Chapter 3 Equilibrium of Coplanar Force Systems 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 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 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