20米预应力空心小箱梁张拉伸长量计算

20米预应力空心小箱梁张拉伸长量计算
一、钢绞线张拉控制力计算
边跨：N1=N2=N3=5×(1860×0.75×140)=976.5KN
中跨：N1=N3=4×（1860×0.75×140)=781.2 KN
N2=5×（1860×0.75×140)=976.5 KN
二、钢绞线伸长量计算
已知θ1=(2×3.14)÷180=0.035
θ2=θ3=（6×3.14）÷180=0.1047
E=2.0×105Mpa A=140mm2
U=0.17 K=0.0015
边跨：
N1 L ab=2.198+(0.05+0.35+0.025)=2.198+0.425=2.623m
L bc=1.047mm L CD=5.256+1.237=6.493m
§=0.75×1860×140=195.3KN
AB段：Pq=195.3×5=976.5KN
Pz=976.5×e-（0.0015×2.623+0.17×0）=974.35KN
Pp=Pq×(1-e-（KX+UQ）)/(KX+UQ)=(Pq+ Pz)/2=(976.5+974.35)/2=975.42KN △L1=Pp*L/(A×E)=975.42×2.623/(5×140×200)×1000=18.34mm
BC段：Pq=974.35KN
Pz=974.35×e-（0.0015×1.047+0.17×0.035）=967.05KN
Pp=（974.35+967.05）÷2=970.7KN
△L2=Pp*L/(A×E)=970.7×1.047÷(5×140×200)×1000=7.26mm
CD段：Pq=967.05KN
Pz=967.05×e-（0.0015×6.493+0.17×0）=957.68KN
Pp=（967.05+957.68）÷2=962.37KN
△L3= 962.37×6.493÷(5×140×200)×1000=44.63mm
则总伸长值为：L=（△L1+△L2+△L3）×2=(18.34+7.26+44.63)×2=140.46mm
N2
L ab=2.637+0.425=3.062m L bc=3.142m L cd=2.716+1.237=3.953m
AB段：Pq=195.3×5=976.5KN
Pz=976.5×e-（0.0015*3.062+0.17*0）=972.03KN
Pp=(976.5+972.03)÷2=974.27KN
△L1=Pp*L/(A*E)=974.27×3.062/(5×140×200)×1000=21.31mm
BC段：Pq=Pzab=972.03KN Pz=972.03×e-（0.0015×3.142+0.17×0.1047）=955.14KN Pp=（972.03+955.14）÷2=963.59KN
△L2= 963.59×3.142÷(5×140×200)×1000=21.63mm
CD段：Pq=955.14KN
Pz=955.14×e-（0.0015×3.953+0.17×0）=950.74KN
Pp=（955.14+950.74）÷2=952.94KN
△L3= 952.94×3.953÷(5×140×200)×1000=26.91mm
则总伸长值为：L=（△L1+△L2+△L3）×2=(21.31+21.63+26.91)×2=139.7mm N3
L ab=5.077+0.425=5.502m L bc=3.142m L cd=0.29+1.237=1.527m
AB段：Pq=195.3×5=976.5KN
Pz=976.5×e-（0.0015×5.502+0.17×0.1047）=951.39KN
Pp=(976.5+951.39)÷2=963.95KN
△L1= 963.95×5.502÷(5×140×200)×1000=37.88mm
BC段：Pq=Pzab=951.39KN
Pz=951.39×e-（0.0015×3.142+0.17×0.1047）=934.86KN
Pp=（951.39+934.86）÷2=943.13KN
△L2= 943.13×3.142÷(5×140×200)×1000=21.17mm
CD段：Pq=934.86KN
Pz=934.86×e-（0.0015×1.527+0.17×0）=933.19KN
Pp=（934.86+933.19）÷2=934.03KN
△L3= 934.03×1.527÷(5×140×200)×1000=10.19mm
则总伸长值为：L=（△L1+△L2+△L3）×2=(37.88+21.17+10.19)×2=138.48mm
中跨:
N1
L ab=2.198+(0.05+0.35+0.025)=2.198+0.425=2.623m
L bc=1.047m L cd=5.256+1.194=6.45m
AB段：Pq=4×（1860×0.75×140)=781.2 KN
Pz=781.2×e-（0.0015×2.623+17×0）=778.81KN
Pp=(781.2+778.81)÷2=780.01KN
△L1= 780.01×2.623÷(4×140×200)×1000=18.27mm
BC段：Pq=778.81KN
Pz=778.81×e-（0.0015×1.047+0.17×0.1047）=767.15KN
Pp=（778.81+767.15）÷2=772.98KN
△L2 =772.98×1.047÷(4×140×200)×1000=7.23mm
CD段：Pq=767.15KN
Pz=767.15×e-（0.0015×6.45+0.17×0）=761.39KN
Pp=（767.15+761.39）÷2=764.27KN
△L3=764.27×6.45÷(4×140×200)×1000=44.01mm
则总伸长值为：L=（△L1+△L2+△L3）×2=(18.27+7.23+44.01)×2=139.02mm N2
L ab=2.637+0.425=3.062m L bc=3.142m L cd=2.716+1.194=3.91m
AB段：Pq=195.3×5=976.5KN
Pz=976.5×e-（0.0015×3.062+0.17×0）=972.03KN
Pp=(976.5+972.03)÷2=974.27KN
△L1 =974.27×3.062÷(5×140×200)×1000=21.31mm
BC段：Pq =972.03KN
Pz=972.03×e-（0.0015×3.142+0.17×0.1047）=955.14KN
Pp=（972.03+955.14）÷2=963.59KN
△L2= 963.59×3.142÷(5×140×200)×1000=21.63mm
CD段：Pq=955.14KN
Pz=955.14×e-（0.0015×3.91+0.17×0）=950.81KN
△L3= 950.81×3.91÷(5×140×200)×1000=26.55mm
则总伸长值为：L=（△L1+△L2+△L3）×2=(21.31+21.63+26.55)×2=138.98mm N3
L ab=5.077+0.425=5.502mm L bc=3.142mm L cd=0.29+1.194=1.484mm
AB段：Pq=4×（1860×0.75×140)=781.2 KN
Pz=781.2×e-（0.0015×5.502+0.17×0）=774.78KN
Pp=(981.2+774.78)÷2=777.99KN
△L1= 777.99×5.502÷(4×140×200)×1000=38.22mm
BC段：Pq =774.78KN
Pz=774.78×e-（0.0015×3.142+0.17×0.1047）=757.53KN
Pp=（774.78+757.53）÷2=766.16KN
△L2= 766.16×3.142÷(4×140×200)×1000=21.49mm
CD段：Pq=757.53KN
Pz=757.53×e-（0.0015×1.484+0.17×0）=755.85KN
Pp=（757.53+755.85）÷2=756.69KN
△L3= 756.69×1.484÷(4×140×200)×1000=10.03mm
则总伸长值为：L=（△L1+△L2+△L3）×2=(38.22+21.49+10.03)×2=139.48mm
设计控制张拉力及伸长量一览表
实际计算控制张拉力及伸长量一览表。