Given Data:
Diameter at the base (D1) = 200mm
Diameter at the top (D2) = 100mm
Height of the post (H) = 8m
Horizontal load (F) = 500N



To calculate the area of the concrete flag post at the base and top, we need to use the formula for the area of a circle:

Area (A) = π * (radius)^2

Area at the base (A1):
Radius at the base (R1) = D1/2 = 200mm/2 = 100mm = 0.1m
A1 = π * (0.1)^2

Area at the top (A2):
Radius at the top (R2) = D2/2 = 100mm/2 = 50mm = 0.05m
A2 = π * (0.05)^2



The pressure exerted by the horizontal load can be calculated using the formula:

Pressure (P) = Load (F) / Area (A)

Pressure at the top (P2):
P2 = F / A2



The compressive stress on the concrete flag post can be calculated using the formula:

Stress (σ) = Pressure (P) / Area (A)

Stress at the top (σ2):
σ2 = P2 / A2



The diameter of the concrete flag post varies from 200mm at the base to 100mm at the top. By calculating the areas at the base (A1) and top (A2) using the formula for the area of a circle, we can determine the cross-sectional areas of the post.

To analyze the pressure exerted by the horizontal load (F), we calculate the pressure at the top (P2) using the formula and the calculated area at the top (A2).

Finally, to determine the compressive stress on the concrete flag post, we divide the pressure at the top (P2) by the area at the top (A2). This stress provides insights into the structural integrity of the post and its ability to withstand the applied load.