Find dmension of strongest rectangular beam, Mechanical Engineering

Assignment Help:

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


Related Discussions:- Find dmension of strongest rectangular beam

Age-hardening of aluminium alloys, Age-hardening of Aluminium Alloys I...

Age-hardening of Aluminium Alloys In specific alloys precipitation from a single phase may arise. The precipitate phase might be in form of determine sub-microscopic particles

Analyze motion of the two bodies connected by string, Analyze motion of the...

Analyze motion of the two bodies connected by string: Analyze motion of the two bodies connected by string one of which is hanging free and other lying on smooth inclined pla

Supply chain management, Supply Chain Management: In this unit, you ha...

Supply Chain Management: In this unit, you have learned that the supply chain is the network of autonomous and semi-autonomous business entities, which are include through ups

Mechanicalthermodynamics, Does this college offer courses in the field of m...

Does this college offer courses in the field of mechanicalthermodynamics?

Evaluate thermal efficiency of the engine, A carnot engines performs betwee...

A carnot engines performs between two reservoirs whose difference in temperature is 200 o C. If the work output of the engine is 0.5 times the heat rejected, make evaluation for th

Locomotive boiler, LOCOMOTIVE BOILER: It is horizontal, natural cir...

LOCOMOTIVE BOILER: It is horizontal, natural circulation, fire tube boiler. It can generate steam at the rate of 7000 kg/hr. at pressure of up to 2.5 Mpa. Earlier it was us

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd