The internal moment due to redistribution M602 is dependent on the creep strains induced by M602 itself.
602 602 201
201 601
601 501
501 101
101
602 ϕ ϕ ϕ ϕ ⋅ϕ
+ ⋅
⋅ ⋅ +
⋅ ⋅ +
⋅ ⋅ +
⋅ ⋅
⋅ = E J
M J
E M J
E M J
E M J
E M J E M
Table 3:
ITERATION PROTOCOL
The creep coefficients ϕ101,ϕ501,ϕ601,ϕ201 are used in the „Right-hand equation side“, but ϕ602 on the „Left-hand side“.
7.4.9 “TSTOP” - Interrupt Creep & Shrinkage
The C&S process for specified structural parts can be halted for specified periods using TSTOP.
This “Interrupt C&S function”, can be advantageously used in a construction schedule where there is a repetitive nature in the construction –it greatly simplifies the input and analysis process resultant from complicated construction time schedules.
A typical example of the advantageous use of this function is in the analysis of a bal- anced cantilever bridges, where the different piers and cantilever arms are not erected at the same time. Each pier with its cantilever arms is an independent structure itself until the balanced cantilevers are connected to each other. The limited amount of construc- tion equipment usually available dictates that a contractor builds the balanced cantile- vers at different times or at least with staggered time intervals. The cycle of construc- tion, however, is of a repetitive nature and can therefore be simplified (for analysis pur- poses) using TSTOP.
Example:
Pier 1 is erected during global time = 0 to global time = 100 [days]
Pier 2 is erected during global time = 20 to global time = 120 [days]
Pier 3 is erected during global time = 40 to global time = 140 [days]
The piers are linked at global time 140 [days]
Creep period (Duration) Load application time
Creep coefficient for this creep period
Time Creep cofficient φ(t)
Concrete Age at load application time
Creep curve for the partial load becoming active at this load applica- tion time
The standard simulation method would require an exact modelling of the time schedule, activating only pier 1 at time 0, pier 1 and 2 at time 20, pier 1,2,and 3 at time 40.
Thus a standard Action Schedule would contain the following:
• All actions for pier 1 from time = 0 to time = 20
• All actions for pier 1 and pier 2 from time = 20 to time = 40
• All actions for pier 1, pier 2 and pier 3 from time = 40 to time 140
• All Actions for the combined system from 140 days to time infinity.
This process will yield a large number of Load Cases to be analysed as all the loads on the separate piers must be treated as separate Load Cases (self weight, creep & shrink- age etc). This will also require a big calculation time (being dependent on the number of Load Cases to be calculated).
The alternative process, using TSTOP, reduces the calculation of the erection phase of all 3 separate piers into one construction stage as follows:
• Perform all Actions for pier 1, 2 and 3 for 140 days.
• Interrupt C&S in pier 2 for 20 days and pier 3 for 40 days by applying
‘TSTOP’ to the corresponding elements at time 120 and 100 respectively.
• Perform all Actions for the combined system from 140 days to infinity.
The ‘TSTOP’ Action shifts the time axis by 20 days for pier 2 and by 40 days for pier 3.
Note: The TSTOP-Action must actually not be applied more than once to each element throughout the whole construction sched- ule. For different element groups it may however be placed on different positions in the Action Table.
TIME, Pier 2 TSTOP
20 days
TSTOP 40 days 0
0
100 100
100 120 100
days days
TIME, Pier 3
0 100 120 140 days TIME, GLOBAL
0 100 120 140 days TIME, Pier 1