Find dmension of strongest rectangular beam, Mechanical Engineering

Q. Find the dimension of strongest rectangular beam that can be cut out of log of 25 mm diameter.

Sol.: b2 +  d2 = 252

d2 = 252 -  b2

As M/I = σ/y; M = σ(I/y) = σ.Z

M is maximum when Z is maximum
Z =  I/y = (bd3/12)/(d/2) =  bd2/6 =  b.(252 -  b2)/6

The value of Z maximum at  dZ/db = 0;

That is, d/db[252b/6 -  b3/6] = 0

252/6 - 3b2/6 = 0b2 = 625/3;

b = 14.43 mm .......ANS

d = 20.41 mm .......ANS
611_beam.png

Posted Date: 10/20/2012 8:24:07 AM | Location : United States







Related Discussions:- Find dmension of strongest rectangular beam, Assignment Help, Ask Question on Find dmension of strongest rectangular beam, Get Answer, Expert's Help, Find dmension of strongest rectangular beam Discussions

Write discussion on Find dmension of strongest rectangular beam
Your posts are moderated
Related Questions
Q.  W rite down the basic formula for maximum bending moment in some ideal cases. Sol.:   Ber m together with nature of load Maximu

Find out the number of revolution: A flywheel of mass 20 kg and radius 100 mm is made to rotate at 600 RPM. Determine the KE of the flywheel. If the frictional couple at its b

Metals and Melting Practices - Alloy,Blowing,Carbon Monoxide Normal 0 false false false EN-IN X-NONE X-NONE Microsoft

Sand Blasting: Historically sand blasting was operated with only using sand only as abrasive media. Today the advance of technologies had brought manufacturer more variety in

Permanent Way: Definition In railway engineering, the permanent way refers to the earthen formation and the track structure over it. Gauge The separation

What does initial velocity mean?

analytical method for determining the acceleration and velocity?

how to find mass of sleeve in porter governor

Occupational Safety Acts The occupational safety Acts are intended to cover every employees (even if single) and all kinds of employers from manufacturing and construction to

what are the practical applications and use of finding uniform distributed load, concentrated point load, inclined point load, roller supported beam.