Numerical - Bending stress, given load & beam dimensions

Q.  A uniformly distributed load of 20 kN/m acts on a simply supported beam of rectangular cross section of width 20 mm and depth 60 mm. What is the maximum bending stress acting on the beam of 5m?
- Published on 21 Sep 15

a. 5030 Mpa
b. 5208 Mpa
c. 6600 Mpa
d. Insufficient data

ANSWER: 5208 Mpa

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    Discussion

  • Azahar   -Posted on 31 May 20
    Length of the beam is not mentioned in question but in the solution length is taken as 5 m how it is taken plz explain.
  • Sravanthi   -Posted on 24 Nov 15
    - Given: udl = 20 kN, length of beam = 5 m, width of rectangle = 20 mm, depth of rectangle = 60 mm.

    Formula:

    Solution:

    1) Position of neutral axis = y = Depth/2 = 60/2 = 30 mm

    2) Bending moment = M = (wL2) / 8 = (20 x 25) / 8 = 62.5 kN

    3) Moment of inertia (I) = (BD3) / 12 = (20 x 603) / 12 = 0.36 x 106 Mpa

    The maximum bending stress is given as σmax = (M/I) y

    = [(62.5 x 103) / (0.36 x 106)] x 30

    = 5208 Mpa

    Therefore,
    The maximum bending stress acting on the beam of 5 m is 5208 Mpa.

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