平面任意力系的简化平面任意力系平衡方程平面汇交力系平衡40

1、东财Dongbei University of Finance Economics静力学基础静力学基础平面任意力系的简化平面任意力系平衡方程平面汇交力系平衡方程平面力偶系平衡方程平面平行力系平衡方程平面力系简化与平衡东财Dongbei University of Finance Economics静力学基础静力学基础平面力系的简化与平衡力系合成的解析法 力在直角坐标轴上的投影 合力投影定理平面任意力系的简化 简化方法 结果讨论掌握平面任意力系、汇交力系、平行力系平衡方程的应用教学要求：掌握力在直角坐标系上的投影及合力投影定理熟悉平面任意力系的简化及简化结果东财Dongbei Universit

2、y of Finance Economics静力学基础静力学基础平面任意力系的简化设平面任意力系如图所示将图2-3所示平面汇交力系和平面力偶系合成，得：FnFRnFOOMM主矢：主矩：东财Dongbei University of Finance Economics静力学基础静力学基础平面任意力系的简化(续)如图2-4 主矢FR和主矩MoFR0Mo=0FR =0Mo 0FR 0Mo 0东财Dongbei University of Finance Economics静力学基础静力学基础平面任意力系平衡方程平衡条件 主矢为零：FR=0 主矩为零：Mo=0即：0)(00FMFFoyx0)(0)(0

3、FMFMFBAx0)(0)(0)(FMFMFMCBA其他形式：二矩式：三矩式：ABx A、B、C不共线东财Dongbei University of Finance Economics静力学基础静力学基础力系合成的解析法力系合成的解析法，就是通过力矢量在直角坐标轴上的投影来表示合力与分力之间的关系。力在平面直角坐标轴上的投影定义：大小计算：Fx=FcosFy=FcosFsin正负规定：投影和分力关系东财Dongbei University of Finance Economics静力学基础静力学基础合力投影定理合力在某一轴的投影，等于各分力在同一轴上投影的代数和。niiynyyyRyniixn

4、xxxRxFFFFFFFFFF121121.合力的投影与各分力投影的关系2cos;cos2222通常：RRRYRRRxRyRxRFFyFFFFxFFFyFxFFF东财Dongbei University of Finance Economics静力学基础静力学基础例1-2用解析法求图示平面汇交力系的合力04404403303302202201101145sin45cos;45sin45cos60sin60cos;30sin30cosFFFFFFFFFFFFFFFFyxyxyxyx解：NFyFNFxFRyRx3 .1123 .129NFFFRyRxR3 .17122040.9753 .1293

5、.112arctgFFarctgRxRyFR=171.3N=40.975东财Dongbei University of Finance Economics静力学基础静力学基础平衡方程平面汇交力系平衡方程00yxFF平面力偶系平衡方程 0)(FMo平面平行力系平衡方程0)(0)(0)(0FMFMFMoFxBA；另外形式：思考：附加条件东财Dongbei University of Finance Economics静力学基础静力学基础应用举例解题步骤： 选取研究对象，画受力图 建立直角坐标系 列平衡方程并求解例1-3如图，已知G100N，求斜面和绳子的约束力解：取小球为研究对象，画受力图并建立坐

6、标系如图；列平衡方程：030cos:0030sin:000GFFyGFFxNTNFNFNT6 .8650解得：若坐标系如图b)建立，平衡方程如何写？东财Dongbei University of Finance Economics静力学基础静力学基础例1-4已知F=15kN，M=3kN.m，求A、B处支座反力解：1、画受力图，并建立坐标系2、列方程00AxxFFkNFMFFFMBBA113/)1523(0230)(kNFFFFFFFBAyBAyy400东财Dongbei University of Finance Economics静力学基础静力学基础返回平面力系简化与平衡 财经大学财经大学

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