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 ___________
Maximum Shear Stress Calculation for Rectangular Beam
The problem asks to find the maximum shear stress ($\tau_{max}$) in a rectangular beam section subjected to a shear force (V).
Given:
- Beam width, $b = 300$ mm
- Beam depth, $d = 500$ mm
- Shear force, $V = 600$ kN $= 600 \times 10^3$ N
Beam Section Properties
The area (A) of the rectangular section is calculated as:
$ A = b \times d $
Substituting the given values:
$ A = 300 \text{ mm} \times 500 \text{ mm} = 150,000 \text{ mm}^2 $
Average Shear Stress Calculation
The average shear stress ($\tau_{avg}$) is the shear force divided by the cross-sectional area:
$ \tau_{avg} = \frac{V}{A} $
$ \tau_{avg} = \frac{600 \times 10^3 \text{ N}}{150,000 \text{ mm}^2} = 4 \text{ N/mm}^2 $
Maximum Shear Stress Determination
For a rectangular section, the maximum shear stress occurs at the neutral axis and is related to the average shear stress by a factor of 1.5:
$ \tau_{max} = 1.5 \times \tau_{avg} $
$ \tau_{max} = 1.5 \times 4 \text{ N/mm}^2 = 6 \text{ N/mm}^2 $
Therefore, the maximum shear stress on the section is $6$ N/mm².
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 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______
- A simply-supported steel beam made of an I-section has a span of $8 \text{ m}$. The beam is carrying a uniformly distributed load of $15 \text{ kN/m}$. The overall depth of the beam is $450 \text{ mm}$. The moment of inertia of the beam section is $18000$ cm$^4$. The maximum bending stress in the beam will be _________ N/mm$^2$. [in integer]
