T形單梁計算全英文課程設(shè)計

1、Design information 1. Simple supported beam with span 31m and the calculated span is 29.66m2. Design load: vehicle load:grade , pedestrian load: 3.0,coefficient for important of the structure: .3. Environment: bridge is located in the wild general areas, grade environment, annual average relative hu

2、midity 75%.4. Material: prestressed reinforcement uses eliminate stress spiral rib wire bundle, characteristic value of tension strength ; design value of tension strength , elastic modulus ;BBRV anchorage.Non-prestressed reinforcement: HRB400, characteristic value of tension strength , design value

3、 of tension strength . When diameter , use HRB335, characteristic value of tension strength, design value of tension strength. Elastic modulus of steel is .Concrete: C50 for main girder, , characteristic value of compression strength, design value of compression strength; characteristic value of ten

4、sion strength, design value of tension strength.5. Design detailing: according to JTG D622004, design as full prestressing concrete structural.6. Construction methods: posttensioning, pre-stressing ducts use embedded metal bellows forming, wire bundles tensioned at both side at the same time with ja

5、cks; cast in place 400mm wet-joint. Finally pave 400mm asphalt deck pavement.1. Dimension of main girder Dimension of all parts of main girder is shown in the chart ( units:mm): 2. Section property of main girder1) Calculation of effective width of compression flange So effective width of compressio

6、n flange is 2) Calculation of section property (summation block)Section property of mid-span and L/4 span NumberArea (mm2)(mm)(mm3)(mm)(mm4)(mm4)b(mm)h(mm)3600009032400000454 10001809600022021120000324 800120320000800256000000-256 200160020000153330660000-989 100200800001700136000000-1156 400200Sum

7、876000544 476180000 1256 Section dimension and property of mid-span and L/4 span are same. 3. Calculation of inner force of main girder As follows:Value of combination for action effects of main girder (units :)Calculation span 29.66 Load Inner force Name Distance mid-span section x=14.83mL/4 sectio

8、n x=7.415m Changed point section x=3.7mSupported section Load Collection Degree M maxVV maxMM maxVV maxMM maxV maxV maxCharacteristic value of one stage of dead load G12421.9 0.0 0.0 2421.9 1816.4 163.3 163.3 1816.4 1057.7 245.1 312.5 22.024Second stage of dead load G2Wet joint cast in place G21224.

9、1 0.0 0.0 224.1 168.1 15.1 15.1 168.1 97.9 22.7 28.9 2.038Pavement and balustrade G22522.9 0.0 0.0 522.9 392.2 35.3 35.3 392.2 228.4 52.9 67.5 4.755Characteristic value of pedestrian load Q265.8 0.0 2.2 32.9 45.2 4.6 4.9 37.0 26.0 6.4 8.2 2.25Characteristic value of vehicle load of grade ( ignore im

10、pact factor )1523.7 64.4 101.6 1143.1 1175.1 287.3 287.3 1175.1 874.0 220.3 326.3 10.5Characteristic value of vehicle load of grade( consider impact factor, =0.083）1650.2 69.7 110.0 1238.0 1272.6 311.1 311.1 1272.6 946.5 238.6 353.4 The variable characteristic value combination of stress calculate i

11、n persistent state (vehicular+pedestrian )1716.0 69.7 112.2 1270.9 1317.8 315.7 316.0 1309.6 972.5 245.0 361.6 Basic combination of ultimate limit state 6186.5 97.6 156.5 5572.6 4684.3 697.2 697.5 4675.1 3015.0 726.1 977.3 The variable design value combination of serviceability limit state in short

12、term 1132.4 45.1 73.3 833.1 867.8 205.7 206.0 859.6 637.8 160.6 236.6 The variable design value combination of serviceability limit state in long term635.8 25.8 41.5 470.4 488.1 116.8 116.9 484.8 360.0 90.7 133.8 4. Calculation of area of reinforcement and arrangement 1) Estimating of reinforcement

13、areaAssuming the distance between gravity center of prestressed steel and blow of section is and distance between centroid axis and composition of prestressed forces action point is ; section area , total cross section of elastic resistance moment crack edges , according to cross-section crack resis

14、tant requirements of mid-span, calculate effective prestressed force of full prestressed concrete members. For wire bundle, control stress for tensioning . Tensioned prestressed loss control stress by 20% estimate, so getting the area of prestressed reinforcement: , designed to use 3×, the actu

15、al area , metal bellows into the hole.2) Arrangement of prestressed reinforcement1 Cross-section of prestressed reinforcement in the arrangement: referring to the drawings having designed, design the initial arrangement of steel of mid-span section.2 Arrangement of anchorage section: as follows 3 Po

16、sition and angle of wire bundle in other section a. Bending shape, angle and radius of wire bundle Using lines-circle type and bending angle of N1, N2, N3 is . Bending radius is b. Location of control point N1:Horizontal distance from traverse point to anchor point: . Horizontal distance from bent p

17、oint to traverse point: .Horizontal distance from bent point to anchor point: Horizontal distance from bent point to mid span section : Horizontal distance from end-bent point to traverse point: Horizontal distance from end-bent point to mid span section : N2:Horizontal distance from traverse point

18、to anchor point: . Horizontal distance from bent point to traverse point: .Horizontal distance from bent point to anchor point: Horizontal distance from bent point to mid span section : Horizontal distance from end-bent point to traverse point: Horizontal distance from end-bent point to mid span sec

19、tion : N3:Horizontal distance from traverse point to anchor point: . Horizontal distance from bent point to traverse point: .Horizontal distance from bent point to anchor point: Horizontal distance from bent point to mid span section : Horizontal distance from end-bent point to traverse point: Horiz

20、ontal distance from end-bent point to mid span section : control elements table of bending wire bundle Number Elevated valuesC(mm)Bending angle( 0°)Bending radius R(mm)Horizontal distance from supported point to anchor point d (mm)Horizontal distance from bent point to mid span section (mm)Hori

21、zontal distance from end-bent point to traverse point (mm)N1151084500015610957358N2800830000256729611472N34008150003121124713335c. Position and angle of each section , calculate the distance to bottom of beam at any point and horizontal bending angle . Calculated table of position and angle of each

22、point Calculated section Number of wire bundle (°) RMid-span section (-)N11095314731166263Negative , steel has not been bent 0 0 100 45000 N27296209820784176Negative , steel has not been bent0 0 100 30000 0N311247104910392088Negative , steel has not been bent0 0 100 15000 L/4 span N110953147311

23、66263(xi-xk)>(Lb1+Lb2)8 446 546 45000 N272962098207841761190.227 0 100 30000 7415N311247104910392088Negative , steel has not been bent0 0 100 15000 Changed point section (-)N11095314731166263(xi-xk)>(Lb1+Lb2)8 968 1068 45000 N2729620982078417638347.346 246 346 30000 11130N311247104910392088Neg

24、ative , steel has not been bent0 0 100 15000 Supported section N11095314731166263(xi-xk)>(Lb1+Lb2)8 1487 1587 45000 N27296209820784176(xi-xk)>(Lb1+Lb2)8 764 864 30000 14830N311247104910392088(xi-xk)>(Lb1+Lb2)8 356 456 15000 d. Position and angle of horizontal bending of wire bundle For N2 a

25、nd N3, use same mode with two curves, angle is . As follows: 3) Calculation of area and arrangement of non-prestressed reinforcementUsing ultimate limit state requirement to calculate the number of non-prestressed reinforcement.Assuming the distance from position of composition force of prestressed

26、and non-prestressed reinforcement to the bottom of section is and effective depth is Assuming the first type T shape section, so and get The area of non-prestressed reinforcement is , so no need to configure non-prestressed reinforcement 5. Section geometric propertyThree construction stage : 1) mai

27、n beam precast and prestressed reinforcement tensioning; 2) Grouting and anchoring, casting 400mm wet joint after main beam hoisted; 3) the construction of pavement, balustrade, and sidewalk and operation.The section geometric property of mid-span as shown in the table and calculating other control

28、section. Section geometric property of mid-span in first construction stage Name Inertia Ii+IXArea of all section concrete 804000584 469.700×1062.850×1011-16212.467×106Area of reserve ducts -3××702/4=-115451700-19.627×1060-1132 -14795.856×106Area of net section An=

29、792454567 450.073×1062.850×1011-14583.389×1062.704×1011 Section geometric property of mid-span in second construction stage Name Inertia Ii+IXArea of all section concrete 804000 584 469.700×1062.850×101124420.857×106Transformed area of prestressed reinforcement （ES

30、-1）Ap=17880 1700 30.396×1060-1092 21302.887×106Area of net section An=820831 608500.096×106 2.850×101121776.645×1063.068×1011 Section geometric property of mid-span in third construction stage Name Inertia Ii+IXArea of all section concrete 876000 544476.180×1063.01

31、3×101122 416.303×106Transformed area of prestressed reinforcement （ES-1）Ap=178801700 30.396×1060-113522964.193×106Area of net section An=892831 567 506.576×106 3.013×101123432.921×1063.248×1011Summary table of geometric property of each control section under d

32、ifferent construction stage Stage Calculated section Frist stageBefore duct grouting Mid-span section 792455 567.9 1232.1 1132.1 2.704×10114.762×1082.195×1082.389×108L/4 section 792455 570.1 1229.9 1129.9 2.741×10114.807×1082.228×1082.426×108Changed point sect

33、ion 792455 573.8 1226.2 1126.2 2.791×10114.864×1082.276×1082.478×108Supported section 1044455 650.6 1149.4 1049.4 3.343×10115.138×1082.909×1083.186×108Second stageThe time between pipeline hardened to wet joint start hardening Mid-span section 821880608.51191.

34、5 1091.5 3.068×10115.042×1082.575×1082.811×108L/4 section 821880605.2 1194.8 1094.8 3.014×10114.979×1082.522×1082.753×108Changed point section 821880599.7 1200.3 1100.3 2.939×10114.900×1082.448×1082.671×108Supported section 1073880655.6 114

35、4.4 1044.4 3.353×10115.114×1082.929×1083.210×108Third stage Wet joint hardened Mid-span section 893880 566.7 1233.3 1133.3 3.248×10115.731×1082.633×1082.866×108L/4 section 893880 563.7 1236.3 1136.3 3.191×10115.661×1082.581×1082.809×108Chan

36、ged point section 893880 558.6 1241.4 1141.4 3.112×10115.572×1082.507×1082.723×108Supported section 1145880 620.0 1180.0 1080.0 3.570×10115.758×1083.026×1083.306×108 6. Calculation of ultimate limit state for long term 1) Carrying capacity of normal section Fo

37、r mid-span, Assuming frist type T shape section ,so and its frist type T shape section and no over-reinforcement.Bending carrying capacity: OK!2) Carrying capacity of inclined section1 Bending resistance ( For changed point section ) , , Upper limit( minimum size of section ): Lower limit(constructi

38、on detailing ): Stirrup using HRB335, 10, double shaft, , , , , OK!2 Shear resistance Because the number of reinforcement has no changed along span and bending angle is small, shear capacity didnt control design 3 Construction detailingSatisfied the construction detailing: and and the spacing of pip

39、eline 7. Estimated of prestressed force lossControl tensioning stress of prestressed reinforcement 1) Friction: , Calculation of friction loss l1Number xkxconl1（°)radian N180.1396 0.0349 14.9860.0225 0.0558 1327.574.03 N212.1450.2120 0.0530 15.0860.0226 0.0728 1327.596.69 N312.1450.2120 0.0530

40、15.1420.0227 0.0729 1327.596.79 Average 89.17 Calculation friction loss of other control section is same Average friction loss of prestressed reinforcement in other control sectionl1 Section Mid-span L/4Changed point Supported l1average 89.1752.4724.170.482) Anchorage slip Getting from table, for BB

41、RV anchorage: anchorage deformation Calculated table of length that antifriction affected Number N11327.574.03 1253.47 149860.004940 6442 N21327.596.691230.81 150860.006409 5656 N31327.596.79 1230.71 151420.006392 5663 All prestressed wire bundle satisfied , so , and Calculated table of prestressed

42、reinforcement loss because of anchorage slip Section Number X (mm)Lf (mm)(MPa)l2 (MPa)Average Mid-span section N1149866442 63.65 x>lf antifriction did not affect section 0.00 N2150865656 72.49 x>lf antifriction did not affect sectionN3151425663 72.40 x>lf antifriction did not affect section

43、L/4 section N175716442 63.65 x>lf antifriction did not affect section0.00 N276715656 72.49 x>lf antifriction did not affect sectionN377275663 72.40 x>lf antifriction did not affect sectionChanged point section N138566442 63.65 25.55 22.81 N239565656 72.49 21.79 N340125663 72.40 21.11 Suppor

44、ted section N11566442 63.65 62.11 66.58 N22565656 72.49 69.21 N33125663 72.40 68.41 3) Elastic shortening (L/4 section ), , So 4) Relaxation (L/4 section ) and , So 5) Creep and shrinkage Relative humidity 75%, age 20d, for secondary stage dead load, age 90d, theoretical calculated thickness , getti

45、ng from table , and For mid-span section: For L/4 section: So , , , , , , Summary table of average prestress loss and effective prestress of control section Section Prestress loss Type Stage Prestressing stage Prestressing stage Effective prestress Prestressing stage Prestressing stage Mid-span sect

46、ion 89.17055.71144.88 32.34127.42159.76 1182.62 1022.86 L/4 section 52.47055.71108.18 32.34127.42159.76 1219.32 1059.56 Changed point section 24.1722.8155.71102.69 32.34127.42159.76 1224.81 1065.05 Supported section 0.4866.5855.71122.77 32.34127.42159.76 1204.73 1044.97 8. Check of stress 1) Normal

47、stress in short term (mid-span )Short term: Transportation and erection stage Limit stress of concrete in construction stage (C45):Compression force: Tension force: there is no tension force , so configure longitudinal non-prestressed reinforcement( ) 2) Normal stress in long term Normal stress of c

48、oncrete section(mid-span ):concrete : OK!Prestress reinforcement OK!Normal stress of concrete section(L/4 ):concrete OK!Prestress reinforcement OK!3) Principal stress in long term (changed point section )1 Area moment of section Calculation table of area moment Type of section Frist stage (x=573.8mm

49、)Secondary stage (x=599.7mm)Third stage (x=558.6mm)Position of point a-ax0-x0b-ba-ax0-x0b-ba-ax0-x0b-bSign of area moment Area moment 1.987×1082.062×1081.380×1082.102×1082.190×1081.552×1082.257×1082.324×1081.616×1082 Calculation of principal stress (a-a)S

50、hear stress Normal stress , Principal stress Calculated table of principal stress of changed point section Calculated fiber Area moment (mm4)Shear stress (MPa)Normal stress (MPa)Principal stress (MPa)Net section in frist stage Transformed section in secondary stage Transformed section in third stage

51、 Tension Compression a-a1.987×1082.102×1082.257×1080.81 4.26 -0.15 4.41 x0-x02.062×1082.190×1082.324×1080.83 4.75 -0.14 4.90 b-b1.380×1081.552×1081.616×1080.59 6.37 -0.05 6.42 3 Check of principal stress Limit value for principal compression stress is , L

52、imit value for principal tension stress is OK!9. Check of cracking resistance 1) Check of cracking resistance of normal section (mid-span section)Compression stress of concrete edge in short term Tension stress of concrete edge in short term Check of short term OK!Tension stress of concrete edge in long term Check of long term OK!2) Check of cracking resistance of incline section (changed point section)Shear stress Normal stress Prin