《理論力學(xué)》第二章 力系的簡化習(xí)題解

1、11F2F3F0135090O1F3F345Oxyz045?A2F第二章第二章力系的簡化習(xí)題解力系的簡化習(xí)題解[習(xí)題習(xí)題21]21]一鋼結(jié)構(gòu)節(jié)點(diǎn)在沿OAOBOC的方向上受到三個力的作用已知kNF11?試求這三個力的合力.kNF41.12?kNF23?解:01?xFkNFy11??)(145cos41.102kNFx????)(145sin41.102kNFy??kNFx23?03?yF)(121030kNFFixiRx???????00

2、1130????????iyiRyFF作用點(diǎn)在O點(diǎn)方向水平向右.122???RyRxRRFF[習(xí)題習(xí)題22]22]計算圖中已知三個力分別在軸上的投影并求合力.已知1F2F3Fzyx.kNF21?kNF12?kNF33?解:kNFx21?01?yF01?zF)(424.0537071.01cos45sin022kNFFx??????)(567.0547071.01sin45sin022kNFFy??????)(707.0707.0145s

3、in022kNFFz????03?xF03?yFkNFz33?)(424.20424.0230kNFFixiRx???????)(567.00567.0030kNFFiyiRy???????)(707.33707.0030kNFFiziRz???????合力的大小:)(465.4707.3567.0424.2222222kNFFFFRzRyRxR???????方向余弦:4429.0465.4424.2cos???RRxFF?1270.0

4、465.4567.0cos???RRyFF?8302.0465.4707.3cos???RRzFF?3O1OCDEM090??[習(xí)題習(xí)題24]24]沿正六面體的三棱邊作用著三個力在平面OABC內(nèi)作用一個力偶.已知NF201?.求力偶與三個力合成的結(jié)果.NF302?NF503?mNM??1解:把向平移得到:1F2F3F1O主矢量:0302050213???????FFFFR)(42.0202.0)(11mNFFMx?????????0)(

5、1?FMy0)(1?FMz)(62.0302.0)(22mNFFMx?????????)(5.415.03015.0)(22mNFFMy??????0)(2?FMz0)(3?FMx)(5.715.05015.0)(33mNFFMy?????????0)(3?FMz的方向由E指向D.M)(25.825.65.2)()(3111mNFMFMMOOOC???????)(8.01502002001sin22mNMMx???????)(6.015

6、02001501cos22mNMMy??????????0?zM)(2.98.0064)(31mNMFMMxiixx?????????????)(6.36.05.75.40)(31mNMFMMyiiyy????????????00000)(31??????????ziizzMFMM主矩:)(88.90)6.3()2.9()()()(222222mNMMMMzyxO?????????????方向余弦:MOABC3F2F1Fmm200mm1