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Statics Chapter 3 Equilibrium of Coplanar Force Systems Equilibrium Equations • Body is equilibrium when resultant of all external forces are zero • • • • All forces All moments Sums of all corresponding rectangular components must be 0 External forces about an arbitrary point must be 0 Free Body Diagram • Is a sketch of a body isolated from its supports or other connected bodies with all external forces indicated • Should included clearly the magnitude direction and location of all external forces, including weight, applied forces, reactions and dimensions and angles • Weight – represents the gravitational attraction of the earth – acting downward through center of gravity • Applied forces – loads that are applied to the free body • Reactions – represents the constraining forces exerted or the free body by the supports or by the connected bodies • Dimensions and angles – must included all dimension and angles and location of all forces • Internal forces must not be included. Types of Supports • Roller supports with one unknown reaction element • Examples – page 105 • Hinge support with two unknown reaction elements • Examples page 105 • Fixed Support with three unknown reaction elements • Examples page 106 • Pulley • Examples page 106 • Linear Spring • F=kx • Example 107 • Example 3-1, 3-2, 3-3 Equilibrium of a concurrent coplanar force system • Body subjected to concurrent coplanar forces is in equilibrium if the resultant of the forces acting on the body is zero. • Moment of the forces about the common point is always zero • Equilibrium conditions would be Sum Fx=0 and sum Fy =0 • Example 3-4 page 111 • Example 3-5 page 112 • Example 3-6 page 113 • Example 3-7 page 114 Equilibrium of a non concurrent coplanar force system • • • • Sum of Fx =0 Sum of Fy =0 Sum of M=0 If a problem contains to moments • • • • • • • • • Sum of Fx =0 Sum of Ma =0 Sum of Mb =0 X axis is arbitrarily and line segment AB must not be perpendicular to the x axis Example 3-8 Example 3-9 Example 3-10 Example 3-11 Example 3-12