工程力學(xué)習(xí)題 答案 廖明成

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1、習(xí)題解答 第四章 平面任意力系 河南理工大學(xué) 第四章 平面任意力系 習(xí) 題 4.1 重W，半徑為r的均勻圓球，用長(zhǎng)為L(zhǎng)的軟繩AB及半徑為R的固定光滑圓柱面支持如圖，A與圓柱面的距離為d。求繩子的拉力及固定面對(duì)圓球的作用力。 解：軟繩AB的延長(zhǎng)線必過(guò)球的中心，力在兩個(gè)圓球圓心線連線上和的關(guān)系如圖所示：AB于y軸夾角為 對(duì)小球的球心O進(jìn)行受力分析： 4.2 吊橋AB長(zhǎng)L，重，重心在中心

2、。A端由鉸鏈支于地面，B端由繩拉住，繩繞過(guò)小滑輪C掛重物，重量已知。重力作用線沿鉛垂線AC，AC=AB。問(wèn)吊橋與鉛垂線的交角θ為多大方能平衡，并求此時(shí)鉸鏈A對(duì)吊橋的約束力。 解：對(duì)AB桿件進(jìn)行受力分析： 解得： 對(duì)整體進(jìn)行受力分析，由: 4.3 試求圖示各梁支座的約束力。設(shè)力的單位為kN，力偶矩的單位為kN·m，長(zhǎng)度單位為m，分布載荷集度為kN／m。 (提示：計(jì)算非均布載荷的投影和與力矩和時(shí)需應(yīng)用積分。) 解： （a）受力如圖所示 （b）受力如圖

3、所示 （c）受力如圖所示 （d）受力如圖所示 4.4 露天廠房立柱的底部是杯形基礎(chǔ)。立柱底部用混凝土砂漿與杯形基礎(chǔ)固連在一起。已知吊車梁傳來(lái)的鉛垂載荷為F＝60 kN，風(fēng)壓集度q＝2kN／m，又立柱自重G=40kN，長(zhǎng)度a=0.5m，h=10m，試求立柱底部的約束力。 解：立柱底部A處的受力如圖所示，取截面A以上的立柱為研究對(duì)象

4、 4.5 圖示三鉸拱在左半部分受到均布力q作用，A，B，C三點(diǎn)都是鉸鏈。已知每個(gè)半拱重kN，m，m，q=10kN／m求支座A，B的約束力。 解：設(shè)A，B處的受力如圖所示， 整體分析，由： 取BC部分為研究對(duì)象 再以整體為研究對(duì)象 4.6 圖示汽車臺(tái)秤簡(jiǎn)圖，BCF為整體臺(tái)面，杠桿AB可繞軸O轉(zhuǎn)動(dòng)，B，C，D均為鉸鏈，杠桿處于水平位置。求平衡時(shí)砝碼重與汽車重的關(guān)系。 4.7 圖示構(gòu)架中

5、，物體重W=1200N，由細(xì)繩跨過(guò)滑輪E而水平系于墻上，尺寸如圖，求支承A和B處的約束力及桿BC的內(nèi)力。 解: （1）取系統(tǒng)整體為研究對(duì)象，畫(huà)出受力如圖所示。 顯然，， 列平衡方程： ，kN ， ， （2）為了求得BC桿受力，以ADB桿為研究對(duì)象，畫(huà)出受力圖所示。 列平衡方程 解得 kN 解得負(fù)值，說(shuō)明二力桿BC桿受壓。 4.8 活動(dòng)梯子置于光滑水平面上，并在鉛垂面內(nèi)，梯子兩部分AC和AB各重為Q，置心在中點(diǎn)，彼次用鉸鏈A和繩子DE連接。

6、一人重為P立于F處，試求繩子DE的拉力和B，C兩點(diǎn)的約束力。 解： 先研究整體如（a）圖所示 再研究AB部分，受力如（b）圖所示 解得 4.9剛架ACB和剛架CD凹通過(guò)鉸鏈C連接。并與地面通過(guò)鉸鏈．A，B，D連接．如圖所示，載荷如圖。試求剛架的支座約束力(尺寸單位為m，力的單位為kN．載荷集度單位為kN/m)。 解： （a）顯然D處受力為0 對(duì)ACB進(jìn)行受力分析，受力如圖所示： （b） 取CD為研究對(duì)象 取

7、整體為研究對(duì)象 4.10 由AC和CD構(gòu)成的組合梁通過(guò)鉸鏈C連接，其支座和載荷如圖所示。已知kN/m，力偶矩kN·m，不計(jì)梁重。求支座A、B、D和鉸鏈C處所受的約束力。 解： 先研究CD梁，如右圖所示 解得 再研究ABC梁，如圖（b） 解得 4.11 承重框架如圖4.11所示，A、D、E均為鉸鏈，各桿件和滑輪的重量不計(jì)。試求A、D、E點(diǎn)的約束力。 解：去整體為研究對(duì)象

8、，受力如圖所示 取ED為研究對(duì)象，受力如圖所示 再去整體為研究對(duì)象 4.12 三角形平板A點(diǎn)鉸鏈支座，銷釘C固結(jié)在桿DE上，并與滑道光滑接觸。已知，各桿件重量略去不計(jì)，試求鉸鏈支座A和D的約束反力。 解： 取ABC為研究對(duì)象 取整體為研究對(duì)象 4.13 兩物塊A和B重疊地放在粗糙水平面上，物塊A的頂上

9、作用一斜力F，已知A重100N，B重200N；A與B之間及物塊B與粗糙水平面間的摩擦因數(shù)均為f=0.2。問(wèn)當(dāng)F=60N，是物塊A相對(duì)物塊B滑動(dòng)呢？還是物塊A，B一起相對(duì)地面滑動(dòng)？ 解：A與B一起作為研究對(duì)象，則與地面摩擦力為 A與B之間的摩擦力為 F力在水平與豎直方向分解 由于 所以是A與B相對(duì)滑動(dòng) 4.14 物塊Ａ，Ｂ分別重kN，kN，Ａ，Ｂ以及Ａ與地面間的摩擦因數(shù)均為fs=0.2，Ａ，Ｂ通過(guò)滑輪C用一繩連接，滑輪處摩擦不計(jì)。今在物塊Ａ上作用一水平力F，求能拉動(dòng)物塊Ａ?xí)r該力的最小值。 解：A與B之間的摩擦力為： A與地面之間的摩擦力為： 4.15

10、 重量為的輪子放在水平面上，并與垂直墻壁接觸。已知接觸面的摩擦因數(shù)為，求使輪子開(kāi)始轉(zhuǎn)動(dòng)所需的力偶矩？ 解： 4.16 均質(zhì)梯長(zhǎng)為，重為N，今有一人重N，試問(wèn)此人若要爬到梯頂，而梯子不致滑倒，B處的靜摩擦因數(shù)至少應(yīng)為多大？已知，。 4.17 磚夾的寬度250mm，桿件AGB和GCED在點(diǎn)G鉸接。磚重為W，提磚的合力F作用在磚夾的對(duì)稱中心線上，尺寸如圖所示。如磚夾與磚之間的靜摩擦因數(shù)fs=0.5，問(wèn)d應(yīng)為多大才能將磚夾起（d是點(diǎn)G到磚塊上所受正壓力作用線的距離）。 解： 設(shè)提起磚時(shí)系統(tǒng)處于平衡狀態(tài)，則由右圖可知 接著取

11、磚為研究對(duì)象（圖（b）），由， 可得再由 得 最后研究曲桿AGB，如圖（c）， 由 解出 磚不下滑滿足條件 由此兩式可得 4.18 一直角尖劈，兩側(cè)面與物體間的摩擦角均為，不計(jì)尖劈自重，欲使尖劈打入物體后不致滑出，頂角α應(yīng)為多大？ 4.19 桁架的載荷和尺寸如圖所示。求桿BH，CD和GD的受力。 解： 桁架中零力桿有BI，HC，GD 所以GD受力為零， 以整體為研究對(duì)象 如圖所示

12、截取左部分 4.20 判斷圖示平面桁架的零力桿（桿件內(nèi)力為零）。 解：（a）1,2 (b) 1,2,5,11,13 (c) 2,3,6,7,11 4.21 利用截面法求出圖中桿1、4、8的內(nèi)力。 解：以G點(diǎn)為研究對(duì)象 以右部分為研究對(duì)象，受力如圖所示 4.22利用截面法求出桿4、5、6的內(nèi)力。 解：

13、 整體分析 以m線截取整體之右部分為研究對(duì)象，受力如圖所示,設(shè)5桿與GH桿夾角為 145 （英文版 ） easily blame, to prevent the broken window effect. Supervise the leading cadres to play an exemplary role, take the lead in the strict implementation of the < code > and < rule >, lead to safeguard the solemnity and author

14、ity of the party discipline, ensure that the party discipline and the laws and regulations for implementation in place. Throughout the discipline in the daily supervision and management , strengthen supervision and inspection, from the thorough investigation of violations of discipline behavior. St

15、rengthen to key areas, key departments and key projects as well as the masses reflect the concentration of the units and departments for supervision. - strengthening supervision, discipline inspection and supervision of cadres to set an example for compliance with the < code > and < rule > is a man

16、must be hexyl, blacksmith needs its own hardware. Discipline inspection organs as the executor of the party discipline, and supervisor of the defenders, for its supervision must be more strictly, discipline inspection and supervision of cadres to firmly establish the awareness of Party Constitution,

17、 sense of discipline and rules consciousness, politics loyalty, sense obey. Action speak Ji Ordinance to set an example of the regulations of the rule of law, strengthen supervision and accept the supervision of the firmness and consciousness, do comply with < > and < >. To firmly establish the disc

18、ipline must first be disciplined, the supervisor will be subject to the supervision of "concept, and consciously safeguard and implement party compasses party, take the lead in practicing" three strict real strict, so loyal, clean, play. To be good at learning, the Constitution and the < code > as m

19、orality, politics and brought to fruition; to implement < >, do not want to, dare not, not with disciplinary ruler to supervision; to discipline a ruler, often the control inspection, and consciously in the ideological red line to draw the row Ming Good accumulation is indeed the bottom line, so tha

20、t the heart has fear, said to have quit, the line has ended. Attached: indifferent to heart, calmly to the table in our life, there are many unpredictable things will happen, some good, some bad things, we cannot control is powerless to stop, but with time, you will find in life sometimes turns out

21、to be not good, some bad things finally turned out to be a good thing, but then we muddy however did not know, this is the life teach us things. 1, life can be complex, can also be simple. Want simple life of precipitation, to have enough time to reflect, to make Become more perfect. Life is the mos

22、t important thing is not to win, but the struggle; not to have conquered, but to have fought well. 2, the plain is the background of life. Live a plain life, give up on themselves is not a coward, but the wise answers; not disillusioned after the heart, such as ashes, but experience the storm after

23、the enlightenment; not unrewarding perfunctorily, but calm attitude of life of unrestrained self-confidence. Plain living, there is no noise noisy, no earthly troubles, more did not fill in the discontent of desire, some just a calm, a calm. 3, memory of heart will not good things to erase the, life

24、 is a When no movie, pain is a beginning, the struggle is a kind of process, death is a kind of ending. Give up this giving up is the helpless, do not give up the abandoned, do not give up this giving up is ignorance, do not give up should not give up is persistent. 4, a thing figured is heaven, thi

25、nk impassability is hell. Since the living, to live better. Sometimes we because of too narrow-minded, too care around the chores and penny wise and pound foolish, not worth the candle. Some things to attract trouble and worry, completely depends on how we look at and deal with it. Don't always take

26、 everything back to things, and don't get into a blind alley, don't want to face, don't be narrow-minded. Poke to care, is a kind of open-minded, a free and easy. 5, I am not afraid of others behind me a knife, I afraid to look back and see stab me, is my intention to treat people; I am not afraid o

27、f the truth to tell the best friend, I'm afraid he turned to it as a joke to tell don't 6, when we are in a positive frame of mind, you will find many good things; and when we are in a negative state of mind, you will find many depressed things; life happy and worry, all is you of life attitude, opt

28、imistic, good luck; loss of sink, Eritrea company. When you are in adversity, may wish to change a point of view to think everything over to the good Think, because good mentality decided the fate of the! 7, people are tired, rest; heart tired, calm. Grow up, mature, this society read. Tired and sad

29、, squat down, to their a hug. Because the world no one can sympathize with you, have mercy on you. You cry, tears is your own; you pain, no one can understand. Then you only tears to smile. 8, each people have youth, Each youth are a story, the life of the world never gets easier, I want what, wish

30、 the world all know, as has been the same; now want anything, for fear that others know, or like to lose the same. 9, the heart move, everything in the world is followed by birth, Rangrang, important thing is often the most difficult to open one's mouth, because words will reduce its importance; to

31、let strangers people care about your life in the good things, the original is not easy 10, do not blame, do not laugh at who, also don't envy who. Like a person is a kind of feeling, not like a person is true. The truth is easy to explain, I feel Is unspeakable. The best travel life is that you in a

32、 strange place found a long lost touched. 11, happy life not in the bustling in, and in the peace of mind; no matter how many grievances, how uncomfortable, and ultimately to heal themselves or their own, others may got you to comfort, but never know your heart is how wanjianchuanxin. 12, ma'am, lik

33、e a movie, learn to appreciate, learn to be grateful, learn tolerance, and goodness, helping others. Instead of accusing the society, as into one; and an exception is better to give than to what 13, don't envy him A sum of, don't lose your life and the life, respectively is: the former is a we exper

34、ienced cannot escape in a day finally will last minute, while the latter is our persistent, we want to cherish the memory of those people and things. 14, learn to smile, learn to strong, the world you know so many people, so many people and you are, you cannot change also can't let everyone like you

35、, so also do not want to do. Life is too short to go crazy to love to go to waste, to chase the dream to regret. 15, when temper, a blessing to go. A wounding elegant people, the key is to control their own emotions. With the mouth is the most stupid behavior. A control negative emotions than a can

36、take a city more powerful water flow slow, language is expensive. People spent two years of time to learn to speak, but to spend a few years time to shut up. That is a kind of ability, that is a kind of wisdom. 16, life is not perfect, sometimes, growth is not a cry, not an eyeful of tears, there is

37、 no trace of emotion, there is no gleam of hope, no desire, no action, no static, there is only one kind of downward sinking feeling, sink A murky? 6? 7? 6? 7 sink? 6? 7? 6? 7 toward the bottom of the sink. 17, in some way, do not go, you will not know the other side scenery is beautiful. To you is

38、not good, you do not mind too much, no one has an obligation to you; you learn knowledge, is you have weapons, you can start from scratch, but not unarmed; how do you treat people, does not represent how others treat you, if cannot see through this point, only inviting worry. 18, time is like a spon

39、ge in the water, as long as you are willing to squeeze, the total water is still there. Every life, after the ups and downs The best test of live, to life, survival and continuation, do not stop the struggle in the joys and sorrows of life on the road, so that different soul to bear life beat, accep

40、tance of suffering. 19, indifferent to heart, calmly in table, elegant and comfortable life, do not take what is so important. The pursuit will be disappointed; to be alive, you will have trouble. Life is the most afraid of what all want to care about, but also what all grasp is not firm, without sc

41、enery, separated populations, such as not to desire, all docked in the fate of the end. Why is too rigid, the natural, to go stay not to live, let go of obsession, revel is 20, if the fate of the broken Hopes of sailing, please don't despair, the coast is still, if the fate of the withered petals of

42、 the beautiful, please do not sink, the spring is still, life will always be endless trouble, please don't helpless, because they are still alive, is still a dream, the sun still, we still. Lost, keep memories; to get, must work to; but the most important is good to cherish their own. 21, life, sele

43、ct the complex, is to choose the pain; choose a simple, is choose to be happy. The complex world like a Significance of pride. Hope is the ornate palace, outside people admiring the magnificent, living in the deep knowledge of living it to pay the price. Simple world as a simple log cabin outside r

44、idiculed shabby, the heart is willing to go live to know the joy. Suffering and joy is their own choice. 22, learn how to use a single powerful heart, let the past be the past, let the future come. Life is really the end of the end of an eagle is flying wings, life is constantly pursuit. Don't miss

45、to regret, don't wait for old just miss. Time to return, seize every moment, again painstakingly again tired also Those struggling to fly. 23, life could not Yimapingchuan, even flat pavement, inevitably there will be a few pieces of roadblocks. Some of the rocks around the past, while others have t

46、o move it out. Just move others put the stone is very easy, because the stone from the appearance we can discern; difficult to myself to move away the heart of stone head. Leave time to spend with her, often reflect my heart, so as to remove your heart of stone. 24, everything does not have to be de

47、manding, come to, everything does not have to care about, over the past; failing to do not frown, laugh it laugh. Results Don't demand, do to; life is a simple, calm and peaceful. Always not to choose their own path and regret, life is like a train, the scenery and then the United States will retrea

48、t, the passage of time and encounter will eventually drifting further and further away, before is always himself. 25, everyone has a weakness, weakness is true humanity. That has no weakness, a shallow person. That people think there is no weakness, mostly false. Life has shortcomings, there are sho

49、rtcomings is the real life. That no one regret, or childish or numbness or Self deception. It is in tolerance of weakness and so on to accept, people live happily. Hello, everyone! I am a party member. The title of my speech is: < study and implement the party's two laws, doing practical play hig

50、hway. 2015 October 18, the Central Committee of the Communist Party of China promulgated the implementation of the < the probity of the Communist Party of China self-discipline criterion > and < Chinese Communist Party discipline and punishment regulations. We Heyuan male passers-by to respond posit

51、ively to the call of the Central Committee of the party, earnestly organize the study "party two regulations", truly grasp the essence and gist, and in their respective positions, to hold the bottom line of the discipline, build a strong ideological line of defense, with the courage to play, the cou

52、rage to fight tough and fearless spirit, at the crucial moment well to complete the task, with practical action to test the study and implement effect Because of discipline in the * * * * * * * * * * * story. Here, let me to cast a brick to attract jade, speak about our highway. Highway line section

53、 of the road surface transformation project, last year "towards the country seized" will be seized one of the items. To complete this arduous task, as a project management office director Comrade, keep in mind from the Communist Party membership, recognize and identify the "bottom line", strict mana

54、gement, and strict adherence to the quality of the project. He not only set an example, honesty and self-discipline, but also requires the management of all the members of the O.K., do not eat the construction unit one meal, do not accept the construction unit a ceremony. In this way, they didn't re

55、ally dare to adhere to the principle. No comrade, constantly put on reworking an emergency meeting to Comrade Zhen to speak louder, management tube too strict. Remember in Dongguan Street, 400 meters long cement concrete surface layer, because of various reasons, the smoothness of the poor in the bo

56、ttom cavity, covering film traces and car imprinting quality problems, * * * inquiries, immediately rushed to the scene to understand and verify the situation, the convening of the management office, the construction units, supervision units, construction units, construction units construction time

57、is tight, the economic loss and other reasons to intercede ******** unmoved. He said, "now a popular word, to the discipline and rules quite in front, there are no rules Radius, you construction team not accordance with the technical specifications, quality problems, it must be to carry out rectific

58、ation. Engineering quality responsibility be weightier than Mount Tai, if we manage to this matter Pavement quality quantity are placed the matter, we this time to learn two regulations have what use? Still what is the Communist Party? "Finally, in his insisted, the road after rework, to solve thes

59、e problems. In the construction of the new comrades and the project all the colleagues efforts, after four months of fighting, the project the main project was finally completed and passed inspection. Thousands of miles of ice, thousands of miles Piao, this is a splendid and romantic scene. But snow

60、 for the highway, it is a disaster, a serious threat to the traffic safety. This year, a month, a century of cold wave swept from North to south, and the snow blowing to Guangdong, but also to bear the blow To * * * * the highway. In January on the evening of 23, Lianping county city temperatures dr

61、opped to minus 2 degrees, a wide range of sudden rain sleet, before and after the provincial S341 line in Jiulianshan Mountain tunnel sections of the road appeared in the snow, lead to the passing vehicles skid, traffic is blocked. In the face of the sudden natural disasters, city and county highway

62、 department immediately launched the emergency plan for disaster prevention. As the front line of the main force, Lianping Highway Bureau of all Party members and cadres to remember the Party member responsibility, braving the biting cold wind, the first time rushed to the scene, on the icy pavement

63、 of salt disposal. Because the temperature is too low, just melt water immediately freezes, addition to the ice work to increase the difficulty. To ensure In addition to the re organization of the depths of the traffic safety, road people braved the icy put reflective cones and warning signs, endure

64、 cold at minus 2,3 of Jiulianshan patrols until one in the morning. Just before dawn, Lianping Highway Bureau personnel on the icy road salt ice melting processing until ten o'clock, ice melting ice success, the road gradually returned to normal traffic. In the cold winter night, which people do not

65、 miss the warm bed, which people do not miss the warm home. However, our highway on the road to the owners of the masses can go home early, the night fighting to secure the avoidance of the road safety and smoothness, fulfill their responsibility. Xi General Secretary Every Party member cadre cautio

66、ned against said: blacksmith needs self hard "." two regulations ", is our own hard standard test, more exercise every party members and cadres of the fire. We should continue to strengthen the party two regulations, conscientiously in practical work, practical play road, the road for the development of the cause of Heyuan and struggle. In the industry domain report the situation of road traffic in recent years, in the province highway departments of the concern and support, our bureau manage