20米箱梁预应力张拉伸长量计算(最终109)

20米箱梁预应力张拉伸长量计算(最终109) 20米箱梁预应力张拉伸长量计算 钢铰线强度:1860MPa 控制应力:1860×0.75,1395 MPa 钢铰线公称面积:140 mm2 单根控制力:1395×140.0,195300 N 伸长量计算公式:?L,Pp×L?(Ap×Ep) 一、 中跨 1#束 ?直线段长 0.537米 ?竖曲线段长 L,π?180?×a×R, 3.1415926?180?×5.5?×30.0,2.880米 ?直线段长 4.869 米 ?平曲线段长 L,π?180?×a×R,3.1415926?180?×1.8?×25.0,0.785?COS5.5?,0.789 ?直线段长 0.728米 ?工具段长 0.74米(由于箱梁板顶预埋筋影响，千斤顶不能靠近锚环，为不弯曲板顶预埋筋，需增加一个过渡环，具体尺寸为:锚环0.046m+限位板0.035m+过渡环0.25m+千斤顶0.363m+锚环0.046m=0.74m) Pp ,P×(1,e-(kx，μθ))?(kx，μθ) Pp,P,195300 N Ep,198 GPa 得: ?的伸长量: e,2.718281828 k,0.0015 x,0.74 μ,0.25 θ,0? 195300×(1-2.71828-(0.0015×0.74))?(0.0015×0.74) ,195191.52 N 195191.52×740?(140×198000),5.21mm ?的伸长量: e,2.718281828 k,0.0015 x,1.468 μ,0.25 θ,0? 195300×(1-2.71828-(0.0015×1.468))?(0.0015×1.468) ,195085.00 N 195085.00×728?(140×198000),5.12mm ?的伸长量: e,2.718281828 k,0.0015 x,2.257 μ,0.25 1.8?×0.017453293,0.03142 θ, 195300×(1-2.71828-(0.0015×2.257，0.25×0.03142))?(0.0015×2.257，0.25×0.03142),194206.34 N 194206.34×789?(140×198000),5.53 mm ?的伸长量: e,2.718281828 k,0.0015 x,7.126 μ,0.25 θ,1.8?×0.017453293,0.03142 ) 195300×(1-2.71828-(0.0015×7.126，0.25×0.03142))?(0.0015×7.126 ，0.25×0.03142),193500.19 N 193500.19×4869?(140×198000),34.00mm ?的伸长量: e,2.71828 k,0.0015 x,10.006 μ,0.25 θ,7.3?×0.017453293,0.12741 195300×(1-2.71828-(0.0015×10.006，0.25×0.12741))?(0.0015×10.006，0.25×0.12741),190794.5 N 190794.5×2880?(140×198000),19.82mm ?的伸长量: e,2.718281828 k,0.0015 x,10.543 μ,0.25 θ,7.3?×0.017453293,0.12741 195300×(1-2.71828-(0.0015×10.543，0.25×0.12741))?(0.0015×10.543，0.25×0.12741),190718.28 N 190718.28×537?(140×198000),3.69mm 1#束的伸长量为: 5.21，5.12，5.53，34.0，19.82，3.69,73.37×2,146.74 mm 2#束 ?直线段长 2.015米 ?竖曲线段长 L,π?180?×a×R, 3.1415926?180?×5.5?×30.0,2.88米 ?直线段长 3.408 米 ?平曲线段长 L,π?180?×a×R,3.1415926?180?×1.8?×25.0,0.785?COS5.5?,0.789 ?直线段长 0.728米 ?工具段长 0.49米(锚环0.046m+限位板0.035m+千斤顶0.363m+锚环0.046m=0.49m) P×(1,e-(kx，μθ))?(kx，μθ) Pp, Pp,P,195300 N Ep,198 GPa 得: ?的伸长量: e,2.718281828 k,0.0015 x,0.49 μ,0.25 θ,0? 195300×(1-2.71828-(0.0015×0.49))?(0.0015×0.49) ,195228.11 N 195228.11×490?(140×198000),3.45 mm ?的伸长量: e,2.718281828 k,0.0015 x,1.218 μ,0.25 θ,0? 195300×(1-2.71828-(0.0015×1.218))?(0.0015×1.218) ,195121.57 N 195121.57×728?(140×198000),5.12mm ?的伸长量: e,2.718281828 k,0.0015 x,2.007 μ,0.25 θ,1.8?×0.017453293,0.03142 195300×(1-2.71828-(0.0015×2.007，0.25×0.03142))?(0.0015×2.007，0.25×0.03142),194242.69 N 194242.69×789?(140×198000),5.53 mm ?的伸长量: e,2.718281828 k,0.0015 x,5.415 μ,0.25 θ,1.8?×0.017453293,0.03142 195300×(1-2.71828-(0.0015×5.415，0.25×0.03142))?(0.0015×5.415，0.25×0.03142),193747.94 N 193747.94×3408?(140×198000),23.82 mm ?的伸长量: e,2.71828 k,0.0015 x,8.295 μ,0.25 θ,7.3?×0.017453293,0.12741 195300×(1-2.71828-(0.0015×8.295，0.25×0.12741))?(0.0015×8.295，0.25×0.12741),191037.63 N 191037.63×2880?(140×198000),19.85 mm ?的伸长量: e,2.718281828 k,0.0015 x,10.31 μ,0.25 θ,7.3?×0.017453293,0.12741 195300×(1-2.71828-(0.0015×10.31，0.25×0.12741))?(0.0015×10.31，0.25×0.12741),190751.34 N 190751.34×2015?(140×198000),13.87 mm 2#束的伸长量为: 3.45，5.12，5.53，23.82，19.85，13.87,71.64×2,143.28 mm 3#束 ?直线段长 7.901米 ?竖曲线段长 L,π?180?×a×R, 3.1415926?180?×1.4?×30.0,0.733米 ?直线段长 1.065 米 ?工具段长 (由于箱梁板顶预埋筋影响，千斤顶不能靠近锚 0.74米 环，为不弯曲板顶预埋筋，需增加一个过渡环，具体尺寸为:锚环0.046m+限位板0.035m+过渡环0.25m+千斤顶0.363m+锚环0.046m=0.74m) Pp,P×(1,e- (kx，μθ))?(kx，μθ) Pp,P,195300 N Ep,198 GPa 得: ?的伸长量: e,2.718281828 k,0.0015 x,0.74 μ,0.25 θ,0? 195300×(1-2.71828-(0.0015×0.74))?(0.0015×0.74) ,195191.52 N 195191.52×740?(140×198000),5.21 mm ?的伸长量: e,2.718281828 k,0.0015 x,1.805 μ,0.25 θ,0? 195300×(1-2.71828-(0.0015×1.805))?(0.0015×1.805) ,195035.72 N 195035.72×1065?(140×198000),7.49 mm ?的伸长量: e,2.71828 k,0.0015 x,2.538 μ,0.25 θ,1.4?×0.017453293,0.02443 195300×(1-2.71828-(0.0015×2.538，0.25×0.02443))?(0.0015×2.538，0.25×0.02443),194334.91 N 194334.91×733?(140×198000),5.14 mm ?的伸长量: e,2.71828 k,0.0015 x,10.439 μ,0.25 θ,1.4?×0.017453293,0.02443 195300×(1-2.71828-(0.0015×10.439，0.25×0.02443))?(0.0015×10.439，0.25×0.02443),193189.76 N 193189.76×7901?(140×198000),55.06mm 3#束的伸长量为: 5.21，7.49，5.14，55.06,72.9×2,145.8 mm 二、 边跨 1#束 ?直线段长 2.148米 ?竖曲线段长 L,π?180?×a×R, 3.1415926?180?×5.5?×30.0,2.880米 ?直线段长 3.308 米 ?平曲线段长 L,π?180?×a×R,3.1415926?180?×1.8? ×25.0,0.785?COS5.5?,0.789 ?直线段长 0.724米 ?工具段长 0.64米(由于箱梁板顶预埋筋影响，千斤顶不能靠近锚环，为不弯曲板顶预埋筋，需增加一个过渡环，具体尺寸为:锚环0.046m+限位板0.035m+过渡环0.15m+千斤顶0.363m+锚环0.046m=0.64m) Pp,P×(1,e-(kx，μθ))?(kx，μθ) Pp,P,195300 N Ep,198 GPa 得: ?的伸长量: e,2.718281828 k,0.0015 x,0.64 μ,0.25 0? θ, 195300×(1-2.71828-(0.0015×0.64))?(0.0015×0.64) ,195206.15 N 195206.15×640?(140×198000),4.51 mm ?的伸长量: e,2.718281828 k,0.0015 x,1.364 μ,0.25 θ,0? 195300×(1-2.71828-(0.0015×1.364))?(0.0015×1.364) ,195100.21 N 195100.21×724?(140×198000),5.10 mm ?的伸长量: e,2.718281828 k,0.0015 x,2.153 μ,0.25 θ,1.8?×0.017453293,0.03142 195300×(1-2.71828-(0.0015×2.153，0.25×0.03142))?(0.0015×2.153，0.25×0.03142),194221.46 N 194221.46×789?(140×198000),5.53 mm ?的伸长量: e,2.718281828 k,0.0015 x,5.461 μ,0.25 θ,1.8?×0.017453293,0.03142 195300×(1-2.71828-(0.0015×5.461，0.25×0.03142))?(0.0015×5.461，0.25×0.03142),193741.28 N 193741.28×3308?(140×198000),23.12 mm ?的伸长量: e,2.71828 k,0.0015 x,8.341 μ,0.25 θ,7.3?×0.017453293,0.12741 195300×(1-2.71828-(0.0015×8.341，0.25×0.12741))?(0.0015×8.341，0.25×0.12741),191031.09 N 191031.09×2880?(140×198000),19.85 mm ?的伸长量: e,2.718281828 k,0.0015 x,10.489 μ,0.25 θ,7.3?×0.017453293,0.12741 195300×(1-2.71828-(0.0015×10.489，0.25×0.12741))?(0.0015×10.489，0.25×0.12741),190725.94 N 190725.94×2148?(140×198000),14.78 mm 1#束的伸长量为: 4.51，5.10，5.53，23.12，19.85，14.78,72.89+73.37,146.26 mm 2#束 ?直线段长 3.608米 ?竖曲线段长 L,π?180?×a×R, 3.1415926?180?×5.5?×30.0,2.88米 ?直线段长 1.84 米 ?平曲线段长 L,π?180?×a×R,3.1415926?180?×1.8?×25.0,0.785?COS5.5?,0.789 ?直线段长 0.724米 ?工具段长 0.64米(由于箱梁板顶预埋筋影响，千斤顶不能靠近锚环，为不弯曲板顶预埋筋，需增加一个过渡环，具体尺寸为:锚环0.046m+限位板0.035m+过渡环0.15m+千斤顶0.363m+锚环0.046m=0.64m) Pp,P×(1,e-(kx，μθ))?(kx，μθ) Pp,P,195300 N Ep,198 GPa 得: ?的伸长量: e,2.718281828 k,0.0015 x,0.64 μ,0.25 θ,0? 195300×(1-2.71828-(0.0015×0.64))?(0.0015×0.64) ,195206.15 N 195206.15×640?(140×198000),4.51 mm ?的伸长量: e,2.718281828 k,0.0015 x,1.364 μ,0.25 θ,0? 195300×(1-2.71828-(0.0015×1.364))?(0.0015×1.364) ,195100.21 N 195100.21×724?(140×198000),5.10 mm ?的伸长量: e,2.718281828 k,0.0015 x,2.153 μ,0.25 θ,1.8?×0.017453293,0.03142 195300×(1-2.71828-(0.0015×2.153，0.25×0.03142))?(0.0015×2.153 ，0.25×0.03142),194221.46 N 194221.46×789?(140×198000),5.53mm ?的伸长量: e,2.718281828 k,0.0015 x,3.993 μ,0.25 θ,1.8?×0.017453293,0.03142 195300×(1-2.71828-(0.0015×3.993，0.25×0.03142))?(0.0015×3.993， 0.25×0.03142),193954.17 N 193954.17×1840?(140×198000),12.87mm ?的伸长量: e,2.71828 k,0.0015 x,6.873 μ,0.25 θ,7.3?×0.017453293,0.12741 195300×(1-2.71828-(0.0015×6.873，0.25×0.12741))?(0.0015×6.873 ，0.25×0.12741),191240.01N 191240.01×2880?(140×198000),19.87 mm ?的伸长量: e,2.718281828 k,0.0015 x,10.481 μ,0.25 θ,7.3?×0.017453293,0.12741 195300×(1-2.71828-(0.0015×10.481，0.25×0.12741))?(0.0015×10.481，0.25×0.12741),190727.08 N 190727.08×3608?(140×198000),24.82 mm 2#束的伸长量为: 4.51，5.10，5.53，12.87，19.87，24.82,72.7+71.64,144.34 mm 3#束 ?直线段长 8.021米 ?竖曲线段长 L,π?180?×a×R, 0.733米 ?直线段长 1.065 米 ?工具段长 3.1415926?180?×1.4?×30.0, 0.74米(由于箱梁板顶预埋筋影响，千斤顶不能靠近锚环，为不弯曲板顶预埋筋，需增加一个过渡环，具体尺寸为:锚环0.046m+限位板0.035m+过渡环0.25m+千斤顶0.363m+锚环0.046m=0.74m) Pp,P×(1,e-(kx，μθ))?(kx，μθ) Pp,P,195300 N Ep,198 GPa 得: ?的伸长量: e,2.718281828 k,0.0015 x,0.74 μ,0.25 θ,0? 195300×(1-2.71828-(0.0015×0.74))?(0.0015×0.74) ,195191.52 N 195191.52×740?(140×198000),5.21 mm ?的伸长量: e,2.718281828 k,0.0015 x,1.805 μ,0.25 θ,0? 195300×(1-2.71828-(0.0015×1.805))?(0.0015×1.805) ,195035.72 N 195035.72×1065?(140×198000),7.49 mm ?的伸长量: e,2.71828 k,0.0015 x,2.538 μ,0.25 θ,1.4?×0.017453293,0.02443 195300×(1-2.71828-(0.0015×2.538，0.25×0.02443))?(0.0015×2.538，0.25×0.02443),194334.91 N 194334.91×733?(140×198000),5.14 mm ?的伸长量: e,2.71828 k,0.0015 x,10.559 μ,0.25 θ,1.4?×0.017453293,0.02443 195300×(1-2.71828-(0.0015×10.559，0.25×0.02443))?(0.0015×10.559， 0.25×0.02443),193172.44 N 193172.44×8021?(140×198000),55.90 mm 3#束的伸长量为: 5.21，7.49，5.14，55.90,73.74+72.9,146.64 mm