三铰拱结构设计T26

第四章ChapterIV铰拱

Three-hingedarches拱

(arches)一、简介Introduction曲梁curvedbeam杆轴线为曲线在竖向荷载作用下不产生水平反力。

Thecentroidalaxisofanarchisacurvedline.Horizontalthrusts

won’tbedevelopedatthesupportsundertheactionofverticalloads.

FP三铰拱Three-hingedarch拱--杆轴线为曲线，在竖向荷载作用下会产生水平推力的结构。

Thecentroidalaxisofanarchisacurvedline.Horizontalthrustswillbedevelopedatthesupportsundertheactionofverticalloads.

拱的有关名称跨度span拱趾铰Footsupport拱趾铰Footsupport顶铰tophinge矢高rise斜拱inclinedarch拉杆拱Tiedarch平拱horizontalarch拱肋拱肋三铰拱Three-hingedarch两铰拱two-hingedarch无铰拱nonhingedarch静定拱staticallydeterminatearch超静定拱staticallyindeterminatearch超静定拱staticallyindeterminatearch二、三铰拱的解法

calculationmethodFAHFBHFAyFByFAy0FBy0a2b1b2lFP1FP2ABCl1l2fFBy=FBy0FAy=FAy0FH=MC0/

fa1等代梁请大家想：由上述公式可得哪些结论？FP1FP2CAB反力计算：列平衡方程可得FromequilibriumEquationsweobtain三铰拱的反力只与荷载及三个铰的位置有关，与拱轴线形状无关Thereactionsarerelatedtothelocationsofthehingesandloads,buthavenorelationshipwiththeformoftheaxiallineofarch.荷载与跨度一定时，水平推力与矢高成反比Givenloadsandspan,thrustisinverselyproportionaltorise1/fKxyxyFAyFByFAy0FBy0a2b1b2a1等代梁FAHFBHlFP1FP2ABCl1l2fKFP1FP2CAB内力计算thedeterminationofinternalforces：请大家对上述公式进行分析由于推力的的存在，拱拱的弯矩比比相应简支支梁的弯矩矩要小。Becauseofthehorizontalthrust,themomentofarchislessthanthatofthecorrespondingsimplebeam.三铰拱在竖竖向荷载作作用下轴向向受压.Undertheactionofverticalloads,thearchisaxiallycompressed.

三铰拱的内力不但与荷载及三个铰的位置有关，而且与拱轴线的形状有关。Theinternalforcesarenotonlydependentofloadsandthepositionsofhinges,butalsooftheformofcentroidalaxis.Example.ConstructtheinternalforcediagramsofthefollowingarchSolution:截面2为集中力作作用处，其其两侧的剪剪力将发生生突变FAyFByFAHFBH斜拱如何求求解？Howtosolvetheinclinedarches?三、三铰拱拱的合理拱拱轴线(Rationalaxiallinesofarches)使拱在给定定荷载下只只产生轴力力的拱轴线线，被称为与该荷载载对应的合理拱轴。。UndertheactionofStationaryloadstheaxiallineofanarchthatwillinducethebendingmomentonthesectionstovanishisreferredtoasrationaloroptimalaxiallineorcentrelineofthearch.只限于三铰铰平拱受竖竖向荷载作作用。合理理轴线横截面上在竖向荷载载作用下，，三铰拱的的合理拱轴线线的的纵纵坐坐标标与与相相应应简简支支梁梁弯弯矩矩图图的的竖标标成成正正比比。。UndertheactionofVerticalloads,theordinatesofoptimalcentrelineisdirectlyproportionaltothoseofthebendingmomentdiagramofthesimplebeam.试求求图图示示对对称称三三铰铰拱拱在在均均布布荷荷载载作作用用下下的的合合理理拱拱轴轴线线determinetherationalaxisofthearchundertheactionofuniformlydistributedload.MC0=ql2/8FH=ql2/8fM0=qlx/2-qx2/2=qx(l-x)/2y=4fx(l-x)/l2抛物物线线试求求三三铰铰拱拱在在垂垂直直于于拱拱轴轴线线的的均均布布荷荷载载作作用用下下的的合合理理拱拱轴轴线线。。Findtheoptimalcentrelineofthearchunderthetheuniformlydistributedloadverticaltothecentrelineofthearch返章园ρFNFN+dFNρFNFN+dFN所以以拱拱的的合合理理轴轴线线为为园园在同同样样荷荷载载作作用用下下铰铰的的相相互互位位置置不不同同，，其其合合理理轴轴线线也也不不同同，，这这是是因因为为支支座座反反力力不不同同。。Rationalaxiallinesofarcheswillnotbethesameifthepositionsofhingesaredifferentevenundertheactionofthesameloads.左图顶顶铰位位置不不同，，合理理轴线线不同同小结结Summary1.三铰拱拱与粱粱的区区别Thedifferencesbetweenthree-hingedarchesandbeams几何方方面ingeometry:几何形形状不不同thegeometricalconfigurationisdifferent受力方方面instaticaspect:三铰拱拱脚有有水平平力horizontalthrustwillbedevelopedinsupports；2.水平推推力依依赖于于何种种因素素Thefactorsinfluencinghorizontalthrust三铰拱拱的反反力只只与荷荷载及及三个个铰的的位置置有关关，与与拱轴轴线形形状无无关Thereactionsarerelatedtothelocationsofthehinges,buthavenorelationshipwiththeformoftheaxiallineofarch.荷载与与跨度度一定定时，，水平平推力力与矢矢高成成反比比3.内力依依赖于于何种种因素素Thefactorsinfluencinginternalforces三铰拱拱的内内力不不但与与荷载载及三三个铰铰的位位置有有关，，而且且与拱拱轴线线的形形状有有关。。Theinternalforcesarenotonlydependentofloadsandthepositionsofhinges,butalsooftheformofcentroidalaxis.4.粱与三三铰拱拱内力力分布布的不不同Thedifferenceoftheinternalforcedistributioninbeamsandthree-hingedarches；由于推推力的的存在在，拱拱的弯弯矩比比相应应简支支梁的的弯矩矩要小小。Becauseofthehorizontalthrust,themomentofarchislessthanthatofthecorrespondingsimplebeam.三铰拱拱在竖竖向荷荷载作作用下下轴向向受压压.Undertheactionofverticalloads,thearchisaxiallycompressed.5.三铰拱的的合理轴轴线Rationalaxiallinesofarches。词汇Vocabulary1.