diameter stress

Question

6.2 The ratio between the outside diameter and the inside diameter of a cast iron pipe is 4 and the length of the pipe is 900 mm when the pipe is not subjected to any load. When a tensile load of 950 kN is applied to the cast iron pipe, its length increases by 0,95 mm. Young's modulus of elasticity for the cast iron is 300 GPa. Calculate the following: 6.2.1 The inside diameter of the pipe 6.2.2 The outside diameter of the pipe 6.3 The compressive stress on a concrete pillar with a square profile of 30 cm x 30 cm is 4,5 MPa. Calculate the maximum allowable load on the pillar.

Answer 1

(6.2.1) and (6.2.2)

The ratio of the inner and outer diameter is 4.

Outer Diameter of  copper pipe is 4x

Inner Diameter of copper pipe is x

Length of the copper pipe is 900 mm.

Tensile load = 950 kN

The Length increases by 0.95 mm.

Young's modulus E = 300 Gpa

We know that E = stress/strain

Stress = E * strain.

strain = change in the length / original length.

Strain = 0.95 / 900 = 1.056 * 10^-3

Stress = E * strain.

Stress = 300 * 10^9 *1.056 * 10^-3

stress =  31.68* 10^7 Pa.

Diameter of outer pipe is 4x then outer radius = 4x/2 = 2x.

Area of the copper pipe = π (2x)²

Stress = Force / area.

Area = Force / stress

Area = (950 * 10 ³) / 31.68 * 10^7

π (2x)² = 2.998 * 10^-3

(2x)² = 9.54 * 10^-4

2x = 0.03089

x = 0.0154

x = 15.4 mm

The Outer diameter of the pipe is 4x = 61.6 mm.

The Inner diameter of the pipe is x = 15.4 mm.

Answer 2

(6.3)

The Compressive Stress = 4.5MPa.

The square profile dimensions are 30 cm * 30cm.

Side of the square profile = 30cm.

Area of the Square Profile = A²

Area = (30 cm)²

Area = 900 cm².

We know that stress = Force / Area.

Force = Stress * area

Force = 4.5 MPa * 900 cm²

Force = 4.5 * 10^6 * 900 *10^-4

        = 405000 N

Force F = 405 kN

Therefore Maximum allowable load on the pillar = 405 kN