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

Robotics, Application of group technology point wise

Application of group technology point wise

Determine mi of unequal angle section, Q .  Determine MI of unequal angl...

Q .  Determine MI of unequal angle section 15cm × 10cm × 1.5cm with longer leg vertical and is flange upwards. Figure Sol. :                      A 1 = 10 ×

String vibration fixed ends, String Vibration Fixed Ends In case of the...

String Vibration Fixed Ends In case of the vibrations of a string, both its ends at  x = 0  and  x = L  may be permanently fixed;  y (x = 0) = 0 , and  y (x = L) = 0 at all  t

Determine the moment of forces, Determine the moment of forces: The si...

Determine the moment of forces: The side of a square ABCD is 1.60 m long .Four forces equal to 6, 5, 4 and 8 N acts respectively along with the line CB, BA, DA, DB. Determine

Foundry shiz, is there any assignment answers

is there any assignment answers

I.c.engine.., proell governor,porter governor,watt governor

proell governor,porter governor,watt governor

Mechanical Engineering Careers Incorporating the Outdoors, Are there jobs i...

Are there jobs in the field of Mechanical Engineering that incorporate the outdoors? I am an outdoorsman for one, and a tradesman at heart and am currently a Mechanical engineering

Draw shear force and bending moment diagrams, A cantilever of length 2m car...

A cantilever of length 2m carries a uniformly distributed load of 1.5 KN/m run over the whole length and appoint load of 2KN at a distance of 0.5 from the free end draw the Shear

Determine and illustrate about the earth pressure at rest, Determine and il...

Determine and illustrate about the earth pressure at rest. EARTH PRESSURE AT REST You have seen that the active pressure is the minimum lateral pressure while the passive pr

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