Project ForgeStrength of Materials
Bending of Beams
GATE 2010
Hard
For the same beam (span 4000 mm, UDL 3000 N/m over the right half from B to C, rectangular cross-section 30 mm × 100 mm, supports at A and C), the maximum magnitude of bending stress (in MPa) is given by
- A60.0
- 67.5
- C200.0
- D225.0
Explanation
At x=2500mm (the zero-shear location from the previous part), Mmax=Ra×2500 - 3000×(500)²/(2×1000)=1500×2500-3000×250000/2000=3,750,000-375,000=3,375,000 N·mm. I=bh³/12=30×100³/12=2,500,000 mm⁴, ymax=50mm. σmax=Mmax·ymax/I=3,375,000×50/2,500,000=67.5 MPa.
Source: GATE ME 2010 (2010)
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