Determine the maximum stress developed in the beam, Mechanical Engineering

Determine the maximum stress developed in the beam:

An I section in Figure is utilized as a beam. The beam is subjected to a bending moment of 2.5 kN m at its neutral axis. Determine the maximum stress developed in the beam.

 1648_Determine the maximum stress developed in the beam.png

Beam Section                                 Bending Stress Distribution

Figure

Solution

 Assume 1713_Determine the maximum stress developed in the beam1.png be the distance of centroid from the bottom face.

Then, 1713_Determine the maximum stress developed in the beam1.png  =∑ ay / ∑ a

   1713_Determine the maximum stress developed in the beam1.png= ((100 × 20) ×10 + (20 ×100) × 70 + (60 × 20) ×130) /((100 × 20) + (20 ×100) + (60 × 20))

= 60.8 mm

 Moment of inertia of the section around the horizontal axis passing through the centriod,

I = [(1/12) ×100 × (20)3 + (100 × 20)(60.8 - 10)2 ]

+[ (1/12) × 20 (100)3 + (20 ×100)(70 - 60.8)2 ]

+ [(1/12) × 60 (20)3 + (60 × 20)(130 - 60.8)2 ]

= 1285.04 × 104 mm4

Topmost layer distance, yt = 140 - 60.8 = 79.2 mm

Bottommost layer distance, yb = 60.8 mm

∴          ymax = yt = 79.2 mm

 Through the relation,  M/ I = σ/ y

We obtain,       σmax = ( M/ I) × ymax

Bending moment,  M = 2.5 kN m

                                   = 2.5 × 106 mm

∴          σmax =  (2.5 × 10 6/1285.04 × 104)  × 79.2 = 15.41 N/mm

∴  The maximum bending stress in the beam = 15.41 N/mm2.

Posted Date: 1/21/2013 7:32:21 AM | Location : United States







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