Question

The compression strength of concrete (the maximum pressure that can be exerted on the base of the structure) is 1.7 × 107 Pa. What is the height of the tallest cylindrical concrete pillar with a radius of 46 cm that will not collapse under its own weight?

Answer 1

Height of cylinder = 679.70 m

Explanation:

Compression strength = 1.7 x 10⁷ Pa

Normal force = Compression strength x Area

Radius = 46 cm = 0.46 m

Area of cylinder = π x 0.46² = 0.665 m²

Normal force =  1.7 x 10⁷ x 0.665 = 1.13 x 10⁷ N

So weight of cylinder = 1.13 x 10⁷ N

Density of concrete = 25 kN/m³ = 25000 N/m³

Volume of cylinder = Base area x Height = 0.665 x h

Weight of cylinder = 25000 x 0.665 x h

Equating

            25000 x 0.665 x h = 1.13 x 10⁷

                   h = 679.70 m

Height of cylinder = 679.70 m