材料力学复习,小抄专用

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1、专业好文档材料力学重点及其公式材料力学的任务（1）强度要求；（2）刚度要求；（3）稳定性要求。变形固体的基本假设（1）连续性假设；（2）均匀性假设；（3）各向同性假设；（4）小变形假设。外力分类：表面力、体积力；静载荷、动载荷。内力：构件在外力的作用下，内部相互作用力的变化量，即构件内部各部分之间的因外力作用而引起的附加相互作用力截面法：（1）欲求构件某一截面上的内力时，可沿该截面把构件切开成两部分，弃去任一部分，保留另一部分研究（2）在保留部分的截面上加上内力，以代替弃去部分对保留部分的作用。（3）根据平衡条件，列平衡方程，求解截面上和内力。应力：正应力、切应力。变形与应变：线应变、切应变。

2、杆件变形的基本形式（1）拉伸或压缩；（2）剪切；（3）扭转；（4）弯曲；（5）组合变形。静载荷：载荷从零开始平缓地增加到最终值，然后不再变化的载荷。动载荷：载荷和速度随时间急剧变化的载荷为动载荷。失效原因：脆性材料在其强度极限破坏，塑性材料在其屈服极限时失效。二者统称为极限应力理想情形。塑性材料、脆性材料的许用应力分别为：，强度条件：，等截面杆轴向拉伸或压缩时的变形：杆件在轴向方向的伸长为：，沿轴线方向的应变和横截面上的应力分别为：，。横向应变为：，横向应变与轴向应变的关系为：。胡克定律：当应力低于材料的比例极限时，应力与应变成正比，即，这就是胡克定律。E为弹性模量。将应力与应变的表达式带入得

3、：静不定：对于杆件的轴力，当未知力数目多于平衡方程的数目，仅利用静力平衡方程无法解出全部未知力。圆轴扭转时的应力变形几何关系圆轴扭转的平面假设。物理关系胡克定律。力学关系圆轴扭转时的应力：；圆轴扭转的强度条件：，可以进行强度校核、截面设计和确定许可载荷。圆轴扭转时的变形：；等直杆：圆轴扭转时的刚度条件：，弯曲内力与分布载荷q之间的微分关系；Q、M图与外力间的关系a）梁在某一段内无载荷作用，剪力图为一水平直线，弯矩图为一斜直线。b）梁在某一段内作用均匀载荷，剪力图为一斜直线，弯矩图为一抛物线。c）在梁的某一截面。，剪力等于零，弯矩有一最大值或最小值。d）由集中力作用截面的左侧和右侧，剪力Q有一突

4、然变化，弯矩图的斜率也发生突然变化形成一个转折点。梁的正应力和剪应力强度条件，提高弯曲强度的措施：梁的合理受力(降低最大弯矩，合理放置支座，合理布置载荷，合理设计截面形状塑性材料：，上、下对称，抗弯更好，抗扭差。脆性材料：，采用T字型或上下不对称的工字型截面。等强度梁：截面沿杆长变化，恰使每个截面上的正应力都等于许用应力，这样的变截面梁称为等强度梁。用叠加法求弯曲变形：当梁上有几个载荷共同作用时，可以分别计算梁在每个载荷单独作用时的变形，然后进行叠加，即可求得梁在几个载荷共同作用时的总变形。简单超静定梁求解步骤：（1）判断静不定度；（2）建立基本系统（解除静不定结构的内部和外部多余约束后所得到

5、的静定结构）；（3）建立相当系统（作用有原静不定梁载荷与多余约束反力的基本系统）；（4）求解静不定问题。二向应力状态分析解析法（1）任意斜截面上的应力；（2）极值应力正应力：，切应力：，（3）主应力所在的平面与剪应力极值所在的平面之间的关系与之间的关系为：，即：最大和最小剪应力所在的平面与主平面的夹角为45扭转与弯曲的组合（1）外力向杆件截面形心简化（2）画内力图确定危险截面（3）确定危险点并建立强度条件按第三强度理论，强度条件为：或，对于圆轴，其强度条件为：。按第四强度理论，强度条件为：，经化简得出：，对于圆轴，其强度条件为：。欧拉公式适用范围（1）大柔度压杆（欧拉公式）：即当，其中时，（2

6、）中等柔度压杆（经验公式）：即当，其中时，（3）小柔度压杆（强度计算公式）：即当时，。压杆的稳定校核（1）压杆的许用压力：，为许可压力，为工作安全系数。（2）压杆的稳定条件：提高压杆稳定性的措施：选择合理的截面形状，改变压杆的约束条件，合理选择材料外力偶矩计算公式（P功率，n转速）弯矩、剪力和荷载集度之间的关系式轴向拉压杆横截面上正应力的计算公式（杆件横截面轴力FN，横截面面积A，拉应力为正）轴向拉压杆斜截面上的正应力与切应力计算公式（夹角a 从x轴正方向逆时针转至外法线的方位角为正）纵向变形和横向变形（拉伸前试样标距l，拉伸后试样标距l1；拉伸前试样直径d，拉伸后试样直径d1）纵向线应变和横

7、向线应变泊松比胡克定律受多个力作用的杆件纵向变形计算公式承受轴向分布力或变截面的杆件，纵向变形计算公式轴向拉压杆的强度计算公式许用应力，脆性材料，塑性材料延伸率截面收缩率剪切胡克定律（切变模量G，切应变g ）拉压弹性模量E、泊松比和切变模量G之间关系式圆截面对圆心的极惯性矩（a）实心圆（b）空心圆圆轴扭转时横截面上任一点切应力计算公式（扭矩T，所求点到圆心距离r）圆截面周边各点处最大切应力计算公式扭转截面系数，（a）实心圆（b）空心圆薄壁圆管（壁厚 R0 /10 ，R0为圆管的平均半径）扭转切应力计算公式圆轴扭转角与扭矩T、杆长l、扭转刚度GHp的关系式同一材料制成的圆轴各段内的扭矩不同或各段

8、的直径不同（如阶梯轴）时或等直圆轴强度条件塑性材料；脆性材料扭转圆轴的刚度条件或受内压圆筒形薄壁容器横截面和纵截面上的应力计算公式, 平面应力状态下斜截面应力的一般公式 ,平面应力状态的三个主应力, , 主平面方位的计算公式面内最大切应力受扭圆轴表面某点的三个主应力，三向应力状态最大与最小正应力 , 三向应力状态最大切应力广义胡克定律四种强度理论的相当应力一种常见的应力状态的强度条件，组合图形的形心坐标计算公式，任意截面图形对一点的极惯性矩与以该点为原点的任意两正交坐标轴的惯性矩之和的关系式截面图形对轴z和轴y的惯性半径, 平行移轴公式（形心轴zc与平行轴z1的距离为a，图形面积为A）纯弯曲梁

9、的正应力计算公式横力弯曲最大正应力计算公式矩形、圆形、空心圆形的弯曲截面系数，几种常见截面的最大弯曲切应力计算公式（为中性轴一侧的横截面对中性轴z的静矩，b为横截面在中性轴处的宽度）矩形截面梁最大弯曲切应力发生在中性轴处工字形截面梁腹板上的弯曲切应力近似公式轧制工字钢梁最大弯曲切应力计算公式圆形截面梁最大弯曲切应力发生在中性轴处圆环形薄壁截面梁最大弯曲切应力发生在中性轴处弯曲正应力强度条件几种常见截面梁的弯曲切应力强度条件弯曲梁危险点上既有正应力又有切应力作用时的强度条件或，梁的挠曲线近似微分方程梁的转角方程梁的挠曲线方程轴向荷载与横向均布荷载联合作用时杆件截面底部边缘和顶部边缘处的正应力计算

10、公式偏心拉伸（压缩）弯扭组合变形时圆截面杆按第三和第四强度理论建立的强度条件表达式，圆截面杆横截面上有两个弯矩和同时作用时，合成弯矩为圆截面杆横截面上有两个弯矩和同时作用时强度计算公式弯拉扭或弯压扭组合作用时强度计算公式剪切实用计算的强度条件挤压实用计算的强度条件等截面细长压杆在四种杆端约束情况下的临界力计算公式压杆的约束条件：（a）两端铰支=l（b）一端固定、一端自由=2（c）一端固定、一端铰支=0.7（d）两端固定=0.5 压杆的长细比或柔度计算公式，细长压杆临界应力的欧拉公式欧拉公式的适用范围压杆稳定性计算的安全系数法压杆稳定性计算的折减系数法关系需查表求得Winger Tuivasa-

11、Sheck, 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

12、have 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

13、 of the 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 eve

14、ry award 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 ma

15、tch at 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

16、of their 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 insult

17、s from 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 l

18、imited 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 commerc

19、ial airliners (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

20、an Olympic 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 Engla

21、nds Josh 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, especia

22、lly on their own goal-line, completing sets and a good kick-chase. Theyve been great at all the unglamorous stuff that often goes unnoticed in the stands but not by your team-mates.It is as though their entire tournament has been preparation for the final.In Johnathan Thurston, Cooper Cronk, Cameron

23、 Smith and either Billy Slater or Greg Inglis at full-back they have a spine that is unmatched in rugby league. They have played in so many high-pressure games - a priceless asset going into Saturday.The Kiwis are a lot less experienced but winning a dramatic match like their semi-final against England will do wonders for their confidence.They defeated Australia in the Four Nations final in 2010 and the last World Cup, and know they can rise to the big occasion.12