N3 N1
支点
N2 N3
1395 1395 1395 1395
55.92856437 1339.071436 0.326391811 1394.673608 0.535577163 1394.464423 0.652707255 1394.347293
4012 156 256 312
0.01394032 7480.160693 0.002092255 19308.11931 0.002092098 19308.84334 0.00209201 19309.2488
We know all
lf?l,the prestress losses after considering friction is :
??x(?l2)?lf?xlf??
. If
x?lf,
?? is the tensioned prestressed losses after considering friction caused by anchor deformation,???2??dlfthen friction have no influence on this section. Calculation of each control section’s ??x(?l2) are shown in the following Table.
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(2)锚具变形，钢丝回缩引起的应力损失 截面 钢束编号 N1 跨中截面xi=0 N3 N1 L/4截面N2 xi=8165 N3 N1 变化点截面N2 xi=11630 N3 支点截面N1 4012 10377 156 11854 150.3373309 131.5969032 92.211 129.87 140.8419546 3956 10361 150.5637822 93.076 91.35958522 8477 10377 3856 11854 150.3373309 131.5969032 27.522 88.791 8421 10361 150.5637822 28.192 31.64640158 13642 10377 8321 11854 150.3373309 影响 131.5969032 39.224 N2 x lf △σ σl2 各截面σl2平均值 13486 11854 13586 10361 131.5969032 x>lf截150.5637822 面不受0 反摩擦31
xi=153630 N2 N3 256 10361 312 10377 150.5637822 150.3373309 146.84 145.82
(3)Concrete elastic compression caused prestress losses
For simple supported beam, calculate l/4 section, and take its value as the whole beam cross-section’s prestressed reinforcement losses’ average value:
?l4?m?1?EP?pc 2mm---Tension batch number, m=3;
?EP---versus of prestressed reinforcement elastic modulus to concrete elastic modulus, calculate as the concrete true
strength when tensioned, fck' is assumed as 90% design value,
fck'?0.9?C50?C45, we can obtain
Ec'?3.35?104MPa
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?EPEP1.95?105???5.82 4Ec'3.35?10?pc---Concrete normal stress that all prestressed reinforcements’ resultant force Np at its application point caused,
2?ppeppc?NA?NI, section features use the first stage in the upper table;
Np?(?con??l1??l2)Ap ?（1395-55.92-29.58?Npe2ppc?NpA?I? 4412.7?1034412792.454?103?273?m?1l4?2m??3?1EPpc ?2?3?5.82?15.36?
(4)Steel relaxation causes pre-stress losses:
The pre-stress losses caused by steel relaxation is :
??pel5?????(0.52f?0.26)??pe
pk?---Tension coefficient, use super tension, so ?=0.9;
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）?3465?4412.7?103?984.22.979?109?21.17(MPa).07MPa.741
?---Steel loose coefficient, to low relaxation strand, ?=0.3;
?pe---Reinforcement stress at force anchor ,
(5)Stress losses caused by concrete creep and shrinkage：
Stress losses caused by concrete creep and shrinkage could calculate by use the following formula:
?l（6tu)?0.9[EP?cs(tu,t0)??EP?pc?(tu,t0)]1?15??ps
?cs(tu,t0)、?(tu,t0)——load age is t, final value of concrete shrinkage strain, and final value of concrete creep. 0t0——Load age，the load age till the 90% of the design strength， 0.9fck?fckG2, the load age
lgt0, t0?20d；To the second stage lg28dead load
?=90d； ?, assume t0t0The bridge is at the common area of field. The relative humidity is 75%，thickness of the member (I－I section), get
2Acu?2?8760005466?321，check
the table, get the final value of creep coefficient ?(tu,t0)??(tu,20)?1.69、
?4?(t,20)?2?10csu?)??(tu,90)?1.25；The final value of concrete shrinkage strain . ?(tu,t0?pc---the average value of normal stress at the mid-span section l/4 section。
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