钢绞线理论伸长值计算

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1、20m空心板梁预应力钢绞线理论伸长值一、材料预应力钢绞线：Φj15.24mm公称截面积为Ap=145mm2，Rby=1860Mp、Ep=1.97×105Mp；锚具：采用YM15-3（4）锚具；钢绞线孔道：采用直径为56mm的预埋波纹管。二、控制张拉力3束585.9KN4束781.2KN三、钢束N1、N2、N3分段计算伸长值后各自己叠加。（一）N1伸长值计算（至跨中）1、直线各参数如下：P=585.9KNθ=0radx=0.631+0.561=1.192mk=0.0015μ=0.225(取0.2~

2、0.25中值)此段理论伸长值：ΔL1=(P×L)/(Ap×Ep)=(585900×1192)/(145×3×1.97×105)=8.15mm2、曲线段各参数如下：曲直交界点张拉力Px1=P×-（kx+μθ）=585900×e-(0.0015×1.192)=584853Nθ=12×π/180=0.20944radx=4.398mk=0.0015μ=0.225(取0.2~0.25中值)平均张拉应力：PP2=Px1（1-e-（kx+μθ））/kx+μθ=584853×（1-e-(0.0015×4.39

3、8+0.225×0.20944)）/（0.0015×4.398+0.225×0.20944）=569421N此段理论伸长值：ΔL2=(PP2×L)/(Ap×Ep)=(569421×4398)/(145×3×1.97×105)=29.22mm3、直线各参数如下：曲直交界点张拉力Px2=Px1×-（kx+μθ）=584853×e-(0.0015×4.398+0.225×0.20944)=554263Nθ=0radx=4.847mk=0.0015μ=0.225(取0.2~0.25中值)平均张拉应力：P

4、P3=Px2（1-e-（kx+μθ））/kx+μθ=554263×（1-e-(0.0015×4.847)）/（0.0015×4.847）=552253N此段理论伸长值：ΔL3=(PP3×L)/(Ap×Ep)=(552253×4847)/(145×3×1.97×105)=31.24mm4、N1理论伸长值ΔL=2×（ΔL1+ΔL2+ΔL3）=2×（8.15+29.22+31.24）=137.22mm（二）N2伸长值计算（至跨中）1、直线各参数如下：P=781.2KNθ=0radx=1.363mk=0

5、.0015μ=0.225(取0.2~0.25中值)此段理论伸长值：ΔL1=(PP1×L)/(Ap×Ep)=(781200×1363)/(145×4×1.97×105)=9.32mm2、曲线段各参数如下：曲直交界点张拉力Px1=P×-（kx+μθ）=781200×e-(0.0015×1.363)=779604Nθ=8×π/180=0.13963radx=2.932mk=0.0015μ=0.225(取0.2~0.25中值)平均张拉应力：PP2=Px1（1-e-（kx+μθ））/kx+μθ=77960

6、4×（1-e-(0.0015×2.932+0.225×0.13963)）/（0.0015×2.932+0.225×0.13963）=765809N此段理论伸长值：ΔL2=(PP2×L)/(Ap×Ep)=(765809×2932)/(145×4×1.97×105)=19.65mm3、直线各参数如下：曲直交界点张拉力Px2=Px1×-（kx+μθ）=779604×e-(0.0015×2.932+0.225×0.13963)=752177Nθ=0radx=6.113mk=0.0015μ=0.225(取

7、0.2~0.25中值)平均张拉应力：PP3=Px2（1-e-（kx+μθ））/kx+μθ=752177×（1-e-(0.0015×6.113)）/（0.0015×6.113）=755636N此段理论伸长值：ΔL3=(PP3×L)/(Ap×Ep)=(755636×6113)/(145×4×1.97×105)=40.43mm4、N1理论伸长值ΔL=2×（ΔL1+ΔL2+ΔL3）=2×（9.32+19.65+40.43）=138.8mm（三）N3伸长值计算（至跨中）1、直线各参数如下：P=781.2K

8、Nθ=0radx=1.328mk=0.0015μ=0.225(取0.2~0.25中值)此段理论伸长值：ΔL1=(PP1×L)/(Ap×Ep)=(781200×1328)/(145×4×1.97×105)=9.08mm2、曲线段各参数如下：曲直交界点张拉力Px1=P×-（kx+μθ）=781200×e-(0.0015×1.328)=779645Nθ=2×π/180=0.0349radx=0.873mk=0.0015μ=0.225(取0.2~0.25中值)平均张拉应力：PP2=Px1（1-e-（kx