Project ForgeA massless beam AC of length 4000 mm rests on a support at A and a support at C. It carries a uniformly distributed load of 3000 N/m over the right half only, from B (2000 mm from A) to C (2000 mm further, i.e. 4000 mm from A). The beam has a rectangular cross-section of width 30 mm and height 100 mm. The maximum bending moment occurs at
- ALocation B
- B2675 mm to the right of A
- 2500 mm to the right of A
- D3225 mm to the right of A
Explanation
Total UDL load=3000×2=6000N, acting at its centroid x=3000mm from A. Taking moments about A: Rc×4000=6000×3000 ⟹ Rc=4500N, Ra=1500N. For 0≤x≤2000mm, V=Ra=1500N (constant, no load on AB). For 2000≤x≤4000mm, V=1500-3000(x-2000)/1000 (x in mm, load in N/mm converted). Setting V=0: x=2000+1500/3=2500mm.
Source: GATE ME 2010 (2010)
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