Engineering Mechanics categories of equilibrium in three dimensions
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There are four categories of equilibrium in three dimensions: 1. Concurrent (at a point) force system requires three force equations but no moment equations. 2. Concurrent (with a line) force system requires all equations except the moment equation about the line. 3. Parallel force system requires one force equation and two moment equations about axes normal to the forces. 4. General force system requires all three force equations and all three moment equations.
Engineering Mechanics categories of equilibrium in three dimensions
- 1. Categories of Equilibrium in Three Dimensions Prof. P. Rajayogan M. Tech., MISTE., MASCE., FACCE FIE., +91 9486026085 Contact Email Id rajayoganp@gmail.com P Rajayo gan Digitally signed by P Rajayogan DN: cn=P Rajayogan, o, ou, email=rajayopganp @gmail.com, c=IN Date: 2014.09.22 19:50:59 +05'30'
- 2. Concurrent (at a point) Force System Free-body Diagram Fx 0 Fy 0 Independent Equations x z F1 F2 F3 F4 F5 Fz 0 Requires all three force equations, but no moment equations because the moment of the forces about any axis through O is zero. O
- 3. Concurrent (with a line) Force System Free-body Diagram My 0 Mz 0 Fx 0 Fy 0 Independent Equations x F z 1 F2 F3 F4 F5 Fz 0 Requires all equations except the moment equation about the line which is automatically satisfied.
- 4. Parallel Force System Free-body Diagram Fx 0 0 y M Independent Equations F2 x z F1 F3 F4 F5 0 z M Requires only one force equation, the one in the direction of the forces and two moment equations about the axes which are normal to the direction of forces.
- 5. General Force System Free-body Diagram 0 y M Fz 0 0 x M Independent Fx 0 Fy 0 M2 F1 F2 F3 F4 M1 x z Equations 0 z M Requires all three force equations and all three moment equations.