A $5 \text{ m}$ long Aluminium tie rod of cross-section $0.20 \text{ m} \times 0.04 \text{ m}$ is subjected to a tensile force induced by its self-weight of $21.20 \text{ kg/m}$ considering gravitational acceleration of $10 \text{ m/s}^2$. If tensile Young's modulus of Aluminium is $70,000 \text{ MPa}$, the maximum tensile strain in the rod is ______________ $\times 10^{-6}$ (rounded off to two decimal places).
To determine the maximum tensile strain in the Aluminium tie rod, follow these steps:
- Calculate the total weight of the rod:
Weight per unit length is \(21.20 \text{ kg/m}\).
Total weight \(W = 21.20 \times 5 = 106 \text{ kg}\). - Convert the weight to force using gravitational acceleration \(g = 10 \text{ m/s}^2\):
\(F = 106 \times 10 = 1060 \text{ N}\). - Calculate the cross-sectional area \(A\) of the rod:
\(A = 0.20 \text{ m} \times 0.04 \text{ m} = 0.008 \text{ m}^2\). - Determine the stress \(\sigma\) in the rod using the formula \(\sigma = \frac{F}{A}\):
\(\sigma = \frac{1060}{0.008} = 132500 \text{ Pa} = 132.5 \text{ kPa}\). - Convert Young's modulus from MPa to kPa for consistency:
\(E = 70,000 \text{ MPa} = 70,000,000 \text{ kPa}\). - Calculate the tensile strain \(\epsilon\) using \(\epsilon = \frac{\sigma}{E}\):
\(\epsilon = \frac{132.5}{70,000,000} = 1.8929 \times 10^{-6}\). - The tensile strain is \(1.89 \times 10^{-6}\) when rounded to two decimal places.
Important Questions from Strength of Materials
- A steel wire of $5.65\text{ mm}$ diameter and $50\text{ m}$ length is used for a hoisting crane. The wire is used to vertically lift a weight of $200\text{ kg}$ attached to its lowest end. Assume the Young's Modulus of Elasticity of Steel as $2 \times 10^5\text{ N/mm}^2$ and gravitational acceleration as $10\text{ m/sec}^2$. The elongation of the steel wire (in mm ) will be ______ [rounded off to two decimal places].
A rectangular beam section of size 300 mm (width) X 500 mm (depth) is loaded with a shear force of 600 kN. The maximum shear stress on the section in N/mm² is ___________
- A load of 30 kN is applied vertically downward at the free end of a cantilever of span 5 m. If the elastic modulus of the cantilever is 30 GPa and the section has a width of 0.3 m and a depth of 0.6 m, then, the elastic deflection (in mm) is ________
- A solid straight steel rod of diameter 100 mm is bent in single curvature into a circular arc by a moment of 50 kNm applied at its ends. If elastic modulus, E, for steel is $2 \times 10^5$ MPa, the radius of curvature (mm) of the arc assuming $\pi=3.14$ is ________
A simply supported RCC beam of cross section $0.4 \text{ m} \times 0.6 \text{ m}$ covers a span of $8 \text{ m}$. It is subjected to a uniformly distributed load of $30 \text{ kN/m}$. If the unit weight of concrete is $24 \text{ kN/m}^3$, the tensile stress (in $N/mm^2$, rounded off to two decimal places) at the bottom of the beam at mid-span is______
