[{"data":1,"prerenderedAt":41},["ShallowReactive",2],{"topic-en-theoretical-mechanics\u002Fstatics\u002Fthree-dimensional-statics":3},{"topic":4,"trail":14,"children":24,"tasks":37,"alternates":38},{"id":5,"name":6,"locale":7,"path":8,"seo_title":9,"seo_description":10,"seo_text":11,"content_html":12,"content_chunks":13},276,"Three-Dimensional Statics","en","theoretical-mechanics\u002Fstatics\u002Fthree-dimensional-statics","Three-Dimensional Statics and Equilibrium","Three-dimensional force systems, equilibrium equations, centers of parallel forces, and centers of gravity.","This section covers three-dimensional force systems, their equilibrium conditions, and the determination of centers of parallel forces and centers of gravity.","\u003Cp>\u003Cstrong>Three-dimensional statics\u003C\u002Fstrong> extends the methods of statics to spatial force systems. Forces and moments may have three components, so complete equilibrium requires both translational and rotational effects to be considered about the three coordinate axes.\u003C\u002Fp>\u003Ch2>Spatial force systems\u003C\u002Fh2>\u003Cp>A general three-dimensional force system can be characterized by a resultant force and a resultant moment about a selected point. For equilibrium, both quantities must vanish.\u003C\u002Fp>\u003Ch2>Equilibrium equations\u003C\u002Fh2>\u003Cp>In the general case there are six scalar equilibrium conditions: three force-component equations and three moment equations. A suitable choice of axes and moment centers can simplify the calculation considerably.\u003C\u002Fp>\u003Ch2>Centers of parallel forces and gravity\u003C\u002Fh2>\u003Cp>Parallel force systems form an important special case. Their resultant passes through the center of parallel forces; for gravitational forces in a uniform field, the corresponding concept leads to the center of gravity.\u003C\u002Fp>",[],[15,19,23],{"id":16,"name":17,"path":18},81,"Theoretical Mechanics","theoretical-mechanics",{"id":20,"name":21,"path":22},136,"Statics","theoretical-mechanics\u002Fstatics",{"id":5,"name":6,"path":8},[25,29,33],{"id":26,"name":27,"path":28},191,"Three-Dimensional Force Systems","theoretical-mechanics\u002Fstatics\u002Fthree-dimensional-statics\u002Fthree-dimensional-force-systems",{"id":30,"name":31,"path":32},192,"Equilibrium Conditions for Three-Dimensional Force Systems","theoretical-mechanics\u002Fstatics\u002Fthree-dimensional-statics\u002Fequilibrium-conditions-three-dimensional-force-systems",{"id":34,"name":35,"path":36},193,"Center of Parallel Forces and Center of Gravity","theoretical-mechanics\u002Fstatics\u002Fthree-dimensional-statics\u002Fcenter-parallel-forces-center-gravity",[],{"en":39,"uk":40},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Ftopics\u002Ftheoretical-mechanics\u002Fstatics\u002Fthree-dimensional-statics","https:\u002F\u002Fmechclassroom.com\u002Ftopics\u002Fteoretychna-mekhanika\u002Fstatyka\u002Fprostorova-statyka",1787712535557]