30m预应力箱梁张拉应力、伸长量计算
一、预应力钢绞线张拉力计算:
根据图纸设计预应力钢绞线锚下控制应力:
δK=0.75Ryb=0.75×1860=1395Mpa 根据公式P=δK×AP×n AP=139mm2 (1)正弯矩四股、五股钢绞线张拉力: P4=1395×139×4=775.6KN P5=1395×139×5=969.5KN (2)负弯矩单根张拉力 P1=1395×139=193.9KN 二、预应力钢绞线的理论伸长值计算:
伸长量ΔL= Pp= -(kL+μθ)ApEp kL+μθ 根据图纸设计及钢绞线的技术指标,取值如下: Ap=139mm2 Ep=1.95×105Mpa δK=1395Mpa 查《桥规》附表C1得k、μ值,k=0.0015 μ=0.17 张拉端张拉力P1=δK×Ap=1395×139=193905N
1、中跨箱梁: (1)N1(2×4):
ΔL1: Pp1=193905×(1-0.96495385)/0.035675=190487N
ΔL1=190487×13.895/(139×1.95×105)=0.09765m
ΔL2: P2=2 Pp1-P1=2×190487-193905=187069N
Pp2=187069×(1-0.99882319)/0.0011775=186959N
ΔL2=186959×0.785/(139×1.95×105)=0.005414m N1的伸长值(ΔL1+ΔL2)×2=20.6cm (2)N2(2×4):
ΔL1: Pp1=193905×(1-0.96728123)/0.033266=190715N
ΔL1=190715×12.289/(139×1.95×105)=0.086467m
ΔL2: P2=2 Pp1-P1=2×190715-193905=187525N
Pp2=187525×(1-0.99639601)/0.0036105=187187N
ΔL2=187187×2.407/(139×1.95×105)=0.016623m N2的伸长值(ΔL1+ΔL2)×2=20.6cm
(3)N3(2×4):
ΔL1: Pp1=193905×(1-0.9696142)/0.030857=190944N
ΔL1=190944×10.683/(139×1.95×105)=0.0752575m
ΔL2: P2=2 Pp1-P1=2×190944-193905=187983N
Pp2=187983×(1-0.99397473)/0.0060435=187416N
ΔL2=187416×4.029/(139×1.95×105)=0.027858m
N3的伸长值(ΔL1+ΔL2)×2=20.6cm (4)N4(2×4):
ΔL1: Pp1=193905×(1-0.99317182)/0.0068516=193242N
ΔL1=193242×1.799/(139×1.95×105)=0.012825m
ΔL2: P2=2 Pp1-P1=2×193242-193905=192579N
Pp2=192579×(1-0.98100816)/0.0191745=190744N
ΔL2=190744×12.783/(139×1.95×105)=0.089956m N4的伸长值(ΔL1+ΔL2)×2=20.5cm
2、边跨箱梁:
P1=δK×Ap=1395×139=193905N
(1)N1(2×5):
ΔL1: Pp1=193905×(1-0.96754025)/0.03299825=190741N
ΔL1=190741×12.1105/(139×1.95×105)=0.085222m
ΔL2: P2=2 Pp1-P1=2×190741-193905=187577N
Pp2=187577×(1-0.99605978)/0.003948=187207N
ΔL2=187207×2.632/(139×1.95×105)=0.0181785m N1的伸长值(ΔL1+ΔL2)×2=20.7cm (2)N2(2×5):
ΔL1: Pp1=193905×(1-0.96985714)/0.0306065=190967N
ΔL1=190967×10.516/(139×1.95×105)=0.07408998m
ΔL2: P2=2 Pp1-P1=2×190967-193905=188029N
Pp2=188029×(1-0.99367211)/0.006348=187433N
ΔL2=187433×4.232/(139×1.95×105)=0.02926458m N2的伸长值(ΔL1+ΔL2)×2=20.67cm
(3)N3(2×5):分段
ΔL1: Pp1=193905×(1-0.97218103)/0.02821325=191195N
ΔL1=191195×8.9205/(139×1.95×105)=0.062924m
ΔL2: P2=2 Pp1-P1=2×191195-193905=188485N
Pp2=188485×(1-0.99129015)/0.008748=187663N
ΔL2=187663×5.832/(139×1.95×105)=0.04037819m N3的伸长值(ΔL1+ΔL2)×2=20.66cm (4)N4(2×4):
ΔL1: Pp1=193905×(1-0.99331038)/0.0067121=193256N
ΔL1=193256×1.706/(139×1.95×105)=0.0121636m
ΔL2: P2=2 Pp1-P1=2×193256-193905=192607N
Pp2=192607×(1-0.98073303)/0.019455=190745N
ΔL2=190745×12.97/(139×1.95×105)=0.09127329m N4伸长值(ΔL1+ΔL2)×2=20.68cm
3、负弯矩伸长值 (1)T1(2×5)
ΔL1: Pp1=193905×(1-0.98955493)/0.0105=192891N
ΔL1=192891×7/(139×1.95×105)=0.05m
T1伸长值(ΔL1)=0.5cm (2)T2(2×5)
ΔL1: Pp1=193905×(1-0.985112)/0.015=192457N
ΔL1=192457×10/(139×1.95×105)=0.071m T2伸长值(ΔL1)=7.1cm (3)T3(3×5)
ΔL1: Pp1=193905×(1-0.97775124)/0.0225=191740N
ΔL1=191740×15/(139×1.95×105)=0.106m
T1伸长值(ΔL1)=10.6cm
预应力钢绞线张拉力对应油表读数
一、根据图纸设计预应力钢绞线锚下控制应力:
δK=0.75Ryb=0.75×1860=1395Mpa 根据公式P=δK×AP×n AP=139mm2 (1)正弯矩四股、五股钢绞线张拉力: P4=1395×139×4=775.6KN P5=1395×139×5=969.5KN (2)负弯矩单根张拉力 P1=1395×139=193.9KN
二、根据千斤顶及压力表检定报告及1#、2#千斤顶回归线型方程:
1#千斤顶(20204#压力表):Y=0.0329X+0.65 2#千斤顶(20208#压力表):Y=0.0329X+0.2 3#千斤顶(20212#压力表):Y=0.2251X+0.79 4#千斤顶(90411#压力表):Y=0.2257X+0.69 计算得到张拉力为10%δK、20%δK、100%δ如下表:
K时油压表读数
1#千斤顶(20204#压力表)
2#千斤顶(20208#压力表)
3#千斤顶(20212#压力表)
4#千斤顶(90411#压力表)
中跨梁钢绞线理论伸长值一览表
边跨梁钢绞线理论伸长值一览表
负弯矩理论伸长值一览表