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1、材料力学双语教学学习资料 第一章 绪 论 Chapter 1 Introduction1-1 材料力学的任务The Tasks of Mechanics of Materials1. 材料力学: Mechanics of Materials2. 构件: Structural Members3. 变形: Deformation4. 强度: Strength5. 刚度: Rigidity6. 稳定性: Stability1-2 变形固体的基本假设Fundamental Assumptions of Solid Deformation Bodies1. 连续性假设: Continuity2. 均匀性
2、假设: Homogeneity3. 各向同性假设: Isotropy1.3 外力及其分类External Forces and Classification1. 分布力: Distributed Force2. 集中力: Point Force3. 静载荷: Static Load4. 动载荷: Dynamic Load1.4 内力、截面法和应力的概念Concepts of Internal Forces， Method of Section and Stress1. 内力: Internal Force2. 截面法: Method of Section3. 截面法的三个步骤：截开，代替，平衡
3、Three steps of method 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 Stress1.5 变形与应变Deformation and Strain1 线应变: Strain2 剪应变: Shearing Strain1.6 杆件变形的基本形式Basic Types of Deformations of
4、 Rods1. 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 2 Tension，Compression and Shear2.1 轴向拉伸与压缩的概念和实例The Concept and Examples of Axial Tension and Compression1. 拉杆: Tensile Rod2. 压杆: Compressive Rod3. 受力特点：外力合力的作用线与杆轴线重合 Characteristic of the External Forc
5、es: The acting line of the resultant of external forces is coincided with the axis of the rod.4. 变形特点：杆沿轴向伸长或缩短Characteristic of Deformation: Rod will elongate or 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 Tension or Compression on the Cross Section1.
6、 横截面: Cross Section2. 轴力: Normal Force3. 轴力图: Diagram of 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 Compression on the Skew Section1. 斜截面: Skew Section2. 2.4 材料在拉伸时的力学性能Mechanical Properties of Materials with Tensile Load1. 标准试件: Specimen2. 低碳钢(C0.3%): Low Carbon Steel3. 弹性阶段:Elasti
7、c Region4. 屈服阶段:Yielding Stage5. 强化阶段:Hardening Stage6. 颈缩阶段: Necking Stage7.p-比例极限: Proportional Limit8.e-弹性极限: Elastic Limit9.s-屈服极限: Yielding Stress10.b-强度极限: Ultimate Stress11. 延伸率: Percent Elongation12. 断面收缩率: Percent Reduction of Area13. 塑性材料: Ductile Materials14. 脆性材料: Brittle Materials15. 铸铁
8、:Cast iron2.7 失效、安全系数和强度计算Failure, Safety factor and Strength calculation1. 许用应力: Allowable Stress2. 安全系数: Safety Factor3. 强度条件: Strength Condition4. 强度校核: Check strength5. 截面设计: Section design6. 确定许可载荷:Determine allowable load2.8 轴向拉伸或压缩时的变形Deformation in Axial Tension or Compression1. 弹性变形: Elasti
9、c Deformation 2. 塑性变形: Plastic Deformation3. 纵向应变: Longitudinal Strain4. 横向应变: Lateral Strain5线弹性变形:Linear Elastic Deformation6. 泊松比:Poissons ratio7.弹性模量-E：表示材料抵抗拉压变形的能力 E- modulus of elasticity：Indicates the capability of materials for resisting tension or compression 8.抗拉刚度-EA:表示构件抵抗拉压变形的能力EA-the
10、axial rigidity: Indicates the capability of constructive members for resisting tension or compression9. 胡克定律（Hookes 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 strain within the elastic region.2.12 应力集中的概念The Concept 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
11、均值的应力，称应力集中。Discontinuities of cross section may result in high localized or concentrated stresses.2. 理论应力集中系数K ：Theoretical Stress-concentration Factor - K2.13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 in Shearing Plane-Shearing
12、Force4. 剪切的实用计算：Practical Calculation of Shear5. 挤压的实用计算：Practical Calculation of Bearing6. 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：Working bearing stress should not exceed the allowable bearing stress.第三章 扭 转Chapter Three Torsion 3.1 扭转的概念和实例Concept and Examples of Torsion1. 电动机: Ge
13、nerator2. 涡轮: 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 perpendicular to the axis of the shaft.4. 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:
14、 Shaft 3.2外力偶矩的计算 扭矩和扭矩图 Calculation of the external torqueInternal torque and Its diagram1扭转外力偶矩的计算：Calculation of the external 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 Torque 3.3 纯剪切 Pure Shear 1. 薄壁圆筒的扭转实验：Experiment of thin-wall
15、ed circular tube under torsion 2. 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 remainunchanged , All cross sections remain unchanged , All the generating lines revolve through an angle .3. 切应力互等定理：Theorem of complementary shearing stresses 4. 切应变：S
16、hearing strain5剪切虎克定律：Hookes law of shear6. 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1. 扭转角: The angle of twist2. 抗扭刚度G Ip ：the torsional rigidity 3. 扭转的刚度条件:
17、 Rigidity condition in torsion4. 单位长度扭转角：The angle of twist per unit lengthExercises1. A bracket（支架） is shown in the figure，The cross-section area of the steel bar AB is A1=6cm2；the cross-section area of the wooden bar BC is A2=300cm2，Knowing the allowable stress of steel is=140MPa , the allowable t
18、ensile stress of wood is L=8MPa, and the allowable compressive stress of wood isY=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 and P=40KN. Try to determine the shearing stress and
19、 bearing stress for the joint.3Two boards are bolted together as shown . 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 same material and have the same allowable stresses 160MPa, =100MPa, 300MPa. Try to design the
20、 tensile force F. 4. 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 same material and have the same allowable stresses 80MPa, =60MPa, 160MPa. The thickness of the bar =15mm, the tensile force F=120KN. Try to
21、design(1) the diameter d of the bolt .(2) the width b of the tensile bar. 5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 with proper 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 English.)第四章 弯曲内力 Chapter Four Intern
22、al Forces in Bending4-1 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 or external the couple vector perpendicular to the axis of the rod.6弯曲的变形特点：杆件的轴线
23、由直线变为曲线。 Characteristics of deformations : the axis of the rod change into curve from original straight lines.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 perpendicular to the axis of the rod makes the axis of the rod ch
24、ange into curve from 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 beam7 .悬臂梁：cantilever beam 4-3 剪力和弯矩4-3 Shearing F
25、orce and Bending Moment1.弯曲内力：internal forces in bending2.剪力：shearing force3.弯矩：bending moment4. 内力的正负规定：sign conventions for 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 and Bending MomentThe Diagrams of Shearing Force and Bending Moment1剪力方程： equation of shearing f
26、orce2弯矩方程： equation 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 and Bending Moment1.微分关系：differential relations2. 规律法：method of regulation3. 控制截面法：method of control sections4.
27、水平直线：horizontal straight line5. 斜直线：inclined straight line6. 突变：sudden change7. 增函数：increasing function8. 减函数：decreasing function9. 盆状抛物线：basin - like curve10. 坟状抛物线：tomb - like curve11. 折向与P相反：flexible opposite to P第五章 弯曲应力 Chapter Five Stresses in Bending5-1 纯弯曲5-1 Pure Bending1. 横力弯曲：transverse b
28、ending2.纯弯曲：pure bending3. 平面假设：横截面变形后仍为平面，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 neutral axes after deformation. 4. 中性层：neutral layer5.中性轴：neutral axis6. 纵向对称轴：longitudinal axis of symmetry5-2 纯弯曲
29、时的正应力5-2 Normal Stress in Pure Bending1 几何关系：geometric relation2 物理关系：physics relation3 静力关系：static relation 4 .抗弯刚度EIz：flexural rigidity 5-3 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 in bending5-4 弯曲切应力5-4 Shearing Stress in Be
30、nding1 矩形截面梁：the beam with rectangular section2 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 in Bending1 合理安排梁的受力情况：arrange the loads of beam reasonably2 跨度：span3 梁的合理截面：reasonable section of b
31、eams4 .等强度梁：equal strength beams第六章 弯曲变形 Chapter Six Deformations in Bending6-1 工程中的弯曲变形问题6-1 The Problems of Deformation Due to Bending 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6-2 The differential equation of deflection curve1. 挠曲线：deflection curve2.挠度：deflecti
32、on3.转角：angle of rotation or slope4. 切线：tangent5. 逆时针：counter-clockwise6. 顺时针：clockwise7. 曲率：curvature8. 曲率半径：radius of curvature6-3 积分法求弯曲变形6-3 Determine the Deformations in Bending by Integration1.微分方程：differential equation2. 边界条件：boundary condition3. 连续性条件：continuity condition4. 积分常数：integral cons
33、tants5.转角方程：equation of angle of rotation6.挠曲线方程： equation of deflection curve7. 刚度条件：rigidity condition8. 镗床：boring machine9. 镗刀：boring tool6-4 叠加法求弯曲变形6-4 Determine the Deformations in Bending by the Method of Superposition1.叠加法：the method of superposition2. 桥式起重机：over head traveling crane6-5 简单超静
34、定梁6-5 Indeterminate Simple Beams 1 静定梁：statically determinate 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 in Bending1 增大抗弯刚度：increase flexural rigidity2 减少跨度或增加支承：decrease span or increase supports3 减小弯矩
35、：decrease bending moment 4 选择合理的截面形状：select the reasonable 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.2. The allowable stress of the wooden beam sh
36、own in the figure is =10MPa. Try to determine the maximum diameter d of the circular hole in case that the strength of the beam is satisfied (neglecting stress concentrations).3Determine 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Cha
37、pter Seven Stress and Strain Analysis Strength Theories71 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 thi
38、s 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: Delegate of a point in the member. It is an infinitesimal geometric body enveloping the studied point. In common use it is a correctitude cubic body. * 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
39、 planes are all zero.* 4主平面：剪应力为零的截面。Principal Planes:The planes on which 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Convention of the order for three principal stresses: In magnitude of the algebraic value.7三向应力状态
40、：三个主应力都不为零的应力状态。State of the triaxial stress（three dimensional state of stress）:State of stress that all the three principal stresses 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
41、为零的应力状态state of the uniaxial stress（unidirectional state of stress）:state of stress that one principal stress is not equal to zero.72 二向应力状态分析解析法72 Analysis of the State of Plane Stress Analytical Method1.任意斜截面上的应力：stresses acting in arbitrary inclined plane2.正负规定：sa 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。 S
42、ign Stipulate ：sa is positive if its direction is the same with one of the external normal line of the section； is positive if it make the element rotate clockwise； A counterclockwise angle is considered to be positive. 73 二向应力状态分析图解法73 Analysis of the State of Plane Stress Graphical Method1.应力圆 ：st
43、ress circle 2.单元体与应力圆的对应关系：Corresponding relation between the element and stress circle(1)a面上的应力(s a，t a) 应力圆上一点(s a，t a)(2)a面的法线 应力圆的半径(3)两面夹角a 两半径夹角2a ；且转向一致。(1) stress(s a，t a) in a plane a point (s a，t a) on the stress circumference(2) normal line of a plane radius of the stress circle(3) angle
44、a between two sections angle 2a between two radiuses；And the direction of rotation is the same.710 强度理论概述710 Concepts of Strength Theories * 1材料的破坏形式： 屈服 断裂 ： Types of failure of materials： yield rupture 2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 f
45、ailure of materials .711 四种常用强度理论711 Four Common Used Strength 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 maximum 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 a