材料力学英文翻译作业

《材料力学》英文阅读作业

英文原文：

CHAPTER OBJECTIVES

Beams and shafts are important structural and mechanical elements in engineering.

In this chapter we will determine the stress in these members caused by bending.

The chapter begins with a discussion of how to establish the shear and moment Diagrams for a beam or shaft. Like the normal-force and torque diagrams, the shear and moment diagrams provide a useful means for determining the largest shear and moment in a member , and they specify where these maximums occur . Once the internal moment at a section is determined , the bending stress can then be calculated . First we will consider members that are straight , have a symmetric cross section , and are made of homogeneous linear-elastic material . Afterward we will discuss special cases involving unsymmetric bending and members made of composite materials . Consideration will also be given to curved members , stress concentrations , inelastic bending ,and residual stresses.

IMPORTANT POINTS

●Beam are long straight members that carry loads perpendicular to their

longitudinal axis . They are classified according to the way they are supported ,

e.g. , simply supported , cantilevered , or overhanging.

●In order to properly design a beam , it is important to know the variation of the

shear and moment along its axis in order to find the points where these values are

a maximum.

●By establishing a sign convention for positive shear and moment , the shear and

moment in the beam can be determined as a function of its position x and these values plotted to form the shear and moment diagrams.

PROCEDURE FOR ANALYSIS

The shear and moment diagrams for a beam can be constructed using the following procedure.

Support Reactions.

●Determine all the reactive forces and couple moments acting on the beam , and

resolve all the forces into components acting perpendicular and parallel to the beam’s axis.

Shear and Moment Functions.

●Specify separate coordinates x having an origin at the beam’s left end and

extending to regions of the beam between concentrated forces and/or couple moment, or where there is no discontinuity of distributed loading.

●Section the beam perpendicular to its axis at each distance x, and draw the

free-body diagram of one of the segments. Be sure V and M are shown acting in their positive sense , in accordance with the sign convention given in Fig. 6-3.

●The shear is obtained by summing forces perpendicular to the beam’s axis.

●The moment is obtained by summing moments about the sectioned end of the

segment.

Shear and Moment Diagrams

●Plot the shear diagram ( V versus x ) and the moment diagram ( M versus x). If

numerical values of the functions describing V and M are positive , the values are plotted above the x axis , whereas negative values are plotted below the axis.

●Generally it is convenient to show the shear and moment diagrams directly below

the free-body diagram of the beam.

中文翻译：

学习目标

梁、轴在工程中是重要的结构和机械元素。在这一章,我们将计算这些结构中的弯曲应力。

这一章开始讨论如何建立梁或轴的剪力和弯矩图。像正应力和转矩图、剪力和弯矩图提供一种有效的手段计算构件中的最大剪力和弯矩,他们指明这些最大值出现的位置。一旦在一个截面上内力矩是确定的,就可以算出弯曲应力。首先我们将认为构件是直的、有对称的截面,并且是用均匀线弹性材料制成的。之后我们将讨论特殊情况：非对称弯曲和由复合材料制成的构件。还将考虑弯曲的构件,应力集中、无弹性弯曲和残余应力。

要点

●梁是承担纵轴垂直荷载的构件。他们按他们的受力方式分类,例如,支持,或简单支撑,悬

臂外伸。

为了合理地设计梁，了解剪力和弯矩沿轴方向的变化规律对于找到他们最大值的位置是十分重要的。

●通过对正剪力和弯矩建立符号约定，梁中的剪力和弯矩作为其位置的函数X可以计算

出来，这些值构成了建立和弯矩图。

分析过程