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
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Date: 2014.09.22
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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.