0.51?10?3?2ftdbh0?0.51?10?3?1.25?1.83?200?1295.3?296.3??0Vd
0.51?10-3fcu,kbh0?0.51?10?350?200?1295.3?934.2KN??0Vd
Section is OK but need to resistance shear steel ?0Vd?Vcs?Vpb
p?100??100? Within this
2940157.8?1.135 ?sv??0.00393
200?1295.3200?200?1?1.0；?2?1.25；?3?1.1；
Choosing R=10mm, HRB335 steel, fsv=280MPa, sv=200 Asv=2*78.54=157.08 mm2
?sv?Asv157.08??0.00393 Svb200?200Vcs??1?2?30.45?10?3bh0(2?0.6p)fcu,k?svfsv?732.119KN
Vpd?0.75?10?3?1260?2940?0.089?247.269KN V?Vcs?Vpd?732.119?247.269?797.388 it’s OK.
(2) shear capacity inclined section
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Incline shear meet the requirements at change point cross section.
8.Estimation of pre-stress losses
1)the control stress
?con?0.75fpk?0.75?1860?1395MPa
2)stress losses in cable
(1)Friction in pre-stressed reinforcement and pipeline:
?l1??con[1?e?(???kx)]
To the mid-span cross section: x?l/2?d; d is the distance from anchor point to bearing central line;? is the
friction coefficient of reinforcement and pipe and k is the local deviation of pipe per meter length’s influence on the friction coefficient, we know ??0.25，k?0.0015; ? is the pipe rolls angle from tensioned place to the mid-span, only N1 is a siphon standpipe,so ?N1??0?8。, N2, N3 is not only a siphon but also a flat bend pipe, the siphon angle
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is: ?v?8。; and the flat bend angle is ?H, so the space angle is ?2?4.569?9.138。
2?N2??N3??H??v2?9.1382?82?12.145。.
钢束编号 N1 N2 N3 钢束编号 N1 N2 N3 钢束编号 N1 N2 N3 θ ° 8 12.145 12.145 9.138 9.138 9.138 θ ° 9.16 12.15 9.14 θμ rad 0.139555556 0.211862778 0.211862778 θ rad 0 0 0 θμ rad 0.01 0.14 0.00 0.00 0.03 0.00 3.86 3.96 4.01 0.01 0.01 0.01 X 0 0 0 0.156 0.256 0.312 0.0348889 0.0529657 0.0529657 θμ 13.486 13.586 13.642 X X kx 跨中截面 1-e-(θμ+kx) 0.0537 0.0708 σcom 1395 1395 1395 σcom 1395 1395 1395 σcom 1395.00 1395.00 1395.00 σl1 74.855 98.714 98.823 σl1 0.3266 0.5359 0.6531 σl1 11.979 55.836 8.3752 0.020229 0.020379 0.020463 0.0708 支点截面 kx 0.000234 0.000384 0.000468 kx 1-e-(θμ+kx) 0.0002 0.0004 0.0005 1-e-(θμ+kx) 0.01 0.04 0.01 Ⅱ-Ⅱ变化点截面 27
钢束编号 N1 N2 N3 θ ° 9.14 11.12 12.15 rad 0.16 0.19 0.21 0.04 0.05 0.05 8.32 8.42 8.48 0.01 0.01 0.01 θμ X kx L/4截面 1-e-(θμ+kx) 0.05 0.06 0.06 σcom 1395.00 1395.00 1395.00 σl1 71.171 82.766 88.736 截面 σl1 跨中Ⅰ-Ⅰ 90.797158 L/4 80.891 变化点Ⅱ-Ⅱ 25.397 支点 0.5052 (2)Anchorage deformation、steel retraction causes stress losses
Post tensioned structure should consider the influence of friction, its influence length is :
lf???l?Ep/??d
?l---the deformation value of anchor in tensioned end, ?l?4mm;
??d---unit length of pipe friction losses of prestress value,??d?(?0??l)/l;
?0---the control stress in tensioned end,
?l---the prestress value of anchor end except the value of pipe friction losses, ?l??0??l1;
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l--- the distance from tensioned to anchor end, the anchor end is mid-span cross-section. The influence length of friction shows in the following Table.
截面
跨中
L/4
变化点
钢束编号 N1
N2 N3 N1
N2 N3 N1
N2
Table of friction influence length
?0??con(MPa)
?（1MPa) ?l??0??l1(MPa)
1395 78.7781269 1316.221873 1395 102.5813114 1292.418689 1395 102.68987
1292.31013
1395 16.2698212 1378.730179 1395 63.75723559 1331.242764 1395 87.7457891 1307.254211 1395
8.045390302 1386.95461
1395
8.253417891 1386.746582
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l
??d?(?0??l)/l(MPa/mm)
0.005087055 0.006581632 0.006565009 7821 0.002080274 7921 0.00804914 7977 0.010999848 3856
0.00208646 3956
0.002086304 lf
12382.66443 10886.30541 10900.07886 19363.64242 9844.021844 8420.811687 19334.91446
19335.63883
15486 15586 15642