【材料课件】第二章 剪切.ppt
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1、,CHAPTER 2 SHEAR,材料力学,第二章 剪切,CHAPTER 2 SHEAR,21 STRENGTH CALCULATION ABOUT SHEAR AND BEARING OF CONNECTING MEMBERS,EXCERCISE LESSONS OF SHEAR AND BEARING,第二章 剪 切,21 连接件的剪切与挤压强度计算,拉压和剪切习题课,Production of the shearing stress,SHEAR,剪切,剪应力的产生,21 STRENGTH CALCULATION ABOUT SHEAR AND BEARING OF CONNECTING
2、MEMBERS,1、Characteristics of loads and deformation of connecting members:,1)Connecting 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
3、:It can pass general loads and can be dismounted.,bolt,SHEAR,21 连接件的剪切与挤压强度计算,一、连接件的受力特点和变形特点:,1、连接件,剪切,在构件连接处起连接作用的部件,称为连接件。例如:螺栓、铆钉、键等。连接件虽小,却起着传递载荷的作用。,特点:可传递一般 力, 可拆卸。,螺栓,rivet,Characteristic: It can pass general loads, but can not be dismounted.for example, the truss in a bridge is connected by
4、 it.,no gap,Characteristic: It can pass torques.,SHEAR,剪切,铆钉,特点:可传递一般 力,不可拆卸。如桥梁桁架结点处用它连接。,无间隙,2)Characteristics of loads and deformation:,Use 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 very close
5、., 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.,SHEAR,2、受力特点和变形特点:,剪切,以铆钉为例:,受力特点: 构件受两组大小相等、方向相反、作用线相距很近(差一个几何平面)的平行力系作用。,变形特点: 构件沿两组平行力系的交界面发生相对错动。,( Resultant ),(Resultant,Shearing plane:
6、 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.,SHEAR,剪切,剪切面: 构件将发生相互的错动面,如n n 。,剪切面上的内力: 内力 剪力Q ,其作用线与剪切面平行。,3)Three kinds of breakage a
7、t 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 connecting plane. Breakage due to tension,The steel plate is weakened in the section in which the riv
8、et holes exist and stress in the weakened section increases so that the steel plate is easily broken due to tension at the connecting position.,SHEAR,剪切,3、连接处破坏的三种形式: 剪切破坏 沿铆钉的剪切面剪断,如 沿n n面剪断 。 挤压破坏 铆钉与钢板在相互接触面 上因挤压而使溃压连接松动, 发生破坏。 拉伸破坏,钢板在受铆钉孔削弱的截面处,应力增大,易在连接处拉断。,2、Practical calculation of shear,Met
9、hod of the practical calculation:According to possibility of breakage of the member some assumptions by which basic characteristic subjected to force actions can be reflected and calculations can be simplified are used. Then calculate its nominal stress, determine the corresponding permissible stres
10、s 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. Such as the connecting pieces etc.,Assumption of practical calculation:Assume that shearing stress is distributed uniformly in the s
11、hearing plane and equal to the average shearing stress.,SHEAR,剪切,二、剪切的实用计算,实用计算方法:根据构件的破坏可能性,采用能反映受力基本特征,并简化计算的假设,计算其名义应力,然后根据直接试验的结果,确定其相应的许用应力,以进行强度计算。 适用:构件体积不大,真实应力相当复杂情况,如连接件等。,实用计算假设:假设剪应力在整个剪切面上均匀分布,等于剪切面上的平均应力。,1)Shearing plane-AQ : Shifting plane. Shearing force-Q:Internal force on the shea
12、ring plane.,2)Nominal shearing force-:,3)Strength condition of shear:,Working stress should not exceed the permissible stress.,SHEAR,where,剪切,1、剪切面-AQ : 错动面。 剪力-Q: 剪切面上的内力。,2、名义剪应力-:,3、剪切强度条件(准则):,工作应力不得超过材料的许用应力。,3、Practical calculations of bearing,1)Bearing forcePjy :The resultant force acting on
13、the touching plane.,Bearing:The phenomenon that there is pressure on the partial area 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.,SHEAR,三、挤压的实用计算,1、挤压力Pjy :接触面上的合
14、力。,剪切,挤压:构件局部面积的承压现象。 挤压力:在接触面上的压力,记Pjy 。,假设:挤压应力在有效挤压面上均匀分布。,2)Bearing area:Area of the projection plane of the touching plane in the direction perpendicular to Pjy,3)Strength condition of bearing: Working bearing stress should not exceed the permissible bearing stress,Bearing area,SHEAR,2、挤压面积:接触面
15、在垂直Pjy方向上的投影面的面积。,3、挤压强度条件(准则): 工作挤压应力不得超过材料的许用挤压应力。,剪切,挤压面积,4、Applications,SHEAR,1)Check the strength,2)Select the cross section area,3)Determine the external load,四、应用,剪切,Example 1 A wooden tenon joint is shown in the figure. Knowing that the quantities are a = b =12cm,h=35cm,c=4.5cm and P=40KN. T
16、ry to determine the shearing stress and bearing stress for the joint.,Solution:Free body diagram is shown in the figure,:Shearing stress and bearing stress,Shearing force is,Bearing force is,SHEAR,例1 木榫接头如图所示,a = b =12cm,h=35cm,c=4.5cm, P=40KN,试求接头的剪应力和挤压应力。,解: 受力分析如图, 剪应力和挤压应力,剪切面和剪力为,挤压面和挤压力为:,剪切,
17、Solution:Free body diagram of the key is shown in the figure,Example 2 A gear and a shaft are connected by a key(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
18、 respectively = 60 MPa and jy= 100 MPa. Try to check the strength of the key.,SHEAR,解:键的受力分析如图,例2 齿轮与轴由平键(bhL=20 12 100)连接,它传递的扭矩m=2KNm,轴的直径d=70mm,键的许用剪应力为= 60M Pa ,许用挤压应力为jy= 100M Pa,试校核键的强度。,剪切,According to the above calculation, strength conditions of the key are satisfied.,Check the strength of
19、shear and bearing,SHEAR,综上,键满足强度要求。,剪应力和挤压应力的强度校核,剪切,Solution:Free body diagram of the key is shown in the figure,Example 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 diameter of the shaft is d =50mm,the permissible she
20、aring stress and the permissible bearing stress of the key are respectively = 80MPa and jy = 240MPa.Try to design the length of the key.,SHEAR,解:键的受力分析如图,例3 齿轮与轴由平键(b=16mm,h=10mm,)连接,它传递的扭矩m=1600Nm,轴的直径d=50mm,键的许用剪应力为= 80M Pa ,许用挤压应力为 jy= 240M Pa,试设计键的长度。,剪切,Strength conditions of the shearing stres
21、s and the bearing stress,According to the above calculation,SHEAR,剪切,剪应力和挤压应力的强度条件,综上,Solution:Free body diagram is shown in the figure,Example 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 = 160MP
22、a. Diameter of the rivet is 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.),SHEAR,解:受力分析如图,例4 一铆接头如图所示,受力P=110kN,已知钢板厚度为 t=1cm,宽度 b=8.5cm ,许用应力为 = 160M
23、 Pa ;铆钉的直径d=1.6cm,许用剪应力为= 140M Pa ,许用挤压应力为jy= 320M Pa,试校核铆接头的强度。(假定每个铆钉受力相等。),剪切,The sections 22 and 33 of the steel plate are the critical sections.,The strength conditions of shear and bearing,Therefore,the tie-in is safe.,SHEAR,钢板的2-2和3-3面为危险面,剪应力和挤压应力的强度条件,综上,接头安全。,剪切,1、Internal-force and axial-
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