2. Benchmark solution#
2.1. Internal movements and efforts#
At node \(A\) all movements are blocked. At nodes \(B\) and \(C\) the load is an effort \(F\) along the axis of the element. The temperature is assigned to the nodes: \(Temper\).
The displacement due to thermal expansion in the axis of the element is:
The displacement due to the force in the axis of the element is:
For beams: \(U_p =\frac{F L}{E S}\)
For the discreet: \(U_d =\frac{F}{K_x}\)
The stiffness of the discrete is chosen so that the movements of the beams and the discretes are identical: \(K_x = \frac{E S}{L}\).
When the load is both the temperature and the effort:
The total displacement is: \(U_{total} = U_{th} + U_{d} = U_{th} + U_{p}\).
The internal effort is: \(F_{normal} = F\).
The supporting reactions are:
For the following elements \(AB\): \(F_x = F\)
For the following elements \(AC\): \(\left[ F_x, F_y, F_z \right] = -F \left[ \cos(\beta) cos(\alpha), \cos(\beta) sin(\alpha), \sin(\beta) \right]\)
2.2. Uncertainties about solutions#
None