Understanding Modulus of Elasticity for Steel

The modulus of elasticity, often denoted by \(E\), is a fundamental mechanical property of a material. It describes a material's stiffness or resistance to elastic deformation under stress. In simpler terms, it tells us how much a material will stretch or compress when a force is applied to it, within its elastic limit.

For isotropic materials like steel, the modulus of elasticity is also known as Young's Modulus.

Standard Value of Modulus of Elasticity of Steel

Steel is widely used in construction and engineering due to its strength and stiffness. The modulus of elasticity of steel is a well-established value used in structural calculations.

The commonly accepted value for the modulus of elasticity of structural steel is approximately 200 GPa (Gigapascals).

Units Conversion

The options provided in the question are in \(\text{KN/mm}^2\). Let's understand how GPa relates to this unit:

• 1 GPa = \(1 \times 10^9\) Pascals (Pa)
• 1 Pa = \(1 \text{ N/m}^2\)
• So, 1 GPa = \(1 \times 10^9 \text{ N/m}^2\)

We need to convert N/m\textsuperscript{2} to KN/mm\textsuperscript{2}:

• 1 KN = \(1000 \text{ N}\)
• 1 mm = \(10^{-3} \text{ m}\)
• So, 1 \(\text{mm}^2\) = \((10^{-3} \text{ m})^2\) = \(10^{-6} \text{ m}^2\)
• \(1 \text{ N/m}^2\) = \(\frac{1 \text{ N}}{1 \text{ m}^2}\)
• To get \(\text{KN/mm}^2\), we can write:
• \(1 \text{ GPa} = 1 \times 10^9 \text{ N/m}^2 = \frac{1 \times 10^9 \text{ N}}{1 \text{ m}^2}\)
• \(\frac{1 \times 10^9 \text{ N}}{1 \text{ m}^2} = \frac{1 \times 10^9 \text{ N}}{1 \times (1000 \text{ mm})^2} = \frac{1 \times 10^9 \text{ N}}{1 \times 10^6 \text{ mm}^2} = \frac{1000 \text{ N}}{\text{mm}^2}\)
• Since 1 KN = 1000 N, we have:
• \(1000 \text{ N/mm}^2 = \frac{1000 \text{ N}}{1 \text{ mm}^2} = \frac{1 \text{ KN}}{1 \text{ mm}^2} = 1 \text{ KN/mm}^2\)

Therefore, \(1 \text{ GPa} = 1 \text{ KN/mm}^2\).

The standard value of modulus of elasticity of steel, 200 GPa, is equivalent to 200 \(\text{KN/mm}^2\).

Comparing with Options

Let's compare the calculated value with the given options:

• Option 1: 200 \(\text{KN/mm}^2\)
• Option 2: 225 \(\text{KN/mm}^2\)
• Option 3: 250 \(\text{KN/mm}^2\)
• Option 4: 275 \(\text{KN/mm}^2\)

The standard value for the modulus of elasticity of steel is 200 \(\text{KN/mm}^2\).

Conclusion on Steel Modulus of Elasticity

Based on standard material properties used in engineering, the modulus of elasticity of steel is assumed to be 200 \(\text{KN/mm}^2\).

Revision Table: Modulus of Elasticity

Additional Information on Steel Properties

Besides the modulus of elasticity, other important properties of steel include:

• Yield Strength: The stress at which the material begins to deform plastically.
• Ultimate Tensile Strength: The maximum stress the material can withstand before fracturing.
• Poisson's Ratio: The ratio of transverse strain to axial strain when a material is stressed axially. For steel, it's typically around 0.3.
• Density: The mass per unit volume, approximately 7850 \(\text{kg/m}^3\) for steel.

These properties are crucial for designing safe and efficient structures using steel.