To calculate the slenderness ratio of the wall, we need to determine the effective length and the least radius of gyration of the wall.

1. Effective Length:
The effective length of a wall is the distance between the cross walls. In this case, the wall is 5 meters long between cross walls. Therefore, the effective length (Le) is 5 meters.

2. Least Radius of Gyration:
The least radius of gyration (r) is a measure of the ability of the wall to resist buckling. It is given by the formula r = √(I/A), where I is the moment of inertia and A is the cross-sectional area of the wall.

To calculate the moment of inertia, we need to know the dimensions and properties of the cross-section. Given that the wall is made of modular bricks, each brick has a standard size of 190 mm x 90 mm x 90 mm.

3. Cross-Sectional Area:
The cross-sectional area (A) of the wall can be calculated by multiplying the thickness of the wall (200 mm) by the height of the wall (3.8 m). Converting the height to mm, we have:

A = 0.2 m x 3800 mm = 760 mm²

4. Moment of Inertia:
The moment of inertia (I) can be calculated by considering the individual moments of inertia of the bricks and summing them up. For a rectangular cross-section, the moment of inertia is given by the formula I = (b * h^3) / 12, where b is the width and h is the height of the cross-section.

Considering a single brick, the width (b) is 90 mm and the height (h) is 190 mm. Converting the dimensions to meters, we have:

I_brick = (0.09 m * 0.19 m^3) / 12 = 0.000291 m^4

Since the wall is made of multiple bricks, we need to consider the number of bricks in the cross-section. Assuming a joint thickness of 10 mm, the effective width of a single brick is 80 mm.

The number of bricks in the width of the wall (N_b) can be calculated by dividing the width of the wall (5 m) by the effective width of a single brick (0.080 m). Therefore:

N_b = 5 m / 0.080 m = 62.5

Since the number of bricks should be an integer, we can round it up to 63.

The moment of inertia of the wall (I_wall) is given by:

I_wall = N_b * I_brick = 63 * 0.000291 m^4 = 0.018333 m^4

5. Least Radius of Gyration:
The least radius of gyration (r) can now be calculated using the formula r = √(I/A):

r = √(0.018333 m^4 / 0.000760 m^2) = √(24.124) = 4.91 m

6. Slenderness Ratio:
Finally, the slenderness ratio (λ) is given by the formula λ = Le / r:

λ = 5 m / 4.91 m = 1.02

Therefore, the slenderness ratio of the wall is approximately