Question

A structural steel rod has a radius of 10mm and a length of 1m. A 100kN force stretches it along its length. Calculate (a) stress (b) elongation and(c) strain on the rod. Young's modulus of structural steel is 2x10¹¹ N/m².

Answer 1

GIVEN :

• Radius of a structural steel rod = 10 mm.
• Length of a structural steel rod = 1 m.
• Tensile force, F = 100 k N.
• Young modulus of structural steel = 2 × 10¹¹ N/m².

TO CALCULATE :

1. Stress = ?
2. Elongation = ?
3. Strain on the rod = ?

FORMULAS USED :

• Stress = Force/cross sectional area.
• Elongation, ∆L = (F/L)/(A/Y).
• Strain = ∆L/L.

SOLUTION :

Stress = Force/cross sectional area.

$\implies$ F/A

$\implies$ 100,100/(π 0.010² pa)

$\implies$ 318.309 MPa.

Elongation, ∆L = (F/L)/(A/Y)

$\implies$ ∆L = 3.18 × 10⁸ × 1/2.0 × 10¹¹

$\implies$ ∆L = 1.59 × 10-³ m.

$\implies$ ∆L = 1.59 mm.

Strain = ∆L/L

$\implies$ 1.59 × 10-³/ 1

$\implies$ 1.59 × 10-³

Answer 2

Explanation:

SOLUTION :

Stress = Force/cross sectional area.

⟹ F/A

⟹ 100,100/(π 0.010² pa)

⟹ 318.309 MPa.

Elongation, ∆L = (F/L)/(A/Y)

⟹ ∆L = 3.18 × 10⁸ × 1/2.0 × 10¹¹

⟹ ∆L = 1.59 × 10-³ m.

⟹ ∆L = 1.59 mm.

Strain = ∆L/L

⟹ 1.59 × 10-³/ 1

⟹ 1.59 × 10-³

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