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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
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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
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Sum of Fx =0
Sum of Fy =0
Sum of M=0
If a problem contains to moments
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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