There is a chimney of 40 m height and 2.5 m diameter. The wind blows at 20^∘ C against the chi

step 1 We treat the wind load as a uniform drag force distributed along the height, and then take momen

There is a chimney of 40 m height and 2.5 m diameter. The...

There is a chimney of $40 \mathrm{~m}$ height and $2.5 \mathrm{~m}$ diameter. The wind blows at $20^{\circ} \mathrm{C}$ against the chimney at 2.0 $\mathrm{m} / \mathrm{s}$, determine the moment that must be developed at its base to hold it in place. Consider the chimney to be a rough cylinder.

Key Concepts

Wind Pressure

Wind pressure is the force per unit area exerted by moving air on a surface. It is typically calculated using the dynamic pressure formula, where the pressure is proportional to the square of the wind speed and the density of air. This concept is fundamental in determining the force that wind applies to structures.

Force on Structures

The force exerted by wind on a structure is found by multiplying the wind pressure by the effective area exposed to the wind. In the case of cylindrical structures, the projected area (which is the product of the height and the diameter for a cylinder) is used to estimate this force, sometimes adjusted by a drag coefficient to account for the influence of shape and surface roughness.

Aerodynamic Drag Coefficient

The aerodynamic drag coefficient quantifies the resistance a structure offers to the flow of air. It is a dimensionless number that characterizes how effectively a structure converts wind pressure into actual force. This coefficient is crucial for accurately determining the wind force acting on irregular or rough surfaces.

Moment (Bending Moment)

The moment, or bending moment, at a particular point in a structure is the product of a force and its lever arm distance from that point. For structures subjected to wind loading, the moment at the base is calculated by multiplying the wind-induced force by the distance from the base to the center of pressure. This concept is essential in analyzing the stability and structural integrity of tall structures under wind loads.

Center of Pressure

The center of pressure is the point on a structure where the total sum of a pressure field acts, resulting in a force distribution with an equivalent single force. Its location is determined by the geometry of the structure and the distribution of wind pressure, and it serves as the effective point at which wind forces are applied for moment calculations.

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