三鉸拱結(jié)構(gòu)設(shè)計(jì)T26

第四章ChapterIV鉸拱

Three-hingedarches拱

(arches)一、簡介Introduction曲梁curvedbeam桿軸線為曲線在豎向荷載作用下不產(chǎn)生水平反力。

Thecentroidalaxisofanarchisacurvedline.Horizontalthrusts

won’tbedevelopedatthesupportsundertheactionofverticalloads.

FP三鉸拱Three-hingedarch拱--桿軸線為曲線，在豎向荷載作用下會(huì)產(chǎn)生水平推力的結(jié)構(gòu)。

Thecentroidalaxisofanarchisacurvedline.Horizontalthrustswillbedevelopedatthesupportsundertheactionofverticalloads.

拱的有關(guān)名稱跨度span拱趾鉸Footsupport拱趾鉸Footsupport頂鉸tophinge矢高rise斜拱inclinedarch拉桿拱Tiedarch平拱horizontalarch拱肋拱肋三鉸拱Three-hingedarch兩鉸拱two-hingedarch無鉸拱nonhingedarch靜定拱staticallydeterminatearch超靜定拱staticallyindeterminatearch超靜定拱staticallyindeterminatearch二、三鉸拱的解法

calculationmethodFAHFBHFAyFByFAy0FBy0a2b1b2lFP1FP2ABCl1l2fFBy=FBy0FAy=FAy0FH=MC0/

fa1等代梁請大家想：由上述公式可得哪些結(jié)論？FP1FP2CAB反力計(jì)算：列平衡方程可得FromequilibriumEquationsweobtain三鉸拱的反力只與荷載及三個(gè)鉸的位置有關(guān)，與拱軸線形狀無關(guān)Thereactionsarerelatedtothelocationsofthehingesandloads,buthavenorelationshipwiththeformoftheaxiallineofarch.荷載與跨度一定時(shí)，水平推力與矢高成反比Givenloadsandspan,thrustisinverselyproportionaltorise1/fKxyxyFAyFByFAy0FBy0a2b1b2a1等代梁FAHFBHlFP1FP2ABCl1l2fKFP1FP2CAB內(nèi)力計(jì)算thedeterminationofinternalforces：請大家對上述公式進(jìn)行分析由于推力的的存在，拱拱的彎矩比比相應(yīng)簡支支梁的彎矩矩要小。Becauseofthehorizontalthrust,themomentofarchislessthanthatofthecorrespondingsimplebeam.三鉸拱在豎豎向荷載作作用下軸向向受壓.Undertheactionofverticalloads,thearchisaxiallycompressed.

三鉸拱的內(nèi)力不但與荷載及三個(gè)鉸的位置有關(guān)，而且與拱軸線的形狀有關(guān)。Theinternalforcesarenotonlydependentofloadsandthepositionsofhinges,butalsooftheformofcentroidalaxis.Example.ConstructtheinternalforcediagramsofthefollowingarchSolution:截面2為集中力作作用處，其其兩側(cè)的剪剪力將發(fā)生生突變FAyFByFAHFBH斜拱如何求求解？Howtosolvetheinclinedarches?三、三鉸拱拱的合理拱拱軸線(Rationalaxiallinesofarches)使拱在給定定荷載下只只產(chǎn)生軸力力的拱軸線線，被稱為與該荷載載對應(yīng)的合理拱軸。。UndertheactionofStationaryloadstheaxiallineofanarchthatwillinducethebendingmomentonthesectionstovanishisreferredtoasrationaloroptimalaxiallineorcentrelineofthearch.只限于三鉸鉸平拱受豎豎向荷載作作用。合理理軸線橫截面上在豎向荷載載作用下，，三鉸拱的的合理拱軸線線的的縱縱坐坐標(biāo)標(biāo)與與相相應(yīng)應(yīng)簡簡支支梁梁彎彎矩矩圖圖的的豎標(biāo)標(biāo)成成正正比比。。UndertheactionofVerticalloads,theordinatesofoptimalcentrelineisdirectlyproportionaltothoseofthebendingmomentdiagramofthesimplebeam.試求求圖圖示示對對稱稱三三鉸鉸拱拱在在均均布布荷荷載載作作用用下下的的合合理理拱拱軸軸線線determinetherationalaxisofthearchundertheactionofuniformlydistributedload.MC0=ql2/8FH=ql2/8fM0=qlx/2-qx2/2=qx(l-x)/2y=4fx(l-x)/l2拋物物線線試求求三三鉸鉸拱拱在在垂垂直直于于拱拱軸軸線線的的均均布布荷荷載載作作用用下下的的合合理理拱拱軸軸線線。。Findtheoptimalcentrelineofthearchunderthetheuniformlydistributedloadverticaltothecentrelineofthearch返章園ρFNFN+dFNρFNFN+dFN所以以拱拱的的合合理理軸軸線線為為園園在同同樣樣荷荷載載作作用用下下鉸鉸的的相相互互位位置置不不同同，，其其合合理理軸軸線線也也不不同同，，這這是是因因?yàn)闉橹её捶戳αΣ徊煌?。。Rationalaxiallinesofarcheswillnotbethesameifthepositionsofhingesaredifferentevenundertheactionofthesameloads.左圖頂頂鉸位位置不不同，，合理理軸線線不同同小結(jié)結(jié)Summary1.三鉸拱拱與粱粱的區(qū)區(qū)別Thedifferencesbetweenthree-hingedarchesandbeams幾何方方面ingeometry:幾何形形狀不不同thegeometricalconfigurationisdifferent受力方方面instaticaspect:三鉸拱拱腳有有水平平力horizontalthrustwillbedevelopedinsupports；2.水平推推力依依賴于于何種種因素素Thefactorsinfluencinghorizontalthrust三鉸拱拱的反反力只只與荷荷載及及三個(gè)個(gè)鉸的的位置置有關(guān)關(guān)，與與拱軸軸線形形狀無無關(guān)Thereactionsarerelatedtothelocationsofthehinges,buthavenorelationshipwiththeformoftheaxiallineofarch.荷載與與跨度度一定定時(shí)，，水平平推力力與矢矢高成成反比比3.內(nèi)力依依賴于于何種種因素素Thefactorsinfluencinginternalforces三鉸拱拱的內(nèi)內(nèi)力不不但與與荷載載及三三個(gè)鉸鉸的位位置有有關(guān)，，而且且與拱拱軸線線的形形狀有有關(guān)。。Theinternalforcesarenotonlydependentofloadsandthepositionsofhinges,butalsooftheformofcentroidalaxis.4.粱與三三鉸拱拱內(nèi)力力分布布的不不同Thedifferenceoftheinternalforcedistributioninbeamsandthree-hingedarches；由于推推力的的存在在，拱拱的彎彎矩比比相應(yīng)應(yīng)簡支支梁的的彎矩矩要小小。Becauseofthehorizontalthrust,themomentofarchislessthanthatofthecorrespondingsimplebeam.三鉸拱拱在豎豎向荷荷載作作用下下軸向向受壓壓.Undertheactionofverticalloads,thearchisaxiallycompressed.5.三鉸拱的的合理軸軸線Rationalaxiallinesofarches。詞匯Vocabulary1.