材料力学双语教学学习资料

1、材料力学双语教学学习资料1第一章绪论Chapter 1 Introduction 1-1 材料力学的任务The Tasks of Mechanics of Materials. 材料力学 : Mechanicsof Materials构件 :Structural Members变形 :Deformation4 . 强度 :Strength5 . 刚度 : Rigidity6 . 稳定性 :Stability 1-2 变形固体的基本假设Fundamental Assumptions of SolidDeformation Bodies1.连续性假设 :Continuity2.均匀性假设 :Hom

2、ogeneity3.各向同性假设:Isotropy 1.3 外力及其分类External Forces and Classification分布力 : Distributed Force集中力 : Point Force静载荷 : Static Load动载荷 : Dynamic Load 1.4 内力、截面法和应力的概念Concepts of Internal Forces ， Method ofSection and Stress1 .内力 : Internal Force2 .截面法 : Method of Section截面法的三个步骤：截开，代替，平衡Three steps of m

3、ethod of section: cut off, substitute, and equilibrium.4 . 应力 : Stress5.平均应力： Average stress6. 应力（全应力）： Whole stress（ sum stress）7 .正应力 :Normal Stress8 .剪应力 (切应力 )： Shearing Stress 1.5 变形与应变Deformation and Strain1 线应变 : Strain2 剪应变 : Shearing Strain 1.6 杆件变形的基本形式Basic Types of Deformations of Rods1

4、. 拉伸或压缩 : Tension or Compression2 . 剪切 : Shear3 . 扭转 : Torsion4 . 弯曲 : Bending第二章拉伸、压缩与剪切 Chapter 2Tension， Compression andShear 2.1 轴向拉伸与压缩的概念和实例TheConcept and Examples of Axial Tensionand Compression拉杆 : Tensile Rod压杆 : Compressive Rod受力特点：外力合力的作用线与杆轴线重合 Characteristicof the External Forces: Theac

5、ting line of the resultant of external forces is coincided with the axisof the rod.变形特点：杆沿轴向伸长或缩短Characteristic of Deformation: Rod will elongateor contract along the axis of the rod.2.2 轴向拉伸或压缩时横截面上的内力和应力Internal Force and Stress of Axial Tensionor Compression on the Cross Section1 .横截面 : Cross Sec

6、tion2 . 轴力 : Normal Force3 .轴力图 : Diagramof Normal Force2.3 直杆轴向拉伸或压缩时斜截面上的应力Stress of Axial Tension or Compressionon the Skew Section1.斜截面 : SkewSection2.cos2sin 22 2.4 材料在拉伸时的力学性能Mechanical Properties of Materialswith Tensile Load标准试件 : Specimen低碳钢 (C 0.3%): Low Carbon Steel 3.弹性阶段 :Elastic Region

7、屈服阶段 :YieldingStage 5.强化阶段 : HardeningStage6.颈缩阶段 : NeckingStage7 . p- 比例极限 :ProportionalLimit8 . e- 弹性极限 : Elastic Limit9 . s- 屈服极限 : Yielding Stress.b - 强度极限 : Ultimate Stress延伸率 : Percent Elongation断面收缩率 : Percent Reduction of Area塑性材料 : Ductile Materials脆性材料 : Brittle Materials铸铁 :Cast iron 2.7失

8、效、安全系数和强度计算Failure, Safety factor and Strengthcalculation1 .许用应力 : Allowable Stress2.安全系数 : Safety Factor3 .强度条件 :Strength ConditionmaxFN A4 . 强度校核 : Check strengthmax5 . 截面设计 : Section designFN FNA 2.8 轴向拉伸或压缩时的变形Deformation in Axial Tension orCompression弹性变形 : Elastic Deformation塑性变形 : Plastic Def

9、ormation纵向应变 : LongitudinalStrainll1ll横向应变 : Lateral Straindd ddd5线弹性变形:Linear Elastic Deformation6.泊松比 : Poisson s ratio7 .弹性模量 -E：表示材料抵抗拉压变形的能力 E-modulus ofelasticity ：Indicates the capability of materials for resisting tension or compression8 .抗拉刚度 - EA: 表示构件抵抗拉压变形的能力EA- the axialrigidity:Indicat

10、esthecapability of constructive members for resisting tension or compression. 胡克定律（ Hooke s Law） :当应力不超过材料的比例极限时，应力与应变成正比.The stress is proportional to the strainwithin the elastic region.EFN LLEA 2.12 应力集中的概念TheConcept of Stress Concentration1.由于截面尺寸的突然变化，使截面上的应力分布不再均匀，在某些部位出现远大于平均值的应力，称应力集中。Discon

11、tinuitiesof cross section may resultin high localized or concentrated stresses.6 . 确定许可载荷 :Determine allowable load2.理论应力集中系数K ： TheoreticalStress-concentration Factor - K 2.13 剪切和挤压的实用计算Practical Calculation of Shear and Bearing1 .剪切： Shear2.剪切面： Shearing Plane3 .剪切面上的内力-剪力： Internal Force inSheari

12、ng Plane-Shearing Force4.剪切的实用计算：Practical Calculation ofInternal torque and Its diagram1扭转外力偶矩的计算：Calculation of theexternal torque2 .扭矩： Internal Torque3.符号规定： Sign convention4 .右手螺旋法则:Right hand screw rule5 .扭矩图： Diagram of Internal Torque3.3 纯剪切ShearFSA Pure Shear1.薄壁圆筒的扭转实验：Experiment ofthin-wa

13、lled circular tube under torsion5.挤压的实用计算：Practical CalculationofBearingFbsbs Abs6.挤压强度条件：工作中的挤压应力不应超过许用挤压应力。Strength condition of bearing ： Workingbearing stress should not exceed theallowable bearing stress.第三章扭转Chapter ThreeTorsion 3.1 扭转的概念和实例Concept and Examples of Torsion1.电动机 :Generator2.涡轮 :

14、Turbine3 . 扭转的受力特点：杆件的两端作用着大小相等，方向相反，且作用面垂直于杆件轴线的力偶。Characteristic of loads:Shaft is loaded by a torsional couple in planes that are perpendicularto the axis of the shaft.变形特点：杆件的任意两个横截面发生绕轴线的相对转动。Characteristic of deformation: any two cross sections will twist along the axis.5 .轴 : Shaft 3.2 外力偶矩的计

15、算扭矩和扭矩图Calculation of the external torque2.变形特点 :Characters of deformations ：截面间的距离不变 ;所有横截面的位置不变 ; 所有纵向线转过了一个角度 。Distances between the sections remain unchanged,All cross sections remain unchanged ,All the generating lines revolve through an angle .3 .切应力互等定理： Theorem ofcomplementaryshearing stress

16、es4 .切应变： Shearing strain5剪切虎克定律：Hookes law of shear.剪切弹性模量 G：Modulus of elasticity of shearing第四节圆轴扭转时的应力Stresses in a round shaft under torsion)1 .Ip ( 极惯性矩 ) - polar moment ofinertia2 .Wp ( 抗扭截面系数)- section modulusin torsion3.5 圆轴扭转时的变形扭转角 : The angle of twist2 . 抗扭刚度G Ip ：the torsional rigidity.

17、 扭转的刚度条件 : Rigidity condition in torsion4.单位长度扭转角：The angle of twist perunit lengthExercises1. A bracket （支架）is shown in the figure ，The cross-section area of the steel bar AB is A1=6cm 2； the cross-section area of the wooden bar BC is A2=300cm 2， Knowing the allowable stress of steel is =140MPa , t

18、he allowable tensile stress of wood is L =8MPa, and the allowable compressive stress of wood is Y =4MPa. Try determine the allowable load P of the bracket.2.A wooden tenon( 榫 ) joint is shown in the figure. Knowing that the quantities are a = b=12cm ，h=35cm ，c=4.5cm andP=40KN. Try to determine the s

19、hearing stress and bearing stress for the joint.A tensile bar and two cover boards are bolted together as shown. Each cover board has a thickness of 8 mm. All the parts are made from the samematerial and have thesameallowablestresses80MPa,=60MPa,bs160MPa. The thicknessofthebar=15mm,thetensileforceF=

20、120KN. Try to designthe diameter d of the bolt .the width b of the tensile bar.hhPacPPbPAA3 Two boards are bolted together PasPshown.Each board has a thickness ( ) of 2 mm, and a width ( b)of 15 mm. The diameter d of the bolt is 4 mm .All the parts are made from the samematerial and have the sameall

21、owable stresses160MPa,=100MPa,bs300MPa. Try to designthe tensile force F .第四章弯曲内力Chapter FourInternal Forces inBending5构件在外力作用下抵抗破坏的能力称为；构件在外力作用下抵抗变形的能力称为；构件在外力作用下保持原有平衡状态的能力称为。 (Please fill in the blanks withproper words in English.)6杆件的基本变形一般有、四种。(Please fill in the blanks with proper words in Eng

22、lish.)4-1 弯曲的概念和实例4-1 The Concepts and Examples in Bending1梁： beam2轴线： axis3纵向对称面： longitudinal plane of symmetry4 平面弯曲：plane bending5 弯曲的受力特点：作用于杆件上的外力或外力偶矩矢垂直于杆件轴线。Characteristics of loads:external forces orexternal the couple vector perpendicularto the axis of the rod.6 弯曲的变形特点：杆件的轴线由直线变为曲线。Chara

23、cteristics of deformations :the axis of therod change into curve from original straightlines.7 弯曲变形：杆件在垂直于杆轴线的外力或两个外力偶的作用下，杆的轴线由直线变为曲线，这种变形称为弯曲变形。BENDING: The action of the external force or external the couple vector perpendicularto the axis of the rod makes the axis of the rod change into curve fr

24、om original straight lines, this deformation is called bending.4-2 受弯杆件的简化4-2 Simplification of Bending Rods1 集中力： concentrated force2 分布力： distributed load3 均布载荷： uniform load4 支座： support5 . 简支粱： simple supported beam6 . 外伸梁： overhanging beam.悬臂梁： cantilever beam4-3 剪力和弯矩4-3 Shearing Force and Ben

25、ding Moment弯曲内力： internal forces in bending. 剪力： shearing force2 .3弯矩： bending moment4. 内力的正负规定：sign conventionsfor the internal forces4-4 剪力方程和弯矩弯矩方程剪力图和弯矩图4-4 The Equations of Shearing Force andBending MomentThe Diagrams of Shearing Force and BendingMoment1 剪力方程：equationof shearing force2 弯矩方程：equ

26、ation of bending moment3剪力图： diagram of shearing force4弯矩图： diagram of bending moment4-5 载荷集度、剪力和弯矩间的关系4-5 Relations among the Intensity of Distributed Load , Shearing Force andBending Moment1. 微分关系： differential relations2 . 规律法： method of regulation3 . 控制截面法： method of control sections水平直线： horizo

27、ntal straight line斜直线： inclined straight line突变： sudden change增函数： increasing function减函数： decreasing function盆状抛物线： basin-like curve坟状抛物线： tomb-like curve折向与 P 相反： flexibleopposite to P第五章弯曲应力Chapter FiveStresses in Bending5-1 纯弯曲5-1 Pure Bending横力弯曲： transverse bending. 纯弯曲： pure bending平面假设：横截面变形

28、后仍为平面，只是绕中性轴发生转动，距中性轴等高处，变形相等。Hypothesis of plane section:The cross sections remain still planes, and only rotate through some angles around their neutralaxes after deformation.4 . 中性层： neutral layer5. 中性轴： neutral axis纵向对称轴： longitudinal axis of symmetry5-2 纯弯曲时的正应力5-2 Normal Stress in Pure Bending

29、1 几何关系： geometric relation2 物理关系： physics relation3 静力关系： static relation4. 抗弯刚度EIz：flexural rigidity5-3 横力弯曲时的正应力5-3 Normal Stress in Transverse Bending1 . 抗弯截面系数W：section factor of bending2 .弯曲的强度条件：strength condition inbending5-4 弯曲切应力5-4 Shearing Stress in Bending1 矩形截面梁：the beam with rectangula

30、rsection2 工字形截面梁：wide-flange beam3 翼缘： flange4 腹板： web5 静矩： static moment6 . 惯性矩： moment of inertia6 焊接： melt7 铆接： rivet5-6 提高弯曲强度的措施5-6 Measures of Increasing Strength inBending1 合理安排梁的受力情况：arrange the loadsof beam reasonably2 跨度： span3 梁的合理截面：reasonable section of beams4 . 等强度梁： equal strength bea

31、ms第六章弯曲变形Chapter Six Deformations in Bending6-1 工程中的弯曲变形问题6-1The Problems of DeformationDue toBending in Engineering1 车床主轴： principal axis of lathe2 振动： vibrate3 噪声： noise6-2 挠曲线的微分方程6-2The differential equation of deflection curve挠曲线： deflection curve2 .挠度： deflection.转角： angle of rotation or slope

32、切线： tangent逆时针： counter-clockwise顺时针： clockwise曲率： curvature曲率半径： radius of curvature6-3 积分法求弯曲变形6-3 Determine the Deformations in Bendingby Integration1. 微分方程： differential equation边界条件： boundary condition连续性条件： continuity condition积分常数： integral constants5. 转角方程： equation of angle of rotation6. 挠曲

33、线方程： equation of deflection curve刚度条件： rigidity condition镗床： boring machine镗刀： boring tool6-4 叠加法求弯曲变形6-4 Determine the Deformations in Bendingby the Method of Superposition1 . 叠加法： the method of superposition桥式起重机： over head traveling crane6-5 简单超静定梁6-5 Indeterminate Simple Beams1 静定梁： statically d

34、eterminate beam2 超静定梁： statically indeterminate beam3 变形协调方程： equation of compatibility of deformations6-6 提高弯曲刚度的一些措施6-6 Measures of Increasing Rigidity inBending1 增大抗弯刚度：increase flexural rigidity2 减少跨度或增加支承：decrease span orincrease supports3 减小弯矩： decrease bending moment4 选择合理的截面形状： select the re

35、asonable sectionsExercises1. A cantilever beam AB. The distributed load of 3kN/m extends over 0.8m of the beam and the 1kN load is applied at point E. Plot the diagrams of sharing force and bending moment.The allowable stress of the wooden beam shown in the figure is =10MPa. Try to determine the max

36、imum diameter dof the circular hole in case that the strength of the beam is satisfied (neglecting stress concentrations).3 Determine the angle of rotation of point A and the deflection of point C by the method of superposition.第七章应力和应变分析强度理论Chapter Seven Stress and Strain AnalysisStrength Theories7

37、1应力状态概述71 Concepts of the State of Stress1 一点的应力状态：过一点有无数的截面，这一点的各个截面上应力情况的集合，称为这点的应力状态。The state of stress at a point: There are countless sections through a point. The gathering of stresses in all sections is called the state of stress at this point.2 单元体：构件内的点的代表物，是包围被研究点的无限小的几何体，常用的是正六面体。Element

38、: Delegateof a point in the member. It isan infinitesimalgeometricbody enveloping the studied point. In common use it is acorrectitudecubicbody.3主单元体：各侧面上剪应力均为零的单元体。Principal element:The element in which the shearing stresses in side planes are all zero.4主平面：剪应力为零的截面。Principal Planes:The planes on w

39、hich the shearing stresses are zero.5主应力：主平面上的正应力。Principal stresses:Normal stresses acting on the principle planes.6主应力排列规定；按代数值大小123Convention of the order for three principal stresses:In magnitudeof the algebraic value.7三向应力状态：三个主应力都不为零的应力状态。State of the triaxialstress （ threedimensional stateofs

40、tress）:State of stress that all the three principalstresses are not equal to zero.二向应力状态：一个主应力为零的应力状态。state of the biaxial stress（ plane state of stress） : state of stress that one principal stress is equal to zero.单向应力状态：一个主应力不为零的应力状态state of the uniaxial stress（ unidirectional state of stress） :st

41、ate of stress that one principal stress is not equal to zero.72 二向应力状态分析解析法72Analysis of the State of PlaneStress AnalyticalMethod1.任意斜截面上的应力： stresses acting inarbitraryinclined plane2.正负规定：截面外法线同向为正；绕研究对象顺时针转为正；逆时针为正。Sign Stipulate： is positive if its direction is the same with one of the external

42、normal line of thesection；is positive if it make the elementrotate clockwise ； A counterclockwise angleis considered to be positive.73 二向应力状态分析图解法73Analysis of the State of PlaneStress GraphicalMethod1.应力圆 ： stresscircle2.单元体与应力圆的对应关系：Corresponding relation between the element andstress circle(1)面上的

43、应力 (，)应力圆上一点(，)(2)面的法线应力圆的半径(3) 两面夹角两半径夹角2 ；且转向一致。(1) stress(，) inplanea point(，) on the stress circumference(2) normal line ofplaneradius ofthe stress circle(3) anglebetween two sectionsanglebetween two radiuses ； And the direction of rotation is the same.710 强度理论概述710Concepts of Strength Theories1

44、材料的破坏形式：屈服断裂：Types of failure of materials ：yieldrupture2强度理论：是关于 “构件发生强度失效起因 ”的假说。theories of strength ：some assumptions about the cause of the strength failure of materials .711 四种常用强度理论711 Four Common UsedStrength Theories1.最大拉应力（第一强度）理论:认为构件的断裂是由最大拉应力引起的。当最大拉应力达到单向拉伸的强度极限时，构件就断了。Theory of the ma

45、ximum tensile stress（the first strength theory ） :This theory considers the main cause of rupture to be the maximum tensile stress. The member will rupture as the maximum tensile stress reaches the strength limit in axial tension.2. 最大伸长线应变（第二强度）理论：认为构件的断裂是由最大伸长线应变引起的。当最大伸长线应变达到单向拉伸试验下的极限应变时，构件就断了Th

46、eory of the maximum tensile strain（ the second strength theory） :This theory considers the main cause of rupture to be the maximum tensile strain. The member will rupture as the maximum tensile strain reaches the limit strain in axial tension 3.最大剪应力（第三强度）理论：认为构件的屈服是由最大剪应力引起的。当最大剪应力达到单向拉伸试验的极限剪应力时，构

47、件就破坏了。Theory of the maximum shearing stress（ the third strength theory） :This theory considers the main cause of rupture to be the maximum shearing stress. The member will rupture as the maximum shearing stress reaches the limit shearing stress in axial tension.4畸变能密度（第四强度）理论：认为构件的屈服是由形状改变比能引起的。当形状改

48、变比能达到单向拉伸试验屈服时的形状改变比能时，构件就破坏了。Theory of the distortional energy density (the fourth strength theory ） :This theory considers the main cause of yield to be the distortional strain energy.The member will rupture as the distortional strain energy reaches the distortional strain energy of yield in axial

49、 tension5.相当应力： equivalent stress6.断裂准则： criterion of rupture 屈服准则 : criterion of yield第八章组合变形Chapter EightComposite Deformation81 组合变形和叠加原理81Composite Deformation andSuperposition Principle1.叠加原理的步骤：The steps for principle of superposition外力分析：外力向形心简化并沿形心主惯性轴分解Analysis of external forces： External

50、forces are reduced along the centroidof section and resolved along principal axes of inertia.内力分析：求每个外力分量对应的内力方程和内力图，确定危险面。Analysis of internal forces ： Determine the internalforce equation and its diagram corresponding to each external force component and the critical section.应力分析：画危险面应力分布图，叠加，建立危险

51、点的强度条件。Analysis of stresses：Plot the distribution diagram of the stress in the critical section ， do the superposition of the stresses and establish the strength condition of the critical point.第九章压杆稳定Chapter NineStabilizationofCompressive Columns91 压杆稳定性的概念91 Concepts of Stability ofCompressed Colu

52、mns1.失稳： loss of stability2.稳定与不稳定平衡:stable and instable equilibrium3.临界压力： critical pressure 92两端铰支细长压杆的临界压力92 Critical Pressure of The SlenderCompressed ColumnWith Two Hinged Ends1.欧拉公式 :Euler s formula2.理想压杆：材料绝对理想；轴线绝对直；压力绝对沿轴线作用。Ideal compressive column: the material is absolutely ideal ； the a

53、xis is absolutely straight ； the compressive force is absolutely along the axis of the column.or constraint coefficient ）2.两端铰支 :two hinged ends3.一端固定另一端自由:one fixed end and one free end 4.两端固定 :two fixed ends5.一端固定另端铰支:onefixed end and one hinged end 94欧拉公式的适用范围经验公式94 Application Range of Euler s F

54、ormulaEmpirical Formula1.临界应力 : 压杆处于临界状态时横截面上的平均应力。Critical stress : average stress in the cross section of the compressive column in the critical state.2.柔度（或长细比） ： flexibility(orslenderness ratio)大柔度杆的临界应力由欧拉公式来求;小柔度杆的临界应力就是它的屈服极限 ;中柔度杆的临界应力由经验公式来求The critical stress of the large flexibility colum

55、nis calculated by Euler s formula.The criticalstress ofsmall flexibilitycolumn isits yield limit.The criticalstressof the middleflexibilitycolumn may be determined by the empirical formula. 95压杆的稳定校核95 Stability Check of Compressed Column1.稳定安全因数：safety coefficient of stability2.稳定条件： stability cond

56、ition 96提高压杆稳定性的措施96 Method to Improve Stability ofCompressed Column选 择 合 理 的 截 面 形 状 :choose reasonable section of the column:93 其它支座条件下细长压杆的临界压力93Critical Pressure of The Slender CompressedColumnWith Other End Conditions2.改变压杆的约束条件 :change constraint condition of the column3.合理选择材料 : choose reasonable material.1.长度系数（约束系数）：length coefficient第十章动载荷Chapter TenDynamic Load101 概述101 Introduction1.静载荷： static loadsThe loads don t change with time (or change very stably and slowly) and acceleration of each member is zero or may be neglect