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

Calculate the whole reaction at block, Calculate the whole reaction at bloc...

Calculate the whole reaction at block: A bar weighing 1 kg/m is bent at right angles into segments 0.60 m and 0.30 m long. It takes the position illustrated in Figure, while t

What are interconnecting pipe racks, Q. What are Interconnecting pipe racks...

Q. What are Interconnecting pipe racks? Interconnecting pipe racks carry the main process inlet, export and transfer lines and utility distribution lines to and from process an

Calculate additional force required to maintain equilibrium, Calculate Addi...

Calculate Additional force required to maintain equilibrium: Fo r the system shown in figure find the additional single force required to maintain equilibrium. Sol.: L

Determine the excavation of soil, Determine the Excavation of soil Exc...

Determine the Excavation of soil Excavation of soil in open well foundations is done  by dredging with grab buckets or similar equipment. The volume of excavated soil always e

Priority rules-conventional priority rules, Priority Rules A main conce...

Priority Rules A main concern rule is an algorithm that evaluates a priority number PN j for all operation j which enters the queue in front of a station (processing, cell, wo

Composite materials, Composite Materials While two various materials w...

Composite Materials While two various materials which neither react chemically nor dissolve in every other are combined together so they form a composite materials. Individual

The same magnitude as it did at the bottom, For the normal force in Figure ...

For the normal force in Figure to have the same magnitude at all points on the vertical track, the stunt driver must adjust the speed to be different at different points. Suppose,

Matlab program of location a point with respect a line, matlab program of l...

matlab program of location a point with respect a line

Applications of spot welding, Applications of spot welding As spot weld...

Applications of spot welding As spot welding can be employed for Al, Cu, Ni and Mg alloys. It is not advisable to spot weld steels with carbon content greater than 0.25 % unles

What is the drilling operation, What is the Drilling operation Drilling...

What is the Drilling operation Drilling operation can only performed in vertical direction. Hence drilling hole at angle is not performed by drilling machine. It is a big drawb

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