MecMovies 4.0 : M5.6: Coaxial Tube and Core

The figure shows the free body diagram of the tube near the free end B. The load on top of the tube is P which equals 30 kilo newtons directed vertically downwards. The reaction force on member 2 is F subscript 2 directed vertically downwards. The reaction force at the base of the tube is F subscript 1 directed vertically downwards.

Write the equilibrium equation for the sum of forces in the $y$ direction:

$\sum_{} F_{y} = - F_{1} - F_{2} - 30 kN = 0$

With two unknown forces $F_{1}$ and $F_{2}$ , this equation cannot be solved. Since this is the only non-trivial equilibrium that can be written for the free-body diagram, statics alone is insufficient to solve the problem. This type of problem is termed statically indeterminate.

To solve the problem, a second equation containing the unknowns $F_{1}$ and $F_{2}$ must be developed.