Find out longest span which beam would carry m uniform load, Mechanical Engineering

Q.  A supported rectangular beam with the symmetrical section 200mm in depth is having moment of inertia of 2.26 x 10-5 m4 about  its neutral axis. Find out longest span over which beam would carry a uniformly distributed load of 4KN/m run such that the stress because of bending does not exceed 125 MN/m2

Sol.: Given:

Depth d = 200mm = 0.2m

I = The moment of inertia = 2.26 × 10-5 m4

UDL = 4KN/m

Bending stress σ = 125 MN/m2 = 125 × 106 N/m2

Span = ?

As we know that Maximum bending moment for supported beam with UDL on its entire span can be given by = WL2/8

That is; M = WL2/8 ...(i)

ymax =  d/2 = 0.2/2 = 0.1m

M = σ.I/ymax = [(125 × 106) × (2.26 × 10-5)]/ 0.1 = 28250 Nm ...(ii)

Substituting this value in the equation (i);

28250 = (4 × 103)L2/8

L = 7.52m .......ANS 

Posted Date: 10/20/2012 8:28:13 AM | Location : United States







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