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中英文对照资料
中英文对照资料

Chapter 1 Stress 应力

1.1 Introduction 概述

statics 静力学

Mechanics of Materials 材料力学

stress 应力

strain 应变

strength of the material 材料强度

deformation 变形

rod 杆

beam 梁

theory of elasticity 弹性理论

theory of plasticity 塑性理论

Mechanics of materials is a branch of mechanics that studies the internal effects of stress and strain in a solid body that is subjected to an external loading.

材料力学是力学的一个分支,主要研究受到外力作用的固体,其应力与应变的内部效应。

Stress is associated with the strength of the material from which the body is made, while strain is a measure of the deformation of the body.

应力主要与该变形体材料的强度联系在一起,而应变则是该变形体变形的表征量。Mechanics of materials includes the study of the body’s stability when a body such as a column is subjected to compressive loading.

材料力学还包括对于受到压缩载荷作用的构件(例如压杆)的稳定性问题研究。

相关知识:

1638年,举世闻名的意大利数学家、天文学家、力学家伽里略(Galileo,1564~1642)在荷兰莱登出版了世界上第一本材料力学教本《两种新的科学》,首先提出了材料的力学性质和强度计算的方法。人们认为,材料力学作为一门学科,就从这里开始。18世纪初,实验法开始在法国广泛应用,法国的科学家泊松(S.D. Poisson,1781~1840)、法国的力学家圣维南(B de Saint-Venant,1797~1886)(此后,法国力学家圣维南于19世纪中叶运用弹性力学方法奠定了柱体扭转理论研究的基础,因而学术界习惯将柱体扭转问题称为圣维南问题)、法国数学家、工程师拉梅(Gabriel. Lame,1795~1870)以及法国的力学家、工程师纳维埃(Navier 1785~1838)等等都对弯曲理论、扭转理论、稳定理论以及材料实验作出卓越的贡献,丰富、发展和完善了材料力学这门学科。瑞士的数学家、力学家欧拉(L.Euler,1707~1783),对数学、刚体力学以及材料力学中的弹性线、稳定理论等都有重大贡献。

1.2 Equilibrium of a Deformable Body 变形体的平衡问题

external loads 外力

surface forces 面力

concentrated forces 集中力

linear distributed loads 线性分布载荷

resultant force 合力

centroid 形心

body forces 体力

gravitation field重力场

gravity 重力

electromagnetic field 电磁场

support reactions 支反力(包括力与力偶)

support 支座

coplanar force system 共面力系

translation 平动

rotation 转动

couple moment 力偶矩

cable 绳索,悬索

roller 滚动支座(移动铰支座)

smooth support 光滑支承

external pin 外部铰链(固定铰支座)

internal pin 内部铰链(连接铰链)

fixed support 固定支承,固定端

equations of equilibrium 平衡方程

balance of forces 力的平衡

balance of moments 力矩平衡

free-body diagram 受力图

internal loadings 内力

cross section 截面

normal force 轴力

shear force 剪力

torsional moment (torque) 扭矩

bending moment 弯矩

vector 矢量

scalar 标量

coplanar loadings 共面载荷(二维问题)

the method of section 截面法

right-hand rule 右手法则

The resultant force F R of w(s) is equivalent to the area under the distributed loading curve, and this resultant acts through the centroid C or geometric center of this area. 分布载荷w(s)的等效合力F R大小等于分布载荷曲线所覆盖的面积大小,力的作用线经过该面积形心或几何中心。

If the support prevents translation in a given direction, then a force must be developed on the member in that direction. Likewise, if rotation is prevented, a couple moment must be exerted on the member.

如果支座约束了(物体)在某一方向上的平动,则该支座对物体在该方向上施加一个约束力。同样,如果支座约束了(物体)的转动,则该支座对物体施加一个约束力偶。

Equilibrium of a body requires both a balance of forces, to prevent the body from translating or having accelerated motion along a straight or curved path, and a balance of moments, to prevent the body from rotating.

物体的平衡要求满足合力的平衡(确保物体不会沿某一直线或曲线路径发生平动或加速运动)以及合力矩的平衡(确保物体不会发生转动)。

Successful application of the equations of equilibrium requires complete specification of all the known and unknown forces that act on the body, and so the best way to account for all these forces is to draw the body’s free-body diagram.

成功应用平衡方程要求明确所有已知和未知的载荷,能够考虑所有载荷的最好办法是绘制该物体的受力图。

By the right-hand rule, the thumb gives the arrowhead sense of this vector and the fingers or curl indicate the tendency for rotation (twisting or banding).

右手法则中,拇指指向该矢量的箭头方向,四指弯曲方向表明转动趋势(扭转或弯曲)方向。

1.3 Stress 应力

stress 应力

tangent 相切的

normal 正交的

the quotient of A and B A比B的商

normal stress 正应力

tensile stress 拉应力

compressive stress 压应力

shear stress 切应力

subscript 下标

prefix 前缀

state of stress 应力状态

Stress describes the intensity of the internal force acting on a specific plane (area) passing through a point.

应力用来描述经过某一点的平面上内力的集度。

1.4 Average Normal Stress in an Axial Loaded Bar 轴向载荷作用下的平均正应力

prismatic bar 等截面杆

homogeneous material 均匀材料

isotropic material 各向同性材料

average normal stress 平均正应力

uniaxial stress 单向应力

normal force diagram 轴力图

Homogeneous material has the same physical and mechanical properties throughout its volume, and isotropic material has these same properties in all directions.

均匀材料在材料内部各处的物理特性和力学特性均相同;各向同性材料在各个方向上的物理特性和力学特性均相同。

As a sign convention, the normal force will be positive if it causes tension in the member, and negative if it causes compression.

根据符号规定,如果轴力导致构件伸长,则轴力为正;如果导致构件缩短,则轴力为负。

1.5 Average Shear Stress 平均切应力

average shear stress 平均切应力

simple shear 简单剪切

direct shear 直接剪切

bolt 螺栓

pin 连接销,连接铰

pure shear 纯剪切

All four shear stresses must have equal magnitude and be directed either toward or away from each other at opposite edges of the element. This is referred to as the complementary property of shear.

所有四个切应力必须大小相等,方向则共同指向或共同背离两平面交线,该理论即为切应力互等定理。

1.6 Allowable Stress 许用应力

allowable stress 许用应力

factor of safety 安全因数

1.7 Design of Simple Connections 简单连接件的设计

bearing stress 挤压应力

The area of the column base plate B is determined from the allowable bearing stress for the concrete.

压杆基座B的面积可以根据混凝土材料的许用挤压应力确定。

The embedded length l of this rod in concrete can be determined using the allowable shear stress of the bond glue.

嵌入混凝土杆子的嵌入长度l可以根据连接胶的许用切应力确定。

The area of the bolt for this lap joint is determined from the shear stress, which is largest between the plates.

连接搭接板的螺栓面积可以根据其切应力确定,其在两板之间取得最大值。Chapter 2 Strain 应变

deformation 变形

strain 应变

normal strain 正应变

shear strain 切应变

dimensionless quantity 无量纲量

parallelepiped 平行六面体

Cartesian strain components直角(笛卡尔)坐标应变分量

The normal strains cause a change in volume of the element, whereas the shear strains cause a change in its shape. Both of these effects occur simultaneously during the deformation.

正应变导致微元体积发生改变,而切应变导致微元形状发生改变。这两种效应在变形中是同时发生的。

Chapter 3 Mechanical Properties of Materials 材料力学特性

3.1 The Tension and Compression Test 拉伸与压缩实验

mechanical properties of materials 材料的力学特性

tension test 拉伸实验

compression test 压缩实验

specimen 实验试件

gauge-length 标距

ball-and-socket joint 球铰支座

caliper 游标卡尺

extensometer 伸长计

electrical-resistance strain gauge 电阻应变仪

The operation of this gauge is based on the change in electrical resistance of a very thin wire or piece of metal foil under strain.

应变仪的工作原理基于细导线或金属箔片在变形条件下电阻的改变情况。

3.2 The Stress-Strain Diagram 应力-应变曲线

stress-stain diagram 应力-应变曲线

nominal stress/strain 名义应力/应变

elastic behavior 弹性行为

linear elastic region 线弹性区域

the proportional limit 比例极限

the elastic limit 弹性极限

yielding 屈服

yielding stress 屈服应力

plastic deformation 塑性变形

upper yield point 屈服上限

lower yield point 屈服下限

carbon steel 碳钢

hot rolled steel 热轧钢

strain hardening 应变硬化

ultimate stress 极限应力

necking 颈缩

fracture stress 断裂应力

Here the curve is actually a straight line throughout most of this region, so that the stress is proportional to the strain. The material in this region is said to be linear elastic.

该阶段的曲线大部分为直线,表明应力与应变成正比关系。该阶段材料(行为)称为线弹性。

A slightly increase in stress above the elastic limit will result in a breakdown of the material and cause it to deform permanently. This behavior is called yielding, and it is indicated by the rectangular dark orange region of the curve.

当应力超过弹性极限后材料会失效,导致永久性变形。(材料的)该行为称为屈服,用(应力-应变)曲线中深桔色的矩形区域表示。

Notice that once the yield point is reached, then as shown in Fig.3-4, the specimen will continue to elongate (strain) without any increase in load. When the material is in this state, it is often referred to as being perfectly plastic.

注意当到达屈服点时,如图3-4所示,试件将在载荷不变的情况下继续伸长。当材料处于该状态下时,被称为完全塑性状态。

When yielding has ended, an increase in load can be supported by the specimen, resulting in a curve that rises continuously but becomes flatter until it reaches a maximum stress referred to as the ultimate stress, ζu.

当屈服阶段结束后,试件上的载荷继续增大,导致(应力-应变)曲线继续上升但逐渐平坦直至到达最大应力,即强度极限ζu。

This decrease is fairly uniform over the specimen’s entire gauge length; however, just after, at the ultimate stress, the cross-sectional area will begin to decrease in a localized form in this region as the specimen elongates further, Fig.3-5a.

试件在其标距范围内(横截面尺寸)缩小是均匀的,但是到达强度极限后,会在局部区域内横截面尺寸进一步缩小,如图3-5a所示。

3.3 Stress-Strain Behavior of Ductile and Brittle Materials 塑性材料和脆性材料的应力-应变行为

ductile material 塑性材料

brittle material 脆性材料

mild steel 低碳钢

percent elongation 延伸率

percent reduction in area 断面收缩率

brass 黄铜

molybdenum 钼

zinc 锌

aluminum 铝

off-set method 偏移法

yield strength 屈服强度

polymer (高分子)聚合物

gray cast iron 灰口铸铁

concrete 混凝土

methacrylate plastic甲基丙烯酸塑料

Any material that can be subjected to large strains before it fractures is called a ductile material.

任何可以在断裂前承受较大应变的材料称作塑性材料。

Actually, this metal often does not have a well-defined yield point, and consequently it is standard practice to define a yield strength using a graphical procedure called the offset method.

实际上,这种材料并没有一个非常明确的屈服点,所以通常标准的做法是使用图解的偏移法来确定屈服强度。

The characteristics of its stress-strain diagram depend primarily on the mix of concrete (water, sand, gravel, and cement) and the time and temperature of curing. (混凝土)的应力-应变曲线特性取决于混凝土的配比(水、砂、石和水泥)以及固化时间和温度。

3.4 Hooke’s Law 胡克定律

Hooke’s law 胡克定律

modulus of elasticity 弹性模量

Young’s modulus 杨氏模量

slope 斜率

rolled steel 轧制钢

tool steel 工具钢

stiffness 刚度

vulcanized rubber 硫化橡胶

permanent set 永久变形

spring back 回弹

interatomic force 原子间力

If a specimen of ductile material, such as steel, is loaded into the plastic region and then unloaded, elastic strain is recovered as the material returns to its equilibrium state. The plastic strain remains, however, and as a result the material is subjected to a permanent set.

如果塑性材料试件,如低碳钢,加载到塑性区域然后卸载,则材料中的弹性应变可以恢复至其平衡状态。材料中的塑性应变将保留,材料中有永久变形。

If the load is reapplied, the atoms in the material will again be displaced until yielding occurs at or near the stress A’, and the stress-strain diagram continues along the same path as before, Fig.3-14b. It should be noted, however, that this new stress-strain diagram, defined by O’A’B, now has a higher yield point (A’), a consequence of strain-hardening. In other words, the material now has a grater elastic region; however, it has less ductility, a smaller plastic region, than when it was in its original state.

重新加载后,材料内的原子被再一次移位直至发生屈服或者到达A’点处,应力应变曲线将沿原有的路径上升,如图3-14b所示。需要注意的是,这条由O’A’B 定义的新应力-应变曲线具有更高的屈服点A’,这是应变硬化的结果。换言之,现在材料具有更大的弹性范围,但塑性降低,即塑性区域比原有状态更小。

3.5 Strain Energy 应变能

strain energy 应变能

strain-energy density 应变能密度

modulus of resilience 回弹模量

modulus of toughness 韧性模量

By definition, work is determined by the product of the force and displacement in the direction of the force.

根据定义,功可以由力与力的方向上的位移之积来确定。

Since the force is increased uniformly from zero to its final magnitude ΔF when the displacement εΔz is attained, the work done on the element by the force is equal to the average force magnitude (ΔF/2) times the displacement εΔz.

由于力的大小从零均匀增加到ΔF,同时位移大小为εΔz,则该力对微元做功的大小等于力的平均值(ΔF/2)乘以位移εΔz。

Physically a material’s resilience represents the ability of the material to absorb energy without any permanent damage to the material.

从物理意义上说,一种材料的回弹模量体现了其在不导致材料永久性破坏条件下吸收能量的能力。

3.6 Poisson’s Ratio泊松比

Poisson’s ratio 泊松比

in the longitudinal direction 在纵向方向上

in the axial direction 在轴向方向上

in the lateral direction 在横向方向上

in the radial direction 在径向方向上

longitudinal elongation 纵向伸长

lateral contraction 横向收缩

Within the elastic range the ratio of the strains in the longitudinal or axial direction and in the lateral or radial direction is a constant.

在弹性范围内,纵向(轴向)正应变和横向(径向)正应变之比为常数。

The negative sign is included there since longitudinal elongation (positive strain) causes lateral contraction (negative strain), and vice versa.

(公式中的)负号表明纵向伸长(正应变)会导致横向收缩(负应变),反之亦然。

3.7 The shear Stress-Strain Diagram剪切应力-应变曲线

shear stress-strain diagram 剪切应力-应变曲线

pure shear 纯剪切

angle of twist 扭转角

ultimate shear stress 极限切应力

shear modulus of elasticity 弹性剪切模量

modulus of rigidity 刚性模量,刚度模量

Chapter 4 Axial Load 轴向载荷(轴力)

4.1 Saint-Venant’s Principle 圣维南原理

the centroidal axis 形心轴

localized deformation 局部变形

Saint-Venant’s principle 圣维南原理

The stress and strain produced at points in a body sufficiently removed from the region of load application will be the same as the stress and strain produced by any applied loadings that have the same statically equivalent result, and are applied to the body within the same region.

物体上各点处所产生的应力和应变,当其位置距离力的作用点足够远时,与在同一区域内作用等效载荷所产生的应力和应变是相同的。

4.2 Elastic Deformation of an Axially Loaded Member 轴向受载构件的弹性变形

elastic deformation 弹性变形

algebraic addition 代数和

sign convention 符号规定

Using the method of sections, a differential element (or wafer) of length dx and cross-sctional area A(x) is isolated frome the bar at the arbitrary position x.

使用截面法,在杆上任意位置x处截取长度为dx,截面积为A(x)的微元。

The displacement of one end of the bar with respect to the other is then found from the algebraic addition of the relative displacements of the ends of each segment. (杆)一端相对于另一端的位移等于每段杆端点相对位移的代数和。

Both the force and displacement are positive if they cause tension and elongation, respectively; whereas a negative force and displacement will cause compression and contraction, respectively.

若(轴)力为拉力,位移为伸长状态时,则(轴)力和位移为正;若(轴)力为压力,位移为收缩状态时,则(轴)力和位移为负。

4.3 Principle of Superposition 叠加原理

deflect 偏转

By subdividing the loading into components, the principle of superposition states that the resultant stress or displacement at the point can be determined by algebraically summing the stress or displacement caused by each load component applied separately to the member.

通过将载荷分解为若干分量,根据叠加原理,某一点处的应力或位移值可以通过代数求和各载荷分量在该点所产生的应力或位移来确定。

4.4 Statically Indeterminate Axially Loaded Member 轴向受载的静不定构件statically determinate problems 静定问题

statically indeterminate problems 静不定问题,超静定问题

compatibility condition (变形)协调条件

kinematic condition 运动学条件

4.5 The Force Method of Analysis for Axially Loaded Members 应用力法分析轴向受载构件

the force method 力法

flexibility method of analysis 柔度分析法

redundant support 多余约束

4.6 Thermal Stress 热应力

the linear coefficient of thermal expansion 热膨胀线性系数

In a statically indeterminate member, these thermal displacements will be constrained by the supports, thereby producing thermal stresses that must be considered in design. 在静不定构件中,热位移由于被支座所限制,会导致(构件内部)产生热应力,这一现象需要在设计中考虑到。

4.7 Stress Concentrations 应力集中

stress concentration 应力集中

grid lines 网格线

fillet 圆角

stress-concentration factor 应力集中因数

fatigue loading 疲劳载荷

elastic perfectly plastic material 弹塑性材料

Not only do complex stress distributions arise just under a concentrated loading, they can also arise at sections where the member’s cross-sectional area changes.

不仅集中载荷的作用点处会产生复杂的应力分布,在构件横截面尺寸发生变化的位置也会产生复杂的应力分布。

Chapter 5 Torsion 扭转

5.1 Torsional Deformation of a Circular Shaft 圆截面轴的扭转变形

shaft 轴

helix 螺旋线

warp 翘曲

the front and rear faces of the element 微元的前后面

circular tube 圆形管

Torque is a moment that tends to twist a member about its longitudinal axis.

扭矩是导致构件绕其纵向轴线发生扭转的力矩。

Note that twisting causes the circles to remain circles, and each longitudinal grid line deforms into a helix that intersects the circles at equal angles.

需要注意到的是扭转变形导致原有的圆形(截面网格)仍然保持圆形,纵向网格则变形为和圆形(截面网格)所成角度相等的螺旋线。

Here a radial line located on the cross section at a distance x from the fixed end of the shaft will rotate through an angleθ(x). The angleθ(x), so defined, is called the angle of twist.

位于距固定端长度为x的横截面上的径向线段将绕着轴线转过角度θ(x),该角度称为扭转角。

The shear strain within the shaft varies linearly along any radial line, from zero at the axis of the shaft to a maximum max at its outer boundary.

轴上的切应变沿径向方向呈线性变化,在轴心处为零,在外圆周上取得最大值γmax。

5.2 The Torsion Formula 扭转公式

polar moment of inertia 极惯性矩

solid shaft 实心轴

annulus 环形面

circumference 周长

tubular shaft 空心轴

geometric property 几何特性

torque diagram 扭矩图

If the material is linear-elastic, then Hooke’s law applies, τ=Gγ, and consequently a linear variation in shear strain, as noted in the previous section, leads to a corresponding linear variation in shear stress along any radial line on the cross section.

如果材料在线弹性范围内,可以应用胡克定律,τ=Gγ,则根据上一节讨论的结果,呈线性变化的切应变会导致在横截面的径向方向上,切应力也呈现线性变化(趋势)。

Not only does the internal torque T develop a linear distribution of shear stress along each radial line in the plane of the cross-section area, but also an associated shear-stress distribution is developed along an axial plane.

扭矩T不仅导致在横截面沿径向方向上线性分布的切应力,还导致在轴向平面内也存在切应力的分布。

As a sign convention, T will be positive if by the right-hand rule the thumb is directed outward from the shaft when the fingers curl in the direction of twist as caused by the torque.

根据符号规定,如果根据右手法则,当四指沿弯矩转动方向弯曲,而拇指指向圆轴截面的外法线方向时,该弯矩T为正。

5.3 Power Transmission 功率传递

angular speed 角速度

instantaneous power 瞬时功率

frequency of a shaft’s rotation 转轴旋转频率

5.4 Angle of twist扭转角

gear 齿轮

bearing 轴承

We will use the right-hand rule, whereby both the torque and angle will be positive, provided the thumb is directed outward from the shaft when the fingers curl to give the tendency for rotation.

我们使用右手法则,当四指沿旋转趋势方向弯曲,拇指指向轴外法线方向时,扭矩和扭转角均为正值。

5.5 Statically Indeterminate Torque-Loaded Members扭转作用下的静不定构件

The necessary condition of compatibility, or the kinematic condition, requires the angle of twist of one end of the shaft with respect to the other end to be equal to zero, since the end supports are fixed.

必要的协调方程或运动条件要求该轴一端相对于另一端的扭转角为零,因为轴的两端支座处均为固定端。

Chapter 6 Bending 弯曲

6.1 Shear and Moment Diagrams 剪力弯矩图

symmetric cross section 对称截面

unsymmetric bending 非对称弯曲

simply supported beam 简支梁

cantilevered beam 悬臂梁

overhanging beam 外伸梁

the boom of a crane 起重机臂架

shear and moment functions 剪力与弯矩方程

a clockwise rotation 顺时针转动

In general, the internal shear and moment functions of x will be discontinuous, or their slope will be discontinuous, at points where a distributed load changes or where concentrated forces or couple moments are applied.

通常情况下,在分布载荷发生变化,或者有集中力或集中力偶矩作用的位置,用x表示的剪力和弯矩方程会不连续,或者方程的斜率会不连续。

The positive directions are as follows: the distributed load acts upward on the beam; the internal shear force causes a clockwise rotation of the beam segment on which it acts; and the internal moment causes compression in the top fibers of the segment such that it bends the segment so that it holds water.

正方向的规定如下:作用在梁上方向向上的分布载荷为正;作用在梁微元上使其顺时针方向转动的剪力为正;导致梁上部受压呈下凹形的弯矩为正。

6.2 Graphical Method for Constructing Shear and Moment Diagrams 几何法绘制剪力弯矩图

thrust bearing 止推轴承

journal bearing 径向轴承

Equation 6-1 states that at a point the slope of the shear diagram equals the intensity of the distributed loading.

方程6-1表明在剪力图上某一点的斜率等于该点分布载荷集度值。

Eq.6-2 states that at a point the slope of the moment diagram is equal to the shear.

方程6-2表明在弯矩图上某一点的斜率等于该点的剪力。

When F acts upward on the beam, ?V is positive so the shear will “jump” upward. Likewise, if F acts downward, the jump (?V) will be downward.

当F方向向上时,?V为正值,此时剪力图将向上跳跃。同样,当F方向向下时,剪力图将向下跳跃。

In this case, if M0is applied clockwise, ?M is positive so the moment diagram will

“jump” upward. Li kewise, when M0acts counterclockwise, the jump (?M) will be downward.

当M0方向为顺时针时,?M为正值,此时弯矩图将向上跳跃。同样,当M0方向为逆时针时,弯矩图将向下跳跃。

6.3 Bending Deformation of a Straight Member 构件的弯曲变形

the neutral surface 中性面,中性层

the neutral axis 中性轴

the radius of curvature 曲率半径

The bending moment causes the material within the bottom portion of the bar to stretch and the material within the top portion to compress. Consequently, between these two regions there must be a surface, called the neutral surface, in which longitudinal fibers of the material will not undergo a change in length.

弯矩导致梁的底部材料伸长,上部材料收缩。因此,在梁的上部和下部之间必然存在一个面,在该面上纵向方向材料的长度不发生变化,该面称为中性面(中性层)。

For any specific cross section, the longitudinal normal strain will vary linearly with y from the neutral axis.

在任意截面上,该截面上各点沿纵向方向的正应变与其距离中性轴的距离y成线性关系。

6.4 The Flexure Formula 弯曲公式

the moment of inertia 惯性矩

The first moment of the member’s cross-sectional area about the neutral axis must be zero. This condition can only be satisfied if the neutral axis is also the horizontal centroidal axis for the cross-sectional area.

构件横截面关于中性轴的一阶矩必须为零。该条件只有当中性轴与截面水平形心轴重合时才满足。

It is used to determine the normal stress in a straight member, having a cross section that is symmetrical with respect to an axis, and the moment is applied perpendicular to this axis.

该公式用于计算截面关于某一轴对称的直线构件的弯曲应力,弯矩垂直于该对称轴。

6.5 Unsymmetric Bending 非对称弯曲

the product of inertia 惯性积

principal axes of inertia 惯性主轴

the axis of symmetry 对称轴

We require the stress distribution acting over the entire cross-sectional area to have a zero force resultant, the resultant internal moment about the y axis to be zero, and the resultant internal moment about the z axis to equal M.

我们要求横截面上应力分布而引起的合力为零,关于y轴的合力矩为零,关于z 轴的合力矩为M。

As indicated in Appendix A, it will indeed be zero provided the y and z axes are chosen as principal axes of inertia for the area.

正如附录A中所示,当y轴和z轴被确定为惯性主轴时,该式(惯性积)确实为零。

If the area has an axis of symmetry, however, the principal axes can easily be established since they will always be oriented along the axis of symmetry and perpendicular to it.

如果截面有对称轴,则截面惯性主轴的方向很容易确定,通常选定对称轴以及与其相垂直的轴。

Sometimes a member may be loaded such that M does not act about one of the principal axes of the cross section. When this occurs, the moment should first be resolved into components directed along the principal axes, then the flexure formula can be used to determine the normal stress caused by each moment component. Finally, using the principle of superposition, the resultant normal stress at the point can be determined.

有些时候,弯矩M作用的方向不一定沿截面的惯性主轴方向。如果出现该情况,则首先需要将弯矩分解到沿惯性主轴方向上,然后应用弯曲公式,求解每一弯矩分量而导致的正应力。最后,应用叠加原理,计算该点的正应力之和。

We will assume θ is positive when it is directed from the +z axis toward the +y axis. 我们假设当θ从z轴正向转向y轴正向时,θ角为正。

Chapter 7 Transverse Shear 横向剪切

7.1 Shear in Straight Members 直杆上的剪切作用

transverse shear 横向剪切

shear flow 剪切流

warp 翘曲

7.2 The Shear Formula 剪切公式

wide-flange beam 工字梁

web 腹板

flange 翼板

tangent 相切

right angle 直角

The element in Fig.7-4b will indeed satisfy ∑F x=0since the stress distribution on each side of the element forms only a couple moment and therefore a zero force resultant.

图7-4b中所示微元确实满足∑F x=0的条件,因为微元两侧的应力分布各产生一对力偶,因此满足合力为零。

Because the resultant moments on each side of the element differ by dM, it can be seen in Fig.7-4c that ∑F x=0 will not be satisfied unless a longitudinal shear stress τacts over the bottom face of the segment.

由于分离体两侧面合力矩之差为dM,因此要满足∑F x=0的条件,则必须在该分

离体的底部平面上存在切应力 的作用。

Although in the derivation we considered only the shear stresses acting on the beam’s longitudinal plane, the formula applies as well for finding the transverse shear stress on the beam’s cross-section. Recall that these stresses are complementary and numerically equal.

尽管在公式推导的过程中,我们仅仅考虑了梁在轴向方向上的切应力,但该公式也可应用于梁横截面上横向切应力的计算。(根据切应力互等定理),这些应力是成对出现且数值相等的。

It should also be pointed out that the shear formula will not give accurate results when used to determine the shear stress at the flange-web junction of a wide-flange beam, since this is a point of sudden cross-sectional change and therefore a stress concentration occurs here.

还需要指出的是,剪切公式不能用于计算工字型梁腹板和翼板连接处的切应力,原因是在该处存在由于横截面尺寸突变而导致的应力集中。

To summarize the above points, the shear formula does not give accurate results when applied to members having cross sections that are short or flat, or at points where the cross section suddenly changes. Nor should it be applied across a section that intersects the boundary of the member at an angle other than 90°.

总结上述几点,当剪切公式应用在横截面短而平(b/h之比较大)的情况下,或是横截面尺寸突变处,以及与截面边界交角不是90°的位置时,计算精度不高。

7.3 Shear Flow in Built-Up Members 组合构件上的剪切流

build-up beam 组合梁

fastener 紧固件,连接件

bolt 螺栓

glue 胶水

Two of these forces, F and F+dF, are developed by normal stresses caused by the moments M and M+dM, respectively. The third force, which for equilibrium equals dF, acts at the juncture and it is to the supported by the fastener.

这些力中的两个分量F和F+dF是由于弯矩M和M+dM引起的正应力分布而产生的。第三个力大小等于dF,作用于连接处,由连接件承受。

The integral represents Q, that is the moment of the segment’s area A’ in Fig.7-14b about the neutral axis for the entire cross section.

积分式代表Q,是图7-14b中分离体截面积A’相对于整个截面中性轴的静矩。Shear flow is a measure of the force per unit length along the axis of a beam. This value is found from the shear formula and is used to determine the shear force developed in fasteners and glue that holds the various segments of a composite beam together.

剪切流表征的是梁沿其轴线方向单位长度上力的大小。该值可以通过剪切公式进行计算,用于确定支撑组合构件各部分的连接件或胶水上所产生的剪力大小。

7.4 Shear Flow in Thin-Walled Members 薄壁构件上的剪切流

The value of q changes over the cross section, since Q will be different for each area

segment A’for which it is determined. In particular, q will vary linearly along segments (flanges) that are perpendicular to the direction of V, and parabolically along segments (web)that are inclined or parallel to V.

剪切流q的值在截面上是不同的,原因是Q对于不同分离体面积进行求解时是不同的。特别是,当剪切流的方向与剪力V方向垂直时(翼板部分),剪切流q 呈线性变化;当剪切流方向与剪力V方向相交或平行时(腹板部分),剪切流q 呈抛物线变化。

q will always act parallel to the walls of the member, since the section on which q is calculated is taken perpendicular to the walls.

剪切流q的方向总是与构件壁相平行,原因是在计算q时截取分离体的截面是沿垂直构件壁方向的。

The directional sense of q is such that the shear appears to “flow” through the cross section, inward at the beam’s top flange, “combining” and then “flowing” downward through the web, since it must contribute to the shear force V, and the separating and “flowing” outward at the bottom flange.

剪切流q方向的判断,剪切流是沿着截面进行流动的,在(工字梁)上翼板剪切流向内流动,汇合后沿腹板向下流动(剪切流方向与剪力V方向在腹板上一致),在(工字梁)下翼板处剪切流分离并向外流动。

Chapter 8 Combined Loadings 组合载荷

8.1 Thin-Walled Pressure Vessels 薄壁压力容器

cylindrical vessel 柱罐容器

spherical vessel 球罐容器

gauge pressure 仪表压力

atmospheric pressure 大气压力

the hoop stress 周向应力

the longitudinal stress 轴向应力

radial stress 径向应力

In both cases, the pressure in the vessel is understood to be the gauge pressure, that is, it measures the pressure above atmospheric pressure, since atmospheric pressure is assumed to exit both inside and outside the vessel’s wall before the vessel is pressurized.

在两种情况下,容器压力都是指仪表压力,即在大气压力之上测得的压力,原因是假设在容器进行加压前,容器的内壁和外壁处都存在大气压力。Consequently, when fabricating cylindrical pressure vessels from rolled-formed plates, the longitudinal joints must be designed to carry twice as much stress as the circumferential joints.

因此,在使用轧制板材制造柱罐容器时,轴向方向上的接头承载能力要是周向接头承载能力的2倍以上。

The above analysis indicates that an element of material taken from either a cylindrical or a spherical pressure vessel is subjected to biaxial stress, i.e., normal stress existing in only two directions.

上述分析表明,从柱罐容器或球罐容器上取出的材料微元上仅存在双轴应力,即只存在两个方向上的正应力。

Actually, the pressure also subjects the material to a radial stress, σ3, which acts along a radial line. This stress has a maximum value equal to the pressure p at the interior wall and it decreased through the wall to zero at the exterior surface of the vessel, since the gauge pressure there is zero.

实际上,内部压力还导致了径向应力σ3的存在。该应力在容器内壁处取得最大值p,在容器壁上逐渐衰减,在容器外壁处取得最小值零,因为此处的仪表压力为零。

8.2 State of Stress Caused by Combined Loadings 组合载荷作用下的应力状态Section the member perpendicular to its axis at the point where the stress is to be determined and obtain the resultant internal normal and shear force components and the bending and torsional moment components.

在需要计算应力的点处,将构件沿垂直其轴线方向进行切割,计算截面处的轴力、剪力、扭矩和弯矩等内力分量。

The force components should act through the centroid of the cross section, and the moment components should be computed about centroidal axes, which represent the principal axes of inertia for the cross section.

内力的作用线需要经过截面的形心,力矩分量的计算需要绕着截面的形心轴,即截面的惯性主轴。

Chapter 9 Stress Transformation 应力变换

9.1 Plane-Stress Transformation 平面应力变换

stress transformation 应力变换

plane-stress 平面应力

The state of plane stress at the point is uniquely represented by two normal stress components and one shear stress component acting on an element that has a specific orientation at the point.

该点沿某一特定方向的平面应力状态可以由两个正应力分量和一个切应力分量唯一表征。

The transformation of stress components, however, is more difficult since the transformation must account for the magnitude and direction of each stress component and the orientation of the area upon which each component acts.

应力分量的变换比力的变换更为复杂,原因是变换过程需要考虑每个应力分量的大小和方向以及每个应力分量作用平面的方向。

9.2 General Equations of Plane-Stress Transformation 平面应力变换的通用公式

trigonometric identity 三角恒等式

The orientation of the plane on which the normal and shear stress components are to be determined will be defined by the angle θ, which is measured from the +x axis to

the +x’ axis. The angle θ will be positive provided it follows the curl of the right-hand fingers, i.e., counterclockwise as shown in Fig.9-5b.

需要确定的正应力和切应力所在的平面方向由θ角来定义,该角度是从x轴正向旋转到x’轴正向。θ角符合右手法则,即在图9-5b中所示逆时针为正。

9.3 Principal Stresses and Maximum In-Plane Shear Stress 主应力和最大面内切应力

in-plane principal stress 面内主应力

the principal planes 主平面

derivative 导数

maximum in-plane shear stress 最大面内切应力

reciprocal 倒数

trigonometric value 三角函数值

This particular set of values are called the in-plane principal stresses, and the corresponding planes on which they act are called the principal planes of stress, Fig.9-9. Furthermore, if the trigonometric relations for θp1 or θp2 are substituted into Eq.9-2, it can be seen that ηx’y’=0; on other words, no shear stress acts on the principal planes.

这一组特殊值叫做面内主应力,相应应力作用的平面叫做主平面,如图9-9所示。除此之外,如果将θp1或θp2的三角函数值带入式9-2,则会发现ηx’y’=0,也就是说在主平面上没有切应力作用。

An element subjected to maximum shear stress will be 45ofrom the position of an element that is subjected to the principal stress.

微元上最大切应力作用的方向与主应力作用的方向成45o角。

9.4 Mohr’s Circle-Plane Stress 莫尔圆(平面应力)

Each point on Mohr’s circle represents the two stress components σx’ and τx’y’ acting on the side of the element defined by the x’axis, when the axis is in a specific direction θ.

莫尔圆上的每一个点代表了两个应力分量σx’和τx’y’,这两个应力作用于与x’轴成θ角的平面上。

Now consider rotating the x’axis 90°, counterclockwise, Fig.9-16b. Then σx’=σy, τx’y’=-τxy. These values are the coordinates of point G(σy, -τxy) on the circle, Fig.9-16c. Hence, the radial line CG is 180° counterclockwise from the “reference line”CA. In other words, a rotation θ of the x’ axis on the element will correspond to a rotation 2θon the circle in the same direction.

现在考虑将x’轴逆时针旋转90°,如图9-16b所示,得到σx’=σy,τx’y’=-τxy。这些值是圆上G点的坐标(σy, -τxy),如图9-16c所示。所以,径向线段CG为“参照线”CA逆时针旋转180°所得。也就是说,x’轴在微元上旋转θ角度对应了在莫尔圆上沿相同方向旋转2θ角度。

Establish a coordinate system such that the horizontal axis represents the normal stress σ, with positive to the right, and the vertical axis represents the shear stress τ, with positive downwards.

建立直角坐标系,横轴代表正应力σ,向右为正方向;纵轴代表切应力τ,向下为正方向。

Plot the “reference point”A having coordinates A(σx, τxy). This point represents the normal and shear stress components on the element’s right-hand vertical face, and since the x’ axis coincides with the x axis, this represents θ=0°.

(在圆上)绘制“参考点”A,其坐标值为(σx, τxy)。改点表示了在微元右侧面上作用的正应力和切应力分量,由于x’轴与x轴重合,因此θ=0°。

9.5Absolute Maximum Shear Stress 绝对最大切应力

absolute maximum shear stress 绝对最大切应力

triaxial stress 三轴应力/三向应力

In the case of plane stress, if the in-plane principal stresses both have the same sign, the absolute maximum shear stress will occur out of the plane and has a value of τabsmax=σmax/2. This value is greater than the in-plane shear stress.

对于平面应力的情况,如果(两个)面内主应力的符号相同,则绝对最大切应力位于平面以外,其值为τabsmax=σmax/2。该值要大于(最大)面内切应力。

If the in-plane principal stresses are of opposite signs, then the absolute maximum shear stress will equal the maximum in-plane shear stress; that is, τabsmax=(σmax-σmin) /2.

如果(两个)面内主应力的符号相反,则绝对最大切应力与最大面内切应力相等,即τabsmax=(σmax-σmin) /2。

Chapter 10 Strain Transformation 应变变换

10.1 Plane Strain平面应变

strain transformation 应变变换

principal strain 主应变

maximum in-plane shear strain 最大面内切应变

absolute maximum shear strain 绝对最大切应变

Although plane strain and plane stress each have three components lying in the same plane, realize that plane stress does not necessarily cause plane strain or vice versa.

虽然平面应变和平面应力都是在同一平面内只存在三个分量,但平面应力不一定导致平面应变,反之亦然。

In general, then, unless ν=0, the Poisson effect will prevent the simultaneous occurrence of plane strain and plane stress.

一般情况下,除非泊松比ν=0,否则泊松效应会阻止平面应变和平面应力同时出现。

10.2 General Equations of Plane-Strain Transformation 平面应变变换的通用公式

Normal strains εx and εy are positive if they cause elongation along the x and y axes, respectively, and the shear strain γxy is positive if the interior angle AOB becomes smaller than 90°.

如果正应变εx和εy导致沿x轴和y轴方向尺寸伸长,则正应变εx和εy为正;如果角AOB的内角小于90°,则切应变γxy为正。

Like stress, an element can be oriented at a point so that the element’s deformation is caused only by normal strains, with no shear strain. When this occurs the normal strains are referred to as principal strains, and if the material is isotropic, the axes along which these strains occur will coincide with the axes that define the planes of principal stress.

与应力类似,某点的微元可以在某一方向上仅存在由正应变导致的变形,而不存在切应变,这种情况下的正应变被称为主应变。如果材料是各向同性的,则主应变所在平面的方向与主应力相同。

10.5 Strain Rosettes 应变花

electrical resistance strain gauge 电阻应变仪(片)

For a general loading on a body, however, the strains at a point on its free surface are determined using a cluster of three electrical-resistance strain gauges, arranged in a specified pattern. This pattern is referred to as a strain rosette, and once the normal strains on the three gauges are measured, the data can then be transformed to specify the state of strain at the point.

对于一般的受载物体,其自由表面上某点的应变使用三个应变片进行测量,该组应变片以特殊的形式进行排布。这种排布方式叫做应变花,三个应变片处的应变测得后,可以通过变换公式计算该点的应变状态。

10.6 Material-Property Relationship 材料属性关系

generalized Hooke’s law 广义胡克定律

dilatation 体应变

bulk modulus 体积模量

hydrostatic loading 静水压力

When a volume element of material is subjected to the uniform pressure p of a liquid, the pressure on the body is the same in all directions and is always normal to any surface on which it acts. Shear stresses are not present, since the shear resistance of liquid is zero.

当体单元收到均匀的液体压力p的作用时,各个方向上的压力大小均相同且垂直于体表面。体单元上没有切应力的作用,因为液体的剪切抗力为零。

If a material existed that did not change its volume then δV=e=0, and k would have to be infinite.

如果材料的体积改变量为零,即δV=e=0,则其体积模量k为无穷大。

The theoretical maximum value for Poisson’s ratio is therefore ν=0.5. During yielding, no actual volume change of the material is observed, and so ν=0.5 is used when plastic yielding occurs.

泊松比的理论最大值为ν=0.5。在屈服过程中,材料的体积不发生变化,所以屈服阶段的泊松比为ν=0.5。

10.7 Theories of Failure 失效理论(强度理论)

PS中英文对照资料

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中文资料 PowerBuilder是著名的数据库应用开发工具生产厂商PowerSoft公司推出的产品(PowerSoft现已被数据库厂商Sybase所收购),它完全按照客户机/服务器体系结构研制设计,在客户机/服务器结构中,它使用在客户机中,作为数据库应用程序的开发工具而存在。由于PowerBuilder采用了面向对象和可视化技术,提供可视化的应用开发环境,使得我们利用PowerBuilder,可以方便快捷地开发出利用后台服务器中的数据和数据库管理系统的数据库应用程序。 在当前,网络技术迅速发展,随之发展的还有OLE,OCX,跨平台等技术,而在PowerBuilder的最新版PowerBuilder中提供了对这些技术的全面支持。总之在数据库开发工具领域,PowerBuilder是其中非常优秀的一个,利用它我们可以开发出功能强大的数据库应用程序。 PowerBuilder提供了对目前流行的大多数关系数据库管理系统的支持,由于在PowerBuilder的应用程序中对数据库访问的部分一般采用国际化标准数据库查询语言SQL,使得用PowerBuilder开发的应用程序可以不做修改或者只做少量的修改就可以在不同的后台数据库管理系统上使用。也就是说用PowerBuilder开发的应用程序是独立于服务器上的数据库管理系统的。 和大多数的windows应用程序一样,PowerBuilder也是事件驱动工作方式。在这种工作方式中,程序的运行没有固定的流程,程序中的代码也是为各种可能发生的事件编写的,当程序开始运行之后,它就可以接受来自系统,用户或者其它应用程序触发的事件,然后执行相应的事件代码。事件驱动的工作方式与面向对象技术是紧密相关的。在PowerBuilder应用程序中,接受发生的事件的往往就是程序界面中的各种可视化对象。 PowerBuilder是一种面向对象的开发工具,各种windows应用程序中常见的窗口、菜单、控件等在PowerBuilder中都是一个个的对象。在PowerBuilder中我们还可以创建自己的用户对象。特别要指出的是PowerBuilder提供了对面向对象方法中的各种技术的全面支持,我们可以利用面向对象方法中的对象的封装性、继承性、多态性等特点使得我们开发的应用程序具有极大的可重用性和可扩展性,而这一点正是软件工程中对应用程序所提出的重要目标。 在当前,由于网络技术的发展,许多种不同的操作系统平台在INTERNET网上同时被使用,这对开发的应用程序的跨平台性提出了更高的

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White House jet with first lady Michelle Obama aboard flew closer than permitted to an Air Force cargo plane due to an air-traffic control slip-up Monday afternoon and had to break off its approach to land at Andrews Air Force Base outside Washington, according to people familiar with the details. 据知情人士透露,周一下午,由于空管员的失误,美国第一夫人米歇尔?奥巴马(Michelle Obama)乘坐的白宫飞机与一架空军货机距离过近,小于允许距离,飞机不得不中止在华盛顿外安德鲁斯空军基地(Andrews Air Force Base)的降落。 The incident didn't pose an imminent hazard to the First Lady's plane, these officials said, because the two planes remained roughly two miles apart and Federal Aviation Administration controllers manning the airport tower took action to alleviate it. When it appeared that the C-17 cargo jet landing in front of the White House aircraft wouldn't depart the runway in time to maintain 'the required amount of separation,' according to the FAA, the pilots of the First Lady's Boeing 737 jet broke off the approach, circled the field and landed safely. 这些官员说,事件没有令第一夫人乘坐的飞机濒临危险,因为两架飞机保持着约两英里的距离,机场控制塔中的美国航空管理局(Federal Aviation Administration)空管员采取措施缓解了险情。据美国航空管理局说,当时看起来这架在白宫飞机之前降落的C-17货机无法及时离开跑道,以保持规定的距离,于是第一夫人乘坐的波音737客机的驾驶员中止降落,飞机在机场上空盘旋,之后安全降落。 An FAA statement said the 'aircraft were never in any danger' and the agency was investigating the incident. 美国航空管理局发表声明说,飞机从未遭遇危险,该机构正在对事件进行调查。 Taiwan is almost as technologically capable as the United States, according to a report released by the World Economic Forum and INSEAD on Tuesday in New York. 据世界经济论坛(World Economic Forum)和欧洲工商管理学院(INSEAD)周二在纽约发布的《2010-2011年全球信息技术报告》(2010-2011 Global Information Technology Report)显示,台湾的科技能力几乎可与美国并肩。 Taiwan jumped to the 6th ranked country in the 2010-2011 Global Information Technology Report, up from 11th in the prior year. The report measures economies' 'preparedness' to use technology effectively. Bloomberg News将数据服务器连接起来的光缆台湾在报告中的排名从去年第11位跃升至今年第六位。报告考量的是各经济体有效使用技术的“充分程度”。 Sweden and Singapore continued to dominate the list, followed by Finland, which jumped three places from its ranking last year to become No. 3. Switzerland and United States hold stable at positions four and five respectively. 瑞典和新加坡继续占据第一和第二的位置,而芬兰较去年上升了三位,今年排名第三。瑞士和美国的排名保持不变,分别是第四和第五位。 China, which was at 59th position five years ago and is currently at position 36, has continued to move up. 'It is making progress in areas like adult literacy and infrastructure,' said Soumitra Dutta, a professor at INSEAD and co-author of the report. India, one of the 中国大陆排名持续上升,从五年前的第59位跃至当前的第36位。欧洲工商管理学院(INSEAD)教授、该报告作者之一杜塔(Soumitra Dutta)说,中国大陆在成人读写能力和基础设施建设等方面不断取得进展。亚洲最大经济体之一印度的排名有所下降,位列第48。杜塔说,印度

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BN 氮化硼 BNE 新型环氧树脂 BNS β-萘磺酸甲醛低缩合物 BOA 己二酸辛苄酯 BOP 邻苯二甲酰丁辛酯 BOPP 双轴向聚丙烯 BP 苯甲醇 BPA 双酚A BPBG 邻苯二甲酸丁(乙醇酸乙酯)酯 BPF 双酚F BPMC 2-仲丁基苯基-N-甲基氨基酸酯 BPO 过氧化苯甲酰 BPP 过氧化特戊酸特丁酯 BPPD 过氧化二碳酸二苯氧化酯 BPS 4,4’-硫代双(6-特丁基-3-甲基苯酚) BPTP 聚对苯二甲酸丁二醇酯 BR 丁二烯橡胶 BRN 青红光硫化黑 BROC 二溴(代)甲酚环氧丙基醚 BS 丁二烯-苯乙烯共聚物 BS-1S 新型密封胶 BSH 苯磺酰肼 BSU N,N’-双(三甲基硅烷)脲 BT 聚丁烯-1热塑性塑料 BTA 苯并三唑 BTX 苯-甲苯-二甲苯混合物 BX 渗透剂 BXA 己二酸二丁基二甘酯 BZ 二正丁基二硫代氨基甲酸锌 C 英文缩写全称 CA 醋酸纤维素 CAB 醋酸-丁酸纤维素 CAN 醋酸-硝酸纤维素 CAP 醋酸-丙酸纤维素 CBA 化学发泡剂

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长句翻译中英对照

1、Just as Darwin discovered the law of development of organic nature, so Marx discovered the law of development of human history: the simple fact, hitherto concealed by an overgrowth of ideology, that mankind must first of all eat, drink, have shelter and clothing, before it can pursue polities, science, art, religion, etc.; that therefore the production of the immediate material means of subsistence and consequently the degree of economic development attained by a given people or during a given epoch form the foundation upon which the state institutions, the legal conceptions, art, and even the ideas on religion, of the people concerned have been evolved, and in the light of which they must, therefore, be explained, instead of vice versa, as had hitherto been the case. 正像达尔文发现有机界的规律一样,马克思发现了人类历史的发展规律,即历来被繁茂芜杂的意识形态所掩盖着的一个简单事实:人们首先必须吃、喝、住、穿,然后才能从事政治、科学、艺术、宗教等活动;所以,直接的物质生活资料的生产和一个民族或一个时代的一定的经济发展程度,便构成为基础,人们的国家制度,法律的概念,艺术以至宗教概念,就是从这个基础上发展起来的,因而,也必须由这个基础来解释,而不像过去那样做得正好相反。 2、Behaviorists suggest that the child who is raised in an environment where there are many stimuli which develop his or her capacity for appropriate responses will experience greater intellectual development. 行为主义者认为, 如果儿童的成长环境里有许多刺激因素, 这些因素又有利于其适当反应能力的发展, 那么, 儿童的智力就会发展到较高的水平。 3、How it happened that a little rocky peninsula in a remote corner of the Mediterranean was able to provide our world in less than two centuries with the complete framework for all our present day experiments in politics, literature, drama, sculpture, chemistry, physics and Heaven knows what else, is a question

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