Page 28 - mechanics

Chapter – 5 Equilibrium of rigid body & Reactions of supports

rigid body in 2D is expressed as

 Fx = 0 ,  Fy = 0, M O = 0 (5.1)

where  Fx and  Fy represent the algebraic sums of the

forces x and y components, respectively, whereas M O

represents the algebraic sum of all moments about a point O,

which may lie either on or off the body.

Three alternative sets of three independent equilibrium

equations may also be used:

1)  Fx = 0 , M A = 0 , M B = 0 (5.2)

with the condition that a line passing through points A and B is

not perpendicular to the x axis.

2)  Fy = 0, M A = 0 , M B = 0 (5.3)

with the condition that a line passing through points A and B is

not perpendicular to the y axis. (5.4)

3) M A = 0 , M B = 0 , MC = 0

with the condition that points A, B, and C do not lie on the

same line. As all sets of 2D equilibrium equations consist of

three independent equations, this indicates that the number of

unknowns in such problems is not to exceed three unknowns

to be fully determined.

The first step in solving problems is to draw a free body

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