【材料課第二章 剪切

1、mechanics of materials2 21 strength calculation about shear 1 strength calculation about shear and bearing of connecting members and bearing of connecting membersexcercise lessons of shear and bearingexcercise lessons of shear and bearing剪剪 切切2 21 1 連接件的剪切與擠壓強度計算連接件的剪切與擠壓強度計算production of the sheari

2、ng stress剪應力的產(chǎn)生剪應力的產(chǎn)生2 21 1 strength calculation about shear and strength calculation about shear and bearing of connecting membersbearing of connecting members1 1、characteristics of loads and deformation of connecting members:characteristics of loads and deformation of connecting members:1)1)connec

3、ting memberconnecting member the structure member that connects one member to another is called the connecting member. such as：bolts、rivets、keys etc. the connecting member is small，but it plays the role of passing loads. characteristic：it can pass general loads and can be dismounted. ppbolt2 21 1 連接

4、件的剪切與擠壓強度計算連接件的剪切與擠壓強度計算一、連接件的受力特點和變形特點：一、連接件的受力特點和變形特點：1 1、連接件、連接件 在構(gòu)件連接處起連接作用的部件，稱為連接件連接件。例如：螺栓、鉚釘、鍵等。連接件雖小，卻起著傳遞載荷的作用。 特點：可傳遞一般 力， 可拆卸。pp螺栓pprivetcharacteristic: it can pass general loads, but can not be dismounted.for example, the truss in a bridge is connected by it.no gapcharacteristic: it can

5、 pass torques.mshaftkeygearmpp鉚釘特點：可傳遞一般 力，不可拆卸。如橋梁桁架結(jié)點處用它連接。無間隙m軸鍵齒輪特點：傳遞扭矩。m2)2)characteristics of loads and deformation：nn（resultant）（resultant）ppuse a rivet as an example： characteristic of loads： the rivet is subjected to two equal and opposite forces. the acting lines of these two forces are v

6、ery close. characteristic of deformation: : two parts subjected to two equal and opposite forces tend to shift over one another along the junction plane of two forces.2 2、受力特點和變形特點：、受力特點和變形特點：nn（合力）（合力）pp以鉚釘為例：受力特點受力特點： 構(gòu)件受兩組大小相等、方向相反、作用線相距很近（差一個幾何平面）的平行力系作用。變形特點變形特點： 構(gòu)件沿兩組平行力系的交界面發(fā)生相對錯動。nn（ resulta

7、nt ）（resultantppshearing plane： the plane along which two parts of the member tend to shift over one another. such as n n .internal force on shearing plane： internal force shearing force q ，its acting line is parallel to the shearing plane.pnnqshearing planenn（合力）（合力）pp剪切面剪切面： 構(gòu)件將發(fā)生相互的錯動面，如n n 。剪切面上

8、的內(nèi)力剪切面上的內(nèi)力： 內(nèi)力 剪力q ，其作用線與剪切面平行。pnnq剪切面nn(resultant )(resultant ）pp3)three kinds of breakage at joint： failure due to shear snip along the shearing plane of the rivet, such as along section n n. breakage due to bearing fail due to mutual bearing between the rivet and the steel plate in their connecti

9、ng plane. breakage due to tensionpnnqshearing plane the steel plate is weakened in the section in which the rivet holes exist and stress in the weakened section increases so that the steel plate is easily broken due to tension at the connecting position. nn（合力）（合力）pp3、連接處破壞的三種形式、連接處破壞的三種形式： 剪切破壞 沿鉚釘

10、的剪切面剪斷，如 沿n n面剪斷 。 擠壓破壞 鉚釘與鋼板在相互接觸面 上因擠壓而使?jié)哼B接松動， 發(fā)生破壞。 拉伸破壞pnnq剪切面鋼板在受鉚釘孔削弱的截面處，應力增大，易在連接處拉斷。 2 2、practical calculation of shearmethod of the practical calculation：according to possibility of breakage of the member some assumptions by which basic characteristic subjected to force actions can be ref

11、lected and calculations can be simplified are used. then calculate its nominal stress, determine the corresponding permissible stress in accordance with the result of direct test. at last do the strength calculation.applying range：volume of the member is not large and real stress is quite complex. s

12、uch as the connecting pieces etc.assumption of practical calculation：assume that shearing stress is distributed uniformly in the shearing plane and equal to the average shearing stress.二、剪切的實用計算二、剪切的實用計算實用計算方法：實用計算方法：根據(jù)構(gòu)件的破壞可能性，采用能反映受力基本特征，并簡化計算的假設，計算其名義應力，然后根據(jù)直接試驗的結(jié)果，確定其相應的許用應力，以進行強度計算。適用適用：構(gòu)件體積不大，

13、真實應力相當復雜情況，如連接件等。實用計算假設：實用計算假設：假設剪應力在整個剪切面上均勻分布，等于剪切面上的平均應力。1)shearing plane-aq ： shifting plane. shearing force-q：internal force on the shearing plane.qaq2)nominal shearing force-：3)strength condition of shear： qaq njxnn（ resultant ）(resultant ）pppnnqshearing planeworking stress should not exceed t

14、he permissible stress.,where1、剪切面-aq ： 錯動面。 剪力-q： 剪切面上的內(nèi)力。qaq2、名義剪應力-：3、剪切強度條件（準則）： aq njx:其中nn（合力）（合力）pppnnq剪切面工作應力不得超過材料的許用應力。3 3、practical calculations of bearing1)bearing forcepjy ：the resultant force acting on the touching plane.bearing：the phenomenon that there is pressure on the partial area

15、of a member.bearing force：the resultant force acting on the bearing plane，designated by pjy.assumption：bearing stresses are distributed uniformly over the effective bearing plane.三、擠壓的實用計算三、擠壓的實用計算1、擠壓力pjy ：接觸面上的合力。擠壓：構(gòu)件局部面積的承壓現(xiàn)象。擠壓力：在接觸面上的壓力，記pjy 。假設：擠壓應力在有效擠壓面上均勻分布。2)bearing area：area of the proje

16、ction plane of the touching plane in the direction perpendicular to p pjy jyjyjyjyap3)strength condition of bearing： working bearing stress should not exceed the permissible bearing stressbearing areadtajy2、擠壓面積：接觸面在垂直pjy方向上的投影面的面積。jyjyjyjyap3、擠壓強度條件（準則）： 工作擠壓應力不得超過材料的許用擠壓應力。擠壓面積dtajy4 4、application

17、sapplications jyjy；1)check the strength jyjyjyqpaqa；2)select the cross section area jyjyjyqapaq；3)determine the external load 1jyjy；、校核強度： 2jyjyjyqpaqa；、設計尺寸： 3jyjyjyqapaq；、設計外載：四、應用四、應用mpa952. 0103512407bhpaqqmpa 4 . 710125 . 4407cbpapjyjyjyexample 1 a wooden tenon joint is shown in the figure. kno

18、wing that the quantities are a = b =12cm，h=35cm，c=4.5cm and p=40kn. try to determine the shearing stress and bearing stress for the joint.solution：free body diagram is shown in the figure：shearing stress and bearing stresspqbhaq ;shearing force isbearing force isppcbajyjy ;ppppppbachqajyahmpa952. 01

19、03512407bhpaqqmpa 4 . 710125 . 4407cbpapjyjyjy 例例1 1 木榫接頭如圖所示，a = b =12cm，h=35cm，c=4.5cm, p=40kn，試求接頭的剪應力和擠壓應力。解： 受力分析如圖 剪應力和擠壓應力剪切面和剪力為 擠壓面和擠壓力為：ppppppbachqajyahpqbhaq ;ppcbajyjy ;solution：free body diagram of the key is shown in the figureexample 2 example 2 a gear and a shaft are connected by a k

20、ey（bhl=20 12 100).the torque that the key can transmit is m=2knm.knowing the diameter of the shaft is d=70mm，the permissible shearing stress and the permissible bearing stress of the key are respectively = 60 mpa and jy= 100 mpa. try to check the strength of the key. kn5707. 0222dmp2hmbhlmdp解：鍵的受力分析

21、如圖 例例2 2 齒輪與軸由平鍵（bhl=20 12 100）連接，它傳遞的扭矩m=2knm，軸的直徑d=70mm，鍵的許用剪應力為= 60m pa ，許用擠壓應力為jy= 100m pa，試校核鍵的強度。 kn5707. 0222dmp2hmbhlmdpaccording to the above calculation, strength conditions of the key are satisfied. mpa6 .281002010573blpaqqcheck the strength of shear and bearing ppqjyjyjyjyjyhlpapmpa3 .95

22、6100105723bhldmq綜上，鍵滿足強度要求。 mpa6 .281002010573blpaqq剪應力和擠壓應力的強度校核ppqjyjyjyjyjyhlpapmpa3 .956100105723bhldmqsolution：free body diagram of the key is shown in the figureexample 3 a gear and a shaft are connected by a key（b =16mm, h =10mm).the torque that the key can transmit is m = 1600nm. knowing the

23、 diameter of the shaft is d =50mm，the permissible shearing stress and the permissible bearing stress of the key are respectively = 80mpa and jy = 240mpa.try to design the length of the key. kn6405. 0160022dmpqpjybhl2hmmmdp解：鍵的受力分析如圖例例3 齒輪與軸由平鍵（b=16mm，h=10mm，）連接，它傳遞的扭矩m=1600nm，軸的直徑d=50mm，鍵的許用剪應力為= 80

24、m pa ，許用擠壓應力為 jy= 240m pa，試設計鍵的長度。 kn6405. 0160022dmpqpjybhlmdp2hmmbhlstrength conditions of the shearing stress and the bearing stress mm50)m(10801664 31bqllbqmm3 .53)m(10240106422 232jyjyjyjyhpllhpaccording to the above calculation mm3 .53 , max21llldmqbhl剪應力和擠壓應力的強度條件 mm50)m(10801664 31bqllbqmm3

25、.53)m(10240106422 232jyjyjyjyhpllhp綜上 mm3 .53 , max21llldmqsolution：free body diagram is shown in the figureexample 4 a riveted tie-in acted by force p=110kn is shown in the figure. knowing the thickness is t =1cm，width of it is b =8.5cm. the permissible stress is = 160mpa. diameter of the rivet is

26、d =1.6cm and the permissible shearing stress is = 140mpa ，the permissible bearing stress is jy= 320mpa. try to check the strength of the riveting . (assume the force acted on each rivet is equal.） 4ppqjybppttdppp11 2233p/4解：受力分析如圖例例4 一鉚接頭如圖所示，受力p=110kn，已知鋼板厚度為 t=1cm，寬度 b=8.5cm ，許用應力為 = 160m pa ；鉚釘?shù)闹?/p>

27、徑d=1.6cm，許用剪應力為= 140m pa ，許用擠壓應力為jy= 320m pa，試校核鉚接頭的強度。（假定每個鉚釘受力相等。） 4ppqjybppttdppp11 2233p/4the sections 22 and 33 of the steel plate are the critical sections.the strength conditions of shear and bearing mpa8 .136106 . 114. 3110722dpaqq mpa7 .15510) 6 . 125 . 8(41103)2(4372dbtpjyjyjyjytdpapmpa9 .

28、171106 . 11411047 mpa4 .15910) 6 . 15 . 8 (1110)(73dbtptherefore，the tie-in is safe.ttdppp11 2233p/4鋼板的2-2和3-3面為危險面剪應力和擠壓應力的強度條件 mpa8 .136106 . 114. 3110722dpaqq mpa7 .15510) 6 . 125 . 8(41103)2(4372dbtpjyjyjyjytdpapmpa9 .171106 . 11411047 mpa4 .15910) 6 . 15 . 8 (1110)(73dbtp綜上，接頭安全。ttdppp11 2233p/

29、41 1、internal-force and axial-force diagrams of the rod in tension and compression1)expression of axial force?2)method to determine axial force?3)positive and negative of axial force?why do we plot the axial-force diagram? what should we pay attention when we do it? 4)axial-force diagram： expressed

30、by the diagram of n = n(x)?panasimple sketchbcppnxp+一、軸向拉壓桿的內(nèi)力及軸力圖一、軸向拉壓桿的內(nèi)力及軸力圖1、軸力的表示?2、軸力的求法?3、軸力的正負規(guī)定?為什么畫軸力圖?應注意什么?4、軸力圖：n=n(x)的圖象表示?panbc簡圖appnxp+simple method to determine axial forces: :take the left part of the section x as the object,the axial force on the section x can be calculated by fo

31、llowing formula: where“p()”and“p()”express the sum of left direction forces and the sum of right direction forces of the left part of the section x. take the right part of the section x as the object, the axial force n(x) of point x can be calculated by the following formulate: where “ ” and “ ”deno

32、te the sum of right direction forces and the sum of left direction forces of the right part of section x. )()()(ppxn)()()(ppxn)(p)(p軸力的簡便求法軸力的簡便求法: : 以x點左側(cè)部分為研究對象,x點的軸力n(x)由下式計算: 其中“p()”與“p()”為x點左側(cè)向左的所有外力與向右的所有外力。 以x點右側(cè)部分為研究對象，x點的軸力n(x) 由下式計算： 其中“p()”與“p()”為x點右側(cè)向右的所有外力與向左的所有外力。)()()(ppxn)()()(ppxnex

33、ample 1 abcdo5p4pp8pnx3p5pp2pabcdo5p4pp8pnx3p5pp2ppositive and negative of stress?1)stress on the cross section:axn)( 2 2、stress of the rod in tension or compressioncritical section and maximum working stress?2sin 2 )2cos(1 2 002)stress on the inclined sectionsaint-venant principle?stress concentrat

34、ions?n(x)px應力的正負規(guī)定?1、橫截面上的應力:axn)( 二、拉壓桿的應力二、拉壓桿的應力危險截面及最大工作應力?2sin 2 )2cos(1 2 002、拉壓桿斜截面上的應力saint-venant原理?應力集中?n(x)px3 3、strength design criterion：1) strength design criterion )()(max( maxxaxn maxcheck strength：design the cross section area： maxminnadesign the load：; maxan )(maxnfp 三、三、強度設計準則（強度設

35、計準則（strength design criterion）：1、強度設計準則、強度設計準則? ? )()(max( maxxaxn max校核強度：設計截面尺寸： maxminna設計載荷：; maxan )(maxnfp eanleapll1)elastic law of the rod with equal axial forces2)elastic law with variable internal forces3)elastic law in uniaxial stressed state 1ellxeaxxnxl)(d)( )d(niiiiiaelnl14、deformation

36、 and strain of the rod in tension or compressionn（x）xd xn(x)dxxppeanleapll1、等軸力拉壓桿的彈性定律2、變內(nèi)力拉壓桿的彈性定律3、單向應力狀態(tài)下的彈性定律 1ellxeaxxnxl)(d)( )d(niiiiiaelnl1四、拉壓桿的變形及應變四、拉壓桿的變形及應變n（x）xd xn(x)dxxpp4)possions ratio（or lateral deformation factor） 5)the enlarged-deformation diagram and the method to determine th

37、e displacement cabcl1l2pc1l2l4、泊松比（或橫向變形系數(shù)） 5、小變形放大圖與位移的求法cabcl1l2pc1l2lassemble stressinitial stress temperature stressequilibrium equations；geometric equationscompatibility equations of deformation；physical equationselastic laws；complementary equations：getting from geometric equations and physical

38、 equations；solving the combined equations including of equilibrium equations and complement equations.6)the steps to solve the statically indeterminate problem 裝配應力預應力溫度應力平衡方程；幾何方程變形協(xié)調(diào)方程；物理方程彈性定律；補充方程：由幾何方程和物理方程得；解由平衡方程和補充方程組成的方程組。6、超靜定問題的處理方法步驟：5 5、mechanical properties of the materials in tension

39、and compression3)unloaded law；cold hardening；cold-drawn time effect.1)elastic lawtg ; eebsjx,2 .04)residual relative elongation00001100lll5)permanent relative reduction of area00010100aaanjx2)limit stress6)permissible stress五、五、 材料在拉伸和壓縮時的力學性能材料在拉伸和壓縮時的力學性能3、卸載定律；冷作硬化；冷拉時效。、許用應力6、極限應力21 、彈性定律tg ; ee

40、bsjx,2 .04、延伸率5、面縮率njx00001100lll00010100aaa1)practical calculation of shear aq6 6、practical calculation of shear and bearing of the connecting member of the rods in tension and compressionnn（resultant）（resultant ）pppnnqshearing plane2)practical calculation of bearingjyjyjyjyap1、剪切的實用計算 aq六、六、 拉拉( (

41、壓壓) )桿連接部分的剪切與擠壓強度計算桿連接部分的剪切與擠壓強度計算nn（合力）（合力）pppnnq剪切面2、擠壓的實用計算jyjyjyjyapbearing areadtajy jyjy； jyjyjyqpaqa； jyjyjyqapaq；check the strengthdesign the dimensiondesign the external load擠壓面積dtajy jyjy；校核強度： jyjyjyqpaqa；設計尺寸： jyjyjyqapaq；設計外載：example example 2 the rods ab、cd、ef and gh in the structure

42、are shown in the figure each of them consists two of rolled unequal-legs steels.knowing =170mpa，e =210gpa . rods ac and eg may be seen as rigid rod. try to select the section dimension of each rod and to determine the displacements of points a、d and c.p=300kn0.8m3.2m1.8m1.2m2m3.4m1.2mabcdfhq0=100kn/

43、msolution：determine the internal force.the free body diagram is shown in the figure.eg 例例2 結(jié)構(gòu)如圖，ab、cd、ef、gh都由兩根不等邊角鋼組成，已知材料的=170 m p a ，e=210 g p a。 ac、eg可視為剛桿，試選擇各桿的截面型號和a、d、c點的位移。p=300kn0.8m3.2m1.8m1.2m2m3.4m1.2mabcdfhq0=100kn/m解：求內(nèi)力，受力分析如圖egkn186enkn24030042 . 3ankn6030048 . 0dnkn174gndq0=100kn/m

44、egacngncnanend=ndp=300kndetermine the area by strength conditioniina 23cm12.1410170240aba2cm5 . 3cda2cm9 .10efa2cm2 .10ghakn186enkn24030042 . 3ankn6030048 . 0dnkn174gndq0=100kn/megacngncnanend=ndp=300kn由強度條件求面積iina 23cm12.1410170240aba2cm5 . 3cda2cm9 .10efa2cm2 .10gha21cm212. 72),55690(2:abaab21cm89

45、. 12),32540(2:cdacd21cm609. 52),54570(2: )(efaghefdetermine the types of the rods reference to the tabledetermine the deformationiiiiealnl mm67. 21054.141 . 24 . 324041ababababealnlmm91. 0cdlmm74. 1eflmm63. 1ghl21cm212. 72),55690(2:abaab21cm89. 12),32540(2:cdacd21cm609. 52),54570(2: )(efaghef試依面積值查表

46、確定型鋼號求變形iiiiealnl mm67. 210424.141 . 24 . 324041ababababealnlmm91. 0cdlmm74. 1eflmm63. 1ghldetermine the displacement.the deformation is shown in the figure.mm61.2cddclmm61.2abalabdfhegmm70.1ghghefdldgegllcc1a1e1d1g1求位移,變形圖如圖mm61.2cddclmm61.2abalabdfhegmm70.1ghghefdldgegllcc1a1e1d1g1example example

47、3 diameters of rod ac and bd in the structure shown in the figure are respectively d1 =25mm, d2 =18mm. knowing =170mpa，e =210gpa . rod ab may be seen as a rigid rod. try to (1) check the strength of each rod and to determine the displacements a and b of points a an b. (2) determine the displacement

48、fof point f when the force p is acted on point a. f= a is a general law, which is called theorem of conjugate displacement.bnbp=100knnaaabcdp=100kn1.5m3m2.5mfabfsolution：determine the internal forcethe free body diagram is shown in the fingure. kn7 .661005 . 43ankn3 .33bn 例例3 結(jié)構(gòu)如圖，ac、bd的直徑分別為:d1 =25

49、mm, d2 =18mm,已知材料的=170 m pa ，e=210 g pa,ab可視為剛桿，試校核各桿的強度;求a、b點的位移a和b。(2)求當p作用于a點時,f點的位移f，f= a是普遍規(guī)律：稱為位移互等定理。bnbp=100knnaaabcdp=100kn1.5m3m2.5mfabf解：求內(nèi)力，受力分析如圖kn7 .661005 . 43ankn3 .33bncheck the strength 24iiiidnan mpa8 .135102514.37 .66492a mpa131bdetermine the deformation and the displacementiiiie

50、alnl mm62. 110251 . 214. 35 . 27 .66422acaacealnlmm56.1bdlmm.56.1 mm,62.1 have wesoba校核強度 24iiiidnan mpa8 .135102514.37 .66492a mpa131b求變形及位移iiiiealnl mm62. 110251 . 214. 35 . 27 .66422acaacealnlmm56.1bdlmm.56.1 mm,62.1badetermine displacement f of point f when force p is acted on point a mm62. 1acf

51、labbfl0 ;kn100bannmm43.210251 .214.35 .2100422aclfacllp=100kn1.5m3m2.5mafafbcd求當p作用于a點時,f點的位移fmm62. 1acflabbfl0 ;kn100bannmm43.210251 .214.35 .2100422aclfacllp=100kn1.5m3m2.5mafafbcd2221111)()(ealggpealgplexample example 4 the structure is shown in the figure. knowing =2mpa ，e=20gpa, unit weight of

52、concrete = 22kn/m. try to design the areas of the two parts and to determine the displacement a of point a 11max1gpnasolution：determine the area in accordance with the strength condition. 212max2ggpnallxeaxxnxl)(d)( )d(p=100kn12m12ma2221111)()(ealggpealgpl 例例4 結(jié)構(gòu)如圖，已知材料的=2mpa ，e=20gpa,混凝土容重=22kn/m，試

53、設計上下兩段的面積并求a點的位移a。 11max1gpna解：由強度條件求面積 212max2ggpnallxeaxxnxl)(d)( )d(p=100kn12m12ma chapter 2 exercises 1、what is the difference between bearing and compression？ 2、knowing the relation between the allowable shearing stressand the allowable tensile stressof the bolt material is =0.6，try to determin

54、e the reasonable ratio of the diameter d of the bolt to the height h of the bolt cap。 solution： 24dpan dhpaqq 6 . 04/2dpdhp4 . 2/hd 第二章第二章 練習題練習題 一、擠壓與壓縮有何區(qū)別？一、擠壓與壓縮有何區(qū)別？ 二、已知螺栓材料的許用剪應力二、已知螺栓材料的許用剪應力 與許用與許用拉應力拉應力 之間的關系為之間的關系為=0.6=0.6 ，試求螺，試求螺栓直徑栓直徑d d與螺栓頭高度與螺栓頭高度h h的合理比值。的合理比值。 24dpan dhpaqq 6 . 04/

55、2dpdhp4 . 2/hd解：解： 3、as shown in the figure, when the safe crosshead is over-loaded, the safe pin will be snipped. knowing for the safe pin, the average diameter is d=5mm and the limit shearing stress is . try to determine the maximum force couple m that can be transmitted by the crosshead.solution：

56、mpajx370jxqddmaq4/2mnddmjx3 .14542 三、圖示安全聯(lián)軸器超載時，安全銷即被剪三、圖示安全聯(lián)軸器超載時，安全銷即被剪斷。已知安全銷的平均直徑斷。已知安全銷的平均直徑d=5mmd=5mm，其極限剪應，其極限剪應力力 , ,試求該聯(lián)軸器允許傳遞的最大試求該聯(lián)軸器允許傳遞的最大力偶矩力偶矩m.m.解：解：mpajx370jxqddmaq4/2mnddmjx3 .14542 大學課件出品 版權歸原作者所有 聯(lián)系qq ：910670854 如侵權，請告知，吾即刪 更多精品文檔請訪問我的個人主頁 http:/ 附贈人生心語附贈人生心語人生太短，聰明太晚人生太短，聰明太晚人生太

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