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
Find out its centre of gravity: A square plate of uniform thickness and density is bent along M 1 M 2 till corner C coincides along with centre C′. Find out its centre of gr

Structural notches In t he case of solid solution strengthened alloys and age hardenabled steel, the variation in heat i/o during welding may cause localized grain coarsening o

Q. Working of Burner Assembly in steam generators? The Steam Generators shall be equipped with a packaged burner assembly consisting of a burner, combustion air fan, ductwork,

Equations of static equilibrium: In particular, if the forces are parallel and we take z-axis parallel to them, then the first, second and last equations are identically satis

Evaluate the centroid of an area: Determine the centroid of an area shown in Figure (a). Solution This problem may be attempted in two ways as illustrated in Figu

Total decrease in length: Q: A hollow cast iron cylinder 4 m long, 300 mm is the outer diameter, and thickness of metal 50 mm is subjected to central load on top when standin

Draw the Gas welding System and label its parts. Illustrate the several types of flames used in gas welding along with temperature range.

A suspended walkway in an underground cavern consists of a deck supported by three tie rods placed symmetrically about the centre as shown below: The rods are each of

Explain desirable properties of modeling and differentiate between the process of casting and modeling. Also highlight the advantages and disadvantages of casting process and model

Short-Term Scheduling And Control The major objective at this stage is to make sure the efficient and smooth operation of the system in the event of unforeseen disturbances. Th