Evaluate the maximum bending stresses, Mechanical Engineering

Evaluate the maximum bending stresses:

A beam of I-section illustrated in Figure is simply supported over a span of 10 m. It carries an uniform load of 4 kN/m over the whole span. Evaluate the maximum bending stresses.

2444_Determine the maximum bending stresses1.png

   Cross-section of Beam                 Bending Stress Distribution

Figure

Solution

Moment of inertia, I =1/12  (BD3 - bd3)

=          (1/12) (300 × 6603 - 280 × 6003)

= 21.474 × 108 mm4

Span of beam, l = 10 m

Uniformly distributed load, w = 4 kN/m

Maximum bending moment at the centre of beam, M = wl 2/ 8

Therefore,        M =4 × 10 2 / 8

= 50 kN m

= 5 × 107 N mm

Neutral axis passes by the centroid of I-section.

 The distance of top and bottom layer from neutral axis, y = 330 mm

 

Thus, Bending stress, σ = (M / I )× y

= (5 × 10 7 / 21.474 × 108 )× 330 = 7.68 N/mm2

So the bending stress at top and bottom layers = 7.68 N/mm2.

Posted Date: 1/22/2013 12:20:08 AM | Location : United States







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