预应力钢的理论伸长值计算.doc

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1、预应力钢筋的理论伸长值计算已知：张拉控制应力σk=1357.8Mpa，Ay=142.6mm2，Ey=197660Mpa，μ=0.175，k=0.0008；1号钢束：实测摩阻力为115Mpa，理论摩阻力为123.1Mpa，张拉力Pk=1357.8×142.6×12=2323.5KN将半个曲线预应力筋分成八段，各段参数表为：线段L(m)θ(rad)e-(kL+μθ)终点力(KN)AB6.20.0690.98312284.2BC3.3200.99732278CD8.50.07280.98062233.8DE3.4500.9972222

2、7.5EF8.10.10080.97622174.5FG4.7900.99622166.2GH8.10.10080.97622114.6HI200.99842112.9将表中数据代入公式：Δl=PL/AyEy，P=P×(1+e-(kL+μθ))/2，得P1=2323.5×(1+0.9831)/2=2303.87KNΔl1=2303.87×103×6.2/(1711.2×197660)=0.0422mP2=2284.2×(1+0.9973)/2=2281.12KNΔl2=2281.12×103×3.32/(1711.2×19766

3、0)=0.02239mP3=2278×(1+0.9806)/2=2255.9KNΔl3=2255.9×103×8.5/(1711.2×197660)=0.05669mP4=2233.8×(1+0.9972)/2=2230.67KNΔl4=2230.67×103×3.45/(1711.2×197660)=0.02275mP5=2227.5×(1+0.9762)/2=2200.99KNΔl5=2200.99×103×8.1/(1711.2×197660)=0.0527mP6=2174.5×(1+0.9962)/2=2170.37KN

4、Δl6=2170.37×103×4.79/(1711.2×197660)=0.0307mP7=2166.2×(1+0.9762)/2=2140.42KNΔl7=2140.42×103×8.1/(1711.2×197660)=0.0513mP8=2114.6×(1+0.9984)/2=2112.91KNΔl8=2112.91×103×2/(1711.2×197660)=0.01249m求得Δl=2×0.29121=0.58242m=58.242cm在梁端处N1钢束伸长量为：29.121cm2号钢束：实测摩阻力为275Mpa，理论摩

5、阻力为134.9Mpa，张拉力Pk=(1357.8+275-134.9)×142.6×12=2563.2KN将半个曲线预应力筋分成六段，各段参数表为：线段L(m)θ(rad)e-(kL+μθ)终点力(KN)AB40.0920.98092514.2BC7.4500.99412499.4CD80.1010.97622439.9DE80.1010.97622381.9EF900.99282364.7FG80.1010.97622308.4将表中数据代入公式：Δl=PL/AyEy，P=P×(1+e-(kL+μθ))/2，得P1=2563

6、.2×(1+0.9809)/2=2538.7KNΔl1=2538.7×103×4/(1711.2×197660)=0.0300mP2=2514.2×(1+0.9941)/2=2506.8KNΔl2=2506.8×103×7.45/(1711.2×197660)=0.0552mP3=2499.4×(1+0.9762)/2=2469.7KNΔl3=2469.7×103×8/(1711.2×197660)=0.0584mP4=2439.9×(1+0.9762)/2=2410.9KNΔl4=2410.7×103×8/(1711.2×19

7、7660)=0.0570mP5=2381.9×(1+0.9928)/2=2373.3KNΔl5=2373.3×103×9/(1711.2×197660)=0.0632mP6=2364.7×(1+0.9762)/2=2336.6KNΔl6=2336.6×103×8/(1711.2×197660)=0.0553m分段求得Δl=2×0.3191=0.6382m=63.82cm在梁端处N2钢束伸长量为：31.91cm横梁计算已知：张拉控制应力σk=1120Mpa，Ay=142.6mm2，Ey=197660Mpa，μ=0.175，k=0.

8、0008；线段L(m)θ(rad)1+e-(kL+μθ)2终点力(KN)AB6.40.5130.95471347.3ΔL=1347.3×10³×6.4/1260×197660=0.0346m横梁张拉压力表读数顶号压力表号初应力100%应力103%应力141.12