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

Torsion, diameter = 100mm length = 470mm power = 4000 w radians = 78 shear ...

diameter = 100mm length = 470mm power = 4000 w radians = 78 shear modulus 60000 n/mm^2 determin the maximum shear stress and angle of twist

Determine the water depth - standard step method, Consider a trapezoidal ch...

Consider a trapezoidal channel with a bottom width of 4 m, side slopes of 3:1 (H:V), and a bottom slope of 0.002 that carries 50 cms. The channel has a Manning's roughness of 0.034

Compute the centroidal moment of inertia, Compute the centroidal moment of ...

Compute the centroidal moment of inertia: Compute the centroidal moment of inertia of a thin homogeneous bar AB of length l and having a mass of m kg Solution The mass

Objectives of motorcycle servicing , Objectives After studyingmotercyc...

Objectives After studyingmotercycle servicing, you should be able to appreciate the importance of regular servicing and maintenance of a motorcycle and also to recommen

Derive eulers equation of motion, (a) Reduce expression for the net pressur...

(a) Reduce expression for the net pressure and depth of centre of pressure in case of an inclined plan surface submerged in a fluid. (b) Derive Euler's equation of motion along

Illustrate reversible-irreversible and quasi-static process, (a) Illustrate...

(a) Illustrate reversible, irreversible and Quasi-static process with examples. (b) What do you mean by terms change of state, path, process, property, cycle. (c) Distinguish

#title.gear train, explain the working of gear trainAsk question explain de...

explain the working of gear trainAsk question explain detail#Minimum 100 words accepted#

Arc welding power sources classify-output characterstics, ARC WELDING POWER...

ARC WELDING POWER SOURCES CLASSIFICATION:OUTPUT CHARACTERSTICS The output characteristic of welding power source is a funct ional relationship between output voltage and load

Disc clutch friction thickness, Disc clutch friction thickness: Check disc...

Disc clutch friction thickness: Check disc clutch friction thickness which should be minimum of 2.6 mm.

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