The problem asks to determine the vertical displacement at a point "I" (likely implied as the midpoint of the horizontal beam) for a given structure subjected to an external load of 9 kN/m. The structure appears to be a rectangular frame fixed at points A and B, with a length L for the horizontal beam at the bottom. There's a uniformly distributed load (UDL) of 9 kN/m acting on the horizontal beam at the top of the frame.

1. Problem Description

The problem asks to determine the vertical displacement at a point "I" (likely implied as the midpoint of the horizontal beam) for a given structure subjected to an external load of 9 kN/m. The structure appears to be a rectangular frame fixed at points A and B, with a length L for the horizontal beam at the bottom. There's a uniformly distributed load (UDL) of 9 kN/m acting on the horizontal beam at the top of the frame.

2. Solution Steps

Since we don't have the material properties (E, I), and to proceed with the available information, we will make some assumptions.

- We will assume linear elastic behavior.

- We can use the principle of virtual work or Castigliano's theorem to solve this problem.

- Since we don't know EI we can only find the displacement in terms of it.

Let's assume the frame consists of 3 beams connected together.

- Two vertical members of length 'h' and a horizontal member of length 'L'.

The uniformly distributed load is 'q' kN/m.

Deflection at the center of a simply supported beam with UDL:

$\delta = \frac{5qL^4}{384EI}$

However, in this case, the horizontal member on top is not simply supported, but rather fixed to the two vertical columns.

For a fixed beam subjected to UDL, the deflection at the center is given by:

$\delta = \frac{qL^4}{384EI}$

Let's assume that the point "I" refers to the midpoint of the top horizontal beam.

Then the vertical displacement at point "I" would be:

$\delta_I = \frac{qL^4}{384EI}$

Substituting the value of q:

$\delta_I = \frac{9L^4}{384EI} = \frac{3L^4}{128EI}$

3. Final Answer

The vertical displacement at point I is: $\frac{3L^4}{128EI}$ where L is the length of the top horizontal beam and EI is the flexural rigidity of the beam.