材料力学公式.pdf

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1、一、应力与强度条件1、拉压 maxmaxAN 2、剪切 AQmax 挤压 挤压挤压挤压AP 3、圆轴扭转 WtTmax 4、平面弯曲 maxzmaxWM maxtmaxtmaxmaxyIMzt maxcmaxmaxyIMzccnax bISQz*max zmaxmax斜弯曲 maxyyzzmaxWMWM 6、拉（压）弯组合 maxmaxzWMAN tmaxtzmaxtyIMANz cmaxczzmaxcANyIM 注意：“5”与“6”两式仅供参考 7、圆轴弯扭组合：第三强度理论 z2n2w2n2wr34WMM 第四强度理论 z2n2w2n2wr475.03WMM 二、变形及刚度条件、拉压 LE

2、AxxNEALNEANLLd)(ii、扭转 ppiipGIdxxTGILTGITL0180pGITL（m/）、弯曲(1)积分法:)()(xMxEIyCxxMxEIxEIyd)()()(DCxxxxMxEIy d d)()(2)叠加法:21,PPf=21PfPf+，21,PP=21PP(3)基本变形表(注意：以下各公式均指绝对值，使用时要根据具体情况赋予正负号)EIMLBEIPLB22EIqLB63 EIMLfB22EIPLfB33EIqLfB84 EIMLB3,EIMLA6EIPLAB162EIqLAB243 EIMLfc162EIPLfc483EIqLfc3844(4)弹性变形能(注：以下只

3、给出弯曲构件的变形能,并忽略剪力影响,其他变形与此相似,不予写出)EILMU22=iiiEILM22=EIdxxM22(5)卡氏第二定理(注：只给出线性弹性弯曲梁的公式)iiPU dxPxMEIxMi 三、应力状态与强度理论、二向应力状态斜截面应力 2sin2cos22xyyxyx2cos2sin2xyyx、二向应力状态极值正应力及所在截面方位角 22minmax)2(2xyyxyxyxxy22tg0、二向应力状态的极值剪应力 22max)2(xyyx 注：极值正应力所在截面与极值剪应力所在截面夹角为 45、三向应力状态的主应力：321 最大剪应力：231max 5、二向应力状态的广义胡克定律

4、 PABMABABqLLL PMABqLAB2/L2/LABLCCC（1）、表达形式之一（用应力表示应变）)(1yxxE)(1xyyE)(yxzEGxyxy（2）、表达形式之二（用应变表示应力）)(12yxxE)(12xyyE0zxyxyG 6、三向应力状态的广义胡克定律 zyxxE1zyx,Gxyxyzxyzxy,7、强度理论（1）111r3212r bbn（2）313r213232221421r ssn 8、平面应力状态下的应变分析（1）2sin22cos22xyyxyx2sin22yx2cos2xy（2）22minmax222xyyxyxyxxy02tg 四、压杆稳定 1、临界压力与临界

5、应力公式（若把直杆分为三类）细长受压杆 p 2min2crLEIP22crE 中长受压杆 spbacr 短粗受压杆 s“”=或 2、关于柔度的几个公式iLp2pEbass 3、惯性半径公式AIiz（圆截面4diz，矩形截面12minbi（b 为短边长度）五、动载荷（只给出冲击问题的有关公式）能量方程 UVT 冲击系数 std211hK（自由落体冲击）st20dgvK（水平冲击）六、截面几何性质 1、惯性矩（以下只给出公式，不注明截面的形状）dAIP2=324d44132DDd 6442ddAyIz44164D123bh123hb 323maxdyIWzz43132D62bh62hb 2、惯性矩

6、平移轴公式 AaII2zcz 图画作文模板 1现象型现象现象 现象意义 现象观点 2观点型观点观点 审题目看图选择模板打第一段草稿 描述图画 阐述意义 现象趋势 建议措施 原因分析 举例说明 有些词汇要有变化，比如少用 picture 而用 drawing 观点型 Indicated above is a vivid cartoon/caricature/graph/bar chart/photo that depicts _.Obviously,_.But this is the key message conveyed by the drawing.The most striking fe

7、ature of drawing is that _is marked as both 名词 and 名词,which indicates that _.The sense of _,Gods greatest gift to mankind,is universally considered the most valuable personality a man can possess.Everybody not only do sth,but also should _.Numerous cases exist to illustrate how important_is.When_,sb

8、 will_.Or when _,sb will_.By doing so,sb have done sth which is like_.现象型 Indicated above is a vivid cartoon/caricature/graph/bar chart/photo that_.In the picture presented to us,_;on the contrary/unexpectedly/ironically/as a comparison,_.Consequently/Accordingly,_.Obviously,（好的现象）this is no flash i

9、n the pan/(坏的现象)this is a mirror of that society.In that mirror,we can see that,over the past couple of years,certain common and disturbing/alarming/exciting changes/phenomena have taken placed in the society and created serious concerns over the role of sth.Simple as the drawing is,the author tends

10、 to convey a more profound meaning that has to be taken seriously.事物 1 in the picture naturally reminds people of _,while 事物 2 is usually associated with _.Thanks to/Due to 原因 1 and 原因 2,图画结果.Should this situation go unleashed/continues,as a famous professor says,趋势一 By the time,趋势二(1)It is imperati

11、ve for us to take positive measures to put it on hold.For one thing,措施一;for another,措施二；still,措施三.Only in this way can we have a brigter future.(2)On the basis of analysis,we can confidently predict that great changes have taken place.This tendency,will be going on in a exiting direction.(3)On the b

12、asis of analysis,we can confidently conclude that _have posed tremendous threat to our life.This tendency will be going on in a disturbing direction.(4)Therefor,it is high time that we took broad actions to put it on hold.As an old saying goes,”Dont fix your roof on a rainy day.”图画作文 1.描述+深入理解+结语 As

13、 vividly revealed in the drawing above,（描述）。Under the picture,there is a thought-provoking sentence:(原话翻译)It is quite obvious that the drawer wishes to draw our attention to the importance of_.s more,_.All the available analysis confirms a sound idea that we should_.Only in this way,can we_.(62)2.描述

14、+原因+办法 As vividly revealed in the drawing above,（描述）。Under the picture,there is a thought-provoking sentence:(原话翻译)It is quite obvious that the drawer wishes to draw our attention to this most unfavorable phenomenon:(名词或句子)。There are numerous reasons why this happened,and I would like to o explore o

15、nly a few of the most important ones here.First of all,(原因一)。In addition,(原因二)。Last but not least,(原因三).If we dont take any effectivemeasures，this phenomenon will get out of our control,and some undesirable result may come out unexpectedly.Therefore,what we should do falls into the following aspects

16、:first,(Aspect 1).Second,(Aspect 2).Third,(Aspect 3).Only in this way,can we.(149)3.描述+现象+办法 As vividly revealed in the drawing above,（描述）。Under the picture,there is a thought-provoking sentence:(原话翻译).It is quite obvious that the drawer wishes to draw our attention to this most unfavorable phenomen

17、on:(名词或句子)。First,(现象一)。In addition,(现象二)。Last but not least,(现象三).If we dont take any effectivemeasures，this phenomenon will get out of our control,and some undesirable result may come out unexpectedly.Therefore,what we should do falls into the following aspects:first,(Aspect 1).Second,(Aspect 2).Th

18、ird,(Aspect 3).Only in this way,can we.(124)4.描述+利弊+结论 As vividly revealed in the drawing above,（描述）。Under the picture,there is a thought-provoking sentence:(原话翻译).It is quite obvious that the drawer wishes to draw our attention to this phenomenon:(名词或句子)。Along with the development of_,more and more

19、_.There is no consensus of opinions among people as to_.Some people claim that_ has been playing an increasingly important role in our daily life and brought us a lot of benefits,but it has created some serious problems as well.They base their argument on the following three reasons:first,_.Second,_

20、.Third,_.On the contrary,some other people argue that(观点 2)for the following reasons.First,_.Second,_.Third,_.As far as I am concerned，I agree with the latter opinion to some extent.As a coin has two sides and _ is not an exception，it has both advantages and disadvantages.All in all,We cannot live w

21、ithout_,but at the same time we must try to find out new ways to cope with the problems that would arise.(195)5.描述+后果+办法 As vividly revealed in the drawing above,（描述）。Under the picture,there is a thought-provoking sentence:(原话翻译)It is quite obvious that the drawer wishes to draw our attention to thi

22、s most unfavorable phenomenon:(名词或句子)。It might cause a lot of serious problems and I would like to explore only a few of the most serious ones here.First,(原因一)。In addition,(原因二)。Last but not least,(原因三).If we dont take any effectivemeasures，this phenomenon will get out of our control,and some undesi

23、rable result may come out unexpectedly.Therefore,what we should do falls into the following aspects:first,(Aspect 1).Second,(Aspect 2).Third,(Aspect 3).Only in this way,can we.(147)6.描述+原因+后果+办法 As vividly revealed in the drawing above,（描述）。Under the picture,there is a thought-provoking sentence:(原话

24、翻译)It is quite obvious that the drawer wishes to draw our attention to this most unfavorable phenomenon:(名词或句子)。There are numerous reasons why this happened,and I would like to explore only a few of the most important ones here.For one thing,(原因一)。For another,(原因二)。Last but not least,(原因三).If we don

25、t take any effectivemeasures，this phenomenon will get out of our control,and some undesirable problems may come out unexpectedly.First,(原因一)。In addition,(原因二)。Finally,(原因三).From the analysis above,we can see how serious the problem will be if we let it go.Therefore,some effective measure must be tak

26、en urgently to prevent the problems.First,(Aspect 1).Second,(Aspect 2).Third,(Aspect 3).Only in this way,can we.(188)墨文博模板 写 实 P1 龙眼 As is vividly(illustrated/depicted/conveyed/revealed/betrayed)in the picture,(图的内容1 the two pet neighbors greet each other politely and amicably,whereas(while/on the o

27、ther hand)the two pets owners seem to ignore between(each other)aloofly).Simple as it is,the drawing sets us pondering a awfully.Accordingly,much inspiration can be drawn from what this far-reaching/thought-provoking picture witness:(图反映的现实2 pets,rather than/instead of people around them,are such an

28、 indispensable part in their daily lifeto the point wherethey are excessively/inordinately fond of their beloved animals while neglecting those who care them,which has aroused great concern and should be given enough consideration).It speaks volumes for the concept that(TS3 indifference should be ru

29、led out,with harmonious society echoed vigorously nowadays in china.)1 批判：先扬后抑 歌颂：先抑后扬 图的内容 原则上用一个主从句表达,功底。两句合一句的途经：1、AND 连结；2、WHICH 或 WHEREAS 连结；3、非谓语 2to the point where加以讲解 excessively/inordinately 负面词汇,作者的态度尽在不言中,回避使用 I believe,I think 之类的句式 3 TS+Background 0204:China is entry into WTO 05:Harmon

30、ious society 06:The honor and disgrace values 0711:Scientific development values-Human life and ecology system TS 的语言组织 Weigh A against B-在 A 和 B 之间权衡利弊（against:在的背景下）Where 定从：1具体 2抽象 to the point where以至于 独主 with+S+V-ing/V-ed(主谓、动宾)1 Nothing+be+adj+than+to+do 2 On no account can we 3 It is time+S+V

31、-ed 4 It 无主句 5ought to be weighed/taken/pondered/seriously 4 注意使用关联词，突出 TS P2 Why do we lay emphasis on this?Several points()analyzed below might equip us with theprofound message of what we are heading for.To begin with,since we have to live on an on-the-move lifestyle,we are denied chances to shar

32、e our feelings with our friends and relatives.In addition,with so many dishonesties running around our society,the indifference happened in turn we have no choice but to enjoy the company of pets.And above all,too many tragedies as to the indifference-seeing someone in mortal danger without lifting

33、a finger to save him-put on the stage of our daily life,which is threatening situation we are unwilling to face(此句仅用于负面评价).No better illustration of this view touched on above can be taken than the case as listed below:(1 a crowd of people remained appallinglynonchalance to the plea of a mother,sinc

34、e she failed to offer the required amount of cash as a price to save her drowning son,the woman at last watched her son sink to death.)2 At the end of the day,no issue in china stands as critical to build up the society in harmony as ironing out of indifference among people.1 例证，举例：1实例 2引语 eg：1 As t

35、he famous saying goes:2 As many famous ecologists put it:3数据 eg：According to the latest survey conducted by concerning department,论点的具体体现：RP 原则 2 小结 1 与 TS 首尾呼应,重复原则 2 为第三段起势 3Benard Show-No issue stands as critical to A as B.在没有比 B 对 A 更关键的了 P3 Judging from what has been argued above,we have come t

36、o recognize that the harms arising from indifference has been,like Pandoras box,the crippling force of establishing the harmony society.It is,therefore,inperative that some effective steps should be taken to(1 点主题 重复原则narrow and bridge the gap among people.)On one hand,(2 依法治国 the government should

37、make law to set up the society in which people live in harmony.)On the other hand,(3 依德治国 people should enhance the awareness of caring each other especially when they were young.)Only by undergoing these measures,can we make our society,where people,even not knowing each other,help among them,appea

38、l to everyone.2010年作文理论篇 2010年图文题 A写实派 主讲内容 约 3H As is illustrated/depicted/conveyed/revealed/betrayed/shown in the picture,(图的内容 原则上用一个主从句表达,功底.两句合一句的途经,1 AND连结 2 WHICH 或 WHEREAS 连结 3 非谓语)the two pet neighbors greet each other politely and amicably,whereas(=WHILE/ON THE OTHER HAND)the two pets owne

39、rs seem to ignore each other.Simple as it is,the drawing sets us thinking too much.(凑字数,其富余时,可省去)Accordingly,what this far-reaching/thought-provoking picture depicts is a common phenomenon in todays society,(反映的现实)pets,rather than/instead of people around them,are such an indispensable part in their

40、 daily life to the point where(加以讲解)they are excessively/inordinately(负面词汇,作者的态度尽在不言中,回避使用 I BELIVE,I THINK 之类的句式)fond of their beloved animals while neglecting those who care them,whichhas aroused great concern and should be givenenough consideration.There is no doubt that its symbolic meaning that

41、(主题句,尽量避免使用 1 主系表 2 THERE BE 结构 主张使用下列句型,1 NOTHING+BE+ADJ+THAN+TO+DO 2 ON NO ACCOUNT CAN WE 3 IT IS TIME+S+V-ED 4 IT 无主句)it is imperative to clear up indifference among people against nowadays of vigorously championing cordial society ought to be weighed/taken/pondered seriously.Why do we lay emphas

42、is on this(指代词表过渡)several points(名词复数,总分总的标志)analyzed below might equip us with the deeper understanding of what we are heading for.For one thing,(分述标志词)since we have to live on an on-the-move lifestyle,we are denied chances to share our feelings with our friends and relatives.For another(分述标志词),wit

43、h so many dishonesties going around in our life and then indifference occurring,we might have no choice but to enjoy the company of pets.And above all(分述标志词),too many tragedies-seeing someone in mortal danger without lifting a finger to save him-put on the stage in our daily life almost everyday,whi

44、ch is threatening situation we are unwilling to face(此句仅用于负面评价).No better illustration of this idea can bethought than the case as listed below,(例证)a crowd of people remained appallingly nonchalance(=indifference,论据是论点的具体体现,主题核心词汇重复)to the plea of a mother,since she failed to offer the required amou

45、nt of cash as a price to save her drowning son,the woman at last watched her son sink to death.Consequently/Accordingly/On balance/Therefore/It follows that,no issue in china is as basic to build up the society in harmony as growing out of indifference among people.(此句为小节,1 与 TS 首尾呼应,重复原则 grow out o

46、f=clear up 2 为第三段起势)Judging from what have been argued above,people have come to realize the harms of indifference has been the crippling force of establishing the harmony society.It is,therefore,necessary that some effective steps be made to(点主题 重复原则)narrow and bridge the gap among people.To begin

47、with,(以法治国)the government should make law to establish the society in which people live in harmony.In addition,(以德治国)people should enhance the awareness of caring each other especially when they were young.Only by undergoing these measures,can we make our society,where the old can be maintained,the

48、young brought up and people,even not knowing each other,help among them,appeal to everyone 附:As is illustrated in the picture,a student is surfing on the net bar who,even after midnight,is still playing cyber games,while the textbooks scatter on the desk.Simple as it is,the picture really sets us th

49、inking.Accordingly,the fact that students being on the rise spent their spare time playing computer games such as CS has aroused great concern and should be given enough consideration.There is no doubt that its symbolic meaning that it is imperative to prevent them from indulging in CG ought to be t

50、aken seriously.To account for the above-mentioned case,several effects arisen from CG should be put forward.To begin with,taking to CG too much impair players health especially eyes,just like being betrayed in the picture.In addition,students on line often pretend to be what they want to be and chea