We consider the linearized elasticity system in a multidomain of ${𝐑}^3$. This multidomain is the union of a horizontal plate with fixed cross section and small thickness ε, and of a vertical beam with fixed height and small cross section of radius $r^{\epsilon }$. The lateral boundary of the plate and the top of the beam are assumed to be clamped. When ε and $r^{\epsilon }$ tend to zero simultaneously, with $r^{\epsilon }\gg {\epsilon }^2$, we identify the limit problem. This limit problem involves six junction conditions.