Mechanical Properties of Solids | Class 11 Physics Notes

8.6 Applications of elastic behaviour of materials

This section discusses the practical importance of elastic properties in engineering and daily life. Knowledge of elastic moduli is essential for designing structures like buildings, bridges, cranes, and machines to ensure they can withstand loads without permanent deformation. For example, steel ropes used in cranes must have sufficient cross-sectional area so that tensile stress does not exceed yield strength, ensuring no permanent elongation. The section explains that ropes are made of many thin wires braided together for flexibility and strength. In bridge and building design, beams must resist bending; the deflection δ of a beam loaded at the center is given by δ = (W × l³) / (4 × b × d³ × Y), where W is load, l length, b breadth, d depth, and Y Young's modulus. Increasing depth d is more effective than breadth b in reducing bending, but deep beams may buckle if load is off-center. Hence, I-shaped cross sections are commonly used to balance strength and weight. Pillars with distributed ends support more load than those with rounded ends. The maximum height of mountains is limited by the elastic limit of rocks; the shear stress at the base must not exceed the critical shearing stress to prevent flow. Calculations show the maximum height is about 10 km, consistent with observed mountain heights. These examples illustrate how elastic properties govern design and natural phenomena.

📊 Diagram: Fig. 8.6 A beam supported at the ends and loaded at the centre.; (a); (b); (c); (a); (b)

🔗 Connection: Prepares for the summary section recapping key concepts of mechanical properties of solids.