ENGINEERING MECHANICS GATE PI PAPER TECHNICAL SECTION PART 2
PARALLEL FORCES ON A PLANE Like parallel forces: Coplanar parallel forces when act in the same direction. | Unlike parallel forces Coplanar parallel forces when act in different direction. Resultant of like parallel forces: Let P and Q are two like parallel forces act at points A and B. R=P+Q
kesulfant of unlike parallel forces: R is in the direction of the force having greater magnitude. Couple Two unlike equal parallel forces form a couple.
. The rotational effect of a couple is measured by its moment. Moment P x I . Sign convention: . Anticlockwise couple (Positive) Clockwise couple (Negative)
CENTRE OF GRAVITY Centre of gravity: . It is that point through which the resultant of the distributed gravity force passes regardless of the orientation of the body in space. . As the point through which resultant of force of gravity (weight) of the body acts. Centroid: Centeroid of an area lies on the axis of symmetry if it exits Centre of gravity is applied to bodies with mass and weight and centroid is applied to plane areas.
Ax, A,x, 1 Moment of area Total area x.dA y.dA ye =
Centroids of different figures SHAPE FIGURE AREA Rectangle d/2 b/2 bd b/2 Triangle 0 h/3 bh/2 Semi circle TTr2/2