Equilibrium
When a system of forces acting on a body has no resultant, the body on which the force system acts is in equilibrium. Newton’s first law of motion states that if the resultant force acting on a particle is zero, the particle will remain at rest or move with a constant velocity.
The resultant of each type of force system studied was determined by obtaining the sum of the forces of the system in certain directions and the sum of the moments of the forces with respect to certain axes.
To study the force system acting upon anybody or any portion of a body, it is first necessary to recognize completely what forces, both known and unknown, act on the body.
Free-Body Diagrams (FBD):
A free body diagram is a sketch of a body, a portion of a body, or to two or more bodies completely isolated or free from all other bodies, showing the forces exerted by all other bodies on the one being considered.
Before presenting a formal procedure as to how to draw a free-body diagram, we will first consider the various types of reactions that occur at supports and points of contact between bodies subjected to coplanar force systems. As a general rule,
Procedure for Analysis
To construct a free-body diagram for a rigid body or any group of bodies considered as a single system, the following steps should be performed:
Draw Outlined Shape. Imagine the body to be isolated or cut “free” from its constraints and connections and draw (sketch) its outlined shape.
Show All Forces and Couple Moments. Identify all the known and unknown external forces and couple moments that act on the body. Those generally encountered are due to (1) applied loadings, (2) reactions occurring at the supports or at points of contact with other bodies, and (3) the weight of the body. To account for all these effects, it may help to trace over the boundary, carefully noting each force or couple moment acting on it. Identify each Loading and give Dimensions. The forces and couple moments that are known should be labeled with their proper magnitudes and directions. Letters are used to represent the magnitudes and direction angles of forces and couple moments that are unknown. Finally, indicate the dimensions of the body necessary for calculating the moments of forces.Important Points
• No equilibrium problem should be solved without first drawing the free-body diagram, so as to account for all the forces and couple moments that act on the body.
• If a support prevents translation of a body in a particular direction, then the support exerts a force on the body in that direction.
• If rotation is prevented, then the support exerts a couple moment on the body.
Study Tables mentioned above.
• Internal forces are never shown on the free-body diagram since they occur in equal but opposite collinear pairs and therefore cancel out.
• The weight of a body is an external force, and its effect is represented by a single resultant force acting through the body’s center of gravity G.
• Couple moments can be placed anywhere on the free-body diagram since they are free vectors. Forces can act at any point along their lines of action since they are sliding vectors.
Example :
Draw the free-body diagram of the uniform beam shown in Figure a. The beam has a mass of 100 kg.
Solution: The free-body diagram of the beam is shown in Figure b. Since the support at A is fixed, the wall exerts three reactions on the beam, denoted as Ax, Ay, and MA. The magnitudes of these reactions are unknown, and their sense has been assumed. The weight of the beam, W = 100(9.81) N = 981 N, acts through the beam’s center of gravity G, which is 3 m from A since the beam is uniform.
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