材料力學(xué)復(fù)習(xí),小抄專用

1、材料力學(xué)重點(diǎn)及其公式材料力學(xué)的任務(wù)（1）強(qiáng)度要求；（2）剛度要求；（3）穩(wěn)定性要求。變形固體的基本假設(shè)（1）連續(xù)性假設(shè)；（2）均勻性假設(shè)；（3）各向同性假設(shè)；（4）小變形假設(shè)。外力分類：表面力、體積力；靜載荷、動(dòng)載荷。內(nèi)力：構(gòu)件在外力的作用下，內(nèi)部相互作用力的變化量，即構(gòu)件內(nèi)部各部分之間的因外力作用而引起的附加相互作用力截面法：（1）欲求構(gòu)件某一截面上的內(nèi)力時(shí)，可沿該截面把構(gòu)件切開成兩部分，棄去任一部分，保留另一部分研究（2）在保留部分的截面上加上內(nèi)力，以代替棄去部分對(duì)保留部分的作用。（3）根據(jù)平衡條件，列平衡方程，求解截面上和內(nèi)力。應(yīng)力：正應(yīng)力、切應(yīng)力。變形與應(yīng)變：線應(yīng)變、切應(yīng)變。桿件變形的

2、基本形式（1）拉伸或壓縮；（2）剪切；（3）扭轉(zhuǎn)；（4）彎曲；（5）組合變形。靜載荷：載荷從零開始平緩地增加到最終值，然后不再變化的載荷。動(dòng)載荷：載荷和速度隨時(shí)間急劇變化的載荷為動(dòng)載荷。失效原因：脆性材料在其強(qiáng)度極限破壞，塑性材料在其屈服極限時(shí)失效。二者統(tǒng)稱為極限應(yīng)力理想情形。塑性材料、脆性材料的許用應(yīng)力分別為：，強(qiáng)度條件：，等截面桿軸向拉伸或壓縮時(shí)的變形：桿件在軸向方向的伸長為：，沿軸線方向的應(yīng)變和橫截面上的應(yīng)力分別為：，。橫向應(yīng)變?yōu)椋?，橫向應(yīng)變與軸向應(yīng)變的關(guān)系為：。胡克定律：當(dāng)應(yīng)力低于材料的比例極限時(shí)，應(yīng)力與應(yīng)變成正比，即，這就是胡克定律。e為彈性模量。將應(yīng)力與應(yīng)變的表達(dá)式帶入得：靜不定：

3、對(duì)于桿件的軸力，當(dāng)未知力數(shù)目多于平衡方程的數(shù)目，僅利用靜力平衡方程無法解出全部未知力。圓軸扭轉(zhuǎn)時(shí)的應(yīng)力變形幾何關(guān)系圓軸扭轉(zhuǎn)的平面假設(shè)。物理關(guān)系胡克定律。力學(xué)關(guān)系圓軸扭轉(zhuǎn)時(shí)的應(yīng)力：；圓軸扭轉(zhuǎn)的強(qiáng)度條件：，可以進(jìn)行強(qiáng)度校核、截面設(shè)計(jì)和確定許可載荷。圓軸扭轉(zhuǎn)時(shí)的變形：；等直桿：圓軸扭轉(zhuǎn)時(shí)的剛度條件：，彎曲內(nèi)力與分布載荷q之間的微分關(guān)系；q、m圖與外力間的關(guān)系a）梁在某一段內(nèi)無載荷作用，剪力圖為一水平直線，彎矩圖為一斜直線。b）梁在某一段內(nèi)作用均勻載荷，剪力圖為一斜直線，彎矩圖為一拋物線。c）在梁的某一截面。，剪力等于零，彎矩有一最大值或最小值。d）由集中力作用截面的左側(cè)和右側(cè)，剪力q有一突然變化，彎

4、矩圖的斜率也發(fā)生突然變化形成一個(gè)轉(zhuǎn)折點(diǎn)。梁的正應(yīng)力和剪應(yīng)力強(qiáng)度條件，提高彎曲強(qiáng)度的措施：梁的合理受力(降低最大彎矩，合理放置支座，合理布置載荷，合理設(shè)計(jì)截面形狀塑性材料：，上、下對(duì)稱，抗彎更好，抗扭差。脆性材料：，采用t字型或上下不對(duì)稱的工字型截面。等強(qiáng)度梁：截面沿桿長變化，恰使每個(gè)截面上的正應(yīng)力都等于許用應(yīng)力，這樣的變截面梁稱為等強(qiáng)度梁。用疊加法求彎曲變形：當(dāng)梁上有幾個(gè)載荷共同作用時(shí)，可以分別計(jì)算梁在每個(gè)載荷單獨(dú)作用時(shí)的變形，然后進(jìn)行疊加，即可求得梁在幾個(gè)載荷共同作用時(shí)的總變形。簡單超靜定梁求解步驟：（1）判斷靜不定度；（2）建立基本系統(tǒng)（解除靜不定結(jié)構(gòu)的內(nèi)部和外部多余約束后所得到的靜定結(jié)構(gòu)

5、）；（3）建立相當(dāng)系統(tǒng)（作用有原靜不定梁載荷與多余約束反力的基本系統(tǒng)）；（4）求解靜不定問題。二向應(yīng)力狀態(tài)分析解析法（1）任意斜截面上的應(yīng)力；（2）極值應(yīng)力正應(yīng)力：，切應(yīng)力：，（3）主應(yīng)力所在的平面與剪應(yīng)力極值所在的平面之間的關(guān)系與之間的關(guān)系為：，即：最大和最小剪應(yīng)力所在的平面與主平面的夾角為45扭轉(zhuǎn)與彎曲的組合（1）外力向桿件截面形心簡化（2）畫內(nèi)力圖確定危險(xiǎn)截面（3）確定危險(xiǎn)點(diǎn)并建立強(qiáng)度條件按第三強(qiáng)度理論，強(qiáng)度條件為：或，對(duì)于圓軸，其強(qiáng)度條件為：。按第四強(qiáng)度理論，強(qiáng)度條件為：，經(jīng)化簡得出：，對(duì)于圓軸，其強(qiáng)度條件為：。歐拉公式適用范圍（1）大柔度壓桿（歐拉公式）：即當(dāng)，其中時(shí)，（2）中等柔度

6、壓桿（經(jīng)驗(yàn)公式）：即當(dāng)，其中時(shí)，（3）小柔度壓桿（強(qiáng)度計(jì)算公式）：即當(dāng)時(shí)，。壓桿的穩(wěn)定校核（1）壓桿的許用壓力：，為許可壓力，為工作安全系數(shù)。（2）壓桿的穩(wěn)定條件：提高壓桿穩(wěn)定性的措施：選擇合理的截面形狀，改變壓桿的約束條件，合理選擇材料外力偶矩計(jì)算公式（p功率，n轉(zhuǎn)速）彎矩、剪力和荷載集度之間的關(guān)系式軸向拉壓桿橫截面上正應(yīng)力的計(jì)算公式（桿件橫截面軸力fn，橫截面面積a，拉應(yīng)力為正）軸向拉壓桿斜截面上的正應(yīng)力與切應(yīng)力計(jì)算公式（夾角a 從x軸正方向逆時(shí)針轉(zhuǎn)至外法線的方位角為正）縱向變形和橫向變形（拉伸前試樣標(biāo)距l(xiāng)，拉伸后試樣標(biāo)距l(xiāng)1；拉伸前試樣直徑d，拉伸后試樣直徑d1）縱向線應(yīng)變和橫向線應(yīng)變泊

7、松比胡克定律受多個(gè)力作用的桿件縱向變形計(jì)算公式承受軸向分布力或變截面的桿件，縱向變形計(jì)算公式軸向拉壓桿的強(qiáng)度計(jì)算公式許用應(yīng)力，脆性材料，塑性材料延伸率截面收縮率剪切胡克定律（切變模量g，切應(yīng)變g ）拉壓彈性模量e、泊松比和切變模量g之間關(guān)系式圓截面對(duì)圓心的極慣性矩（a）實(shí)心圓（b）空心圓圓軸扭轉(zhuǎn)時(shí)橫截面上任一點(diǎn)切應(yīng)力計(jì)算公式（扭矩t，所求點(diǎn)到圓心距離r）圓截面周邊各點(diǎn)處最大切應(yīng)力計(jì)算公式扭轉(zhuǎn)截面系數(shù)，（a）實(shí)心圓（b）空心圓薄壁圓管（壁厚 r0 /10 ，r0為圓管的平均半徑）扭轉(zhuǎn)切應(yīng)力計(jì)算公式圓軸扭轉(zhuǎn)角與扭矩t、桿長l、扭轉(zhuǎn)剛度ghp的關(guān)系式同一材料制成的圓軸各段內(nèi)的扭矩不同或各段的直徑不同

8、（如階梯軸）時(shí)或等直圓軸強(qiáng)度條件塑性材料；脆性材料扭轉(zhuǎn)圓軸的剛度條件或受內(nèi)壓圓筒形薄壁容器橫截面和縱截面上的應(yīng)力計(jì)算公式, 平面應(yīng)力狀態(tài)下斜截面應(yīng)力的一般公式 ,平面應(yīng)力狀態(tài)的三個(gè)主應(yīng)力, , 主平面方位的計(jì)算公式面內(nèi)最大切應(yīng)力受扭圓軸表面某點(diǎn)的三個(gè)主應(yīng)力，三向應(yīng)力狀態(tài)最大與最小正應(yīng)力 , 三向應(yīng)力狀態(tài)最大切應(yīng)力廣義胡克定律四種強(qiáng)度理論的相當(dāng)應(yīng)力一種常見的應(yīng)力狀態(tài)的強(qiáng)度條件，組合圖形的形心坐標(biāo)計(jì)算公式，任意截面圖形對(duì)一點(diǎn)的極慣性矩與以該點(diǎn)為原點(diǎn)的任意兩正交坐標(biāo)軸的慣性矩之和的關(guān)系式截面圖形對(duì)軸z和軸y的慣性半徑, 平行移軸公式（形心軸zc與平行軸z1的距離為a，圖形面積為a）純彎曲梁的正應(yīng)力計(jì)

9、算公式橫力彎曲最大正應(yīng)力計(jì)算公式矩形、圓形、空心圓形的彎曲截面系數(shù)，幾種常見截面的最大彎曲切應(yīng)力計(jì)算公式（為中性軸一側(cè)的橫截面對(duì)中性軸z的靜矩，b為橫截面在中性軸處的寬度）矩形截面梁最大彎曲切應(yīng)力發(fā)生在中性軸處工字形截面梁腹板上的彎曲切應(yīng)力近似公式軋制工字鋼梁最大彎曲切應(yīng)力計(jì)算公式圓形截面梁最大彎曲切應(yīng)力發(fā)生在中性軸處圓環(huán)形薄壁截面梁最大彎曲切應(yīng)力發(fā)生在中性軸處彎曲正應(yīng)力強(qiáng)度條件幾種常見截面梁的彎曲切應(yīng)力強(qiáng)度條件彎曲梁危險(xiǎn)點(diǎn)上既有正應(yīng)力又有切應(yīng)力作用時(shí)的強(qiáng)度條件或，梁的撓曲線近似微分方程梁的轉(zhuǎn)角方程梁的撓曲線方程軸向荷載與橫向均布荷載聯(lián)合作用時(shí)桿件截面底部邊緣和頂部邊緣處的正應(yīng)力計(jì)算公式偏心拉

10、伸（壓縮）彎扭組合變形時(shí)圓截面桿按第三和第四強(qiáng)度理論建立的強(qiáng)度條件表達(dá)式，圓截面桿橫截面上有兩個(gè)彎矩和同時(shí)作用時(shí)，合成彎矩為圓截面桿橫截面上有兩個(gè)彎矩和同時(shí)作用時(shí)強(qiáng)度計(jì)算公式彎拉扭或彎壓扭組合作用時(shí)強(qiáng)度計(jì)算公式剪切實(shí)用計(jì)算的強(qiáng)度條件擠壓實(shí)用計(jì)算的強(qiáng)度條件等截面細(xì)長壓桿在四種桿端約束情況下的臨界力計(jì)算公式壓桿的約束條件：（a）兩端鉸支=l（b）一端固定、一端自由=2（c）一端固定、一端鉸支=0.7（d）兩端固定=0.5 壓桿的長細(xì)比或柔度計(jì)算公式，細(xì)長壓桿臨界應(yīng)力的歐拉公式歐拉公式的適用范圍壓桿穩(wěn)定性計(jì)算的安全系數(shù)法壓桿穩(wěn)定性計(jì)算的折減系數(shù)法關(guān)系需查表求得winger tuivasa-sheck

11、, who scored two tries in the kiwis 20-18 semi-final win over england, has been passed fit after a lower-leg injury, while slater has been named at full-back but is still recovering from a knee injury aggravated against usa.both sides boast 100% records heading into the encounter but australia have

12、not conceded a try since josh charnleys effort in their first pool match against england on the opening day.aussie winger jarryd hayne is the competitions top try scorer with nine, closely followed by tuivasa-sheck with eight.but it is recently named rugby league international federation player of t

13、he year sonny bill williams who has attracted the most interest in the tournament so far.the kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the world cup in both rugby league and rugby union after triumphing with the all blacks in 2011.id give every aw

14、ard back in a heartbeat just to get across the line this weekend, said williams.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match a

15、t chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of th

16、eir fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults fro

17、m fans of cska. baumgartner the disappointing news: mission aborted.the supersonic descent could happen as early as sunda.the weather plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limite

18、d cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial a

19、irliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an ol

20、ympic diving platform.they blew it in 2008 when they got caught cold in the final and they will not make the same mistake against the kiwis in manchester.five years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored by englands j

21、osh charnley in the opening game of the tournament.that could be classed as a weakness, a team under-cooked - but i have been impressed by the kangaroos focus in their games since then.they have been concentrating on the sort of stuff that wins you tough, even contests - strong defence, especially on their own goal-line, completing sets and a good kick-