Solid Mechanics
posted by rakesh .
Determine the ratio of strenghts of a solid steel column to that a hollow column of the same material and having the same cross sectional area. The internal diameter of the hollow column is 1/2 of its external diameter. Both the columns are same length and are pinned at their both ends

Hints:
Axial stress is the same because the same load is distributed over the same area.
However, buckling strength is widely different.
Calculate the ratio of the area moments of inertia, and compare buckling their strengths using Euler's buckling formula:
F=π²2EI/(KL)²
where E,I are Young's modulus, I=area moment of inertia, K=end condition constant, equals 1 when pinned, and L=length of columns.
See also for more explanation on buckling:
http://en.wikipedia.org/wiki/Buckling
or other textbooks on strength of materials.
Respond to this Question
Similar Questions

chemistry
Reaction 1: I2(aq)Cu^+2(aq) Ag^+(aq)Br2(aq) Column 1Column 2Column 3Column 4Column 5 I(aq)XXTT Cu(s)TXTT Ag(s)XXXT Br(aq)XXXX Reaction of metals and solution of ions Reaction … 
Chemistry
Hi, I have a question on column length for HPLC (high performance liquid chromatography). If the column length is increased,eg from 100mm to 150mm and all other column parameters e.g. particle size of stationary phase, internal diameter..etc.remain … 
physics
A hollow steel shaft has an external diameter of 120 mm and is 10 mm thick. It is coupled to a solid shaft of the same material, 100 mm in diameter. If the length of the hollow shaft is 960 mm, find the length of the solid shaft, so … 
solid mechanics
A hollow cylindrical steel tube of 3.8 cm external dia & 2.5 thick is used as a column of 2.3 m long with both ends hinged. Determine the safe load by I.S Code. 
solid mechanics
Find the Euler's crippling load for a hollow cylindrical steel column of 3.8 mm external diameter and 2.5 mm thick. Take length of the column as 2.3 m and hinged at its both ends crippling load by Rankine's formula. Using constants … 
Engineering
Steel column is 80 feet tall. Column is a W 14 x 730(wideflange beam) The cross sectional area is 215 sq in. Supports a floor load of 6600 K. Determine the stress in the column and how much it will shorten due to the 6600K load. (Assume … 
Physics matter and its properties
A circular metal column is to support a load of 500 Tonne and it must not compress more than 0.1 mm. The modulus of elasticity is 210 GPa. the column is 2 m long. Calculate the cross sectional area and the diameter. (0.467 m^2 and … 
physics
Each vertical steel column of an office building supports a weight of 1.30 x 10^5 N and is compressed to 5.90 x 10^3 A) Find the compression in each column if a wegith of 5.50 x 10^5 N is supported. B)If the compression of each steel … 
mechanics
Short column of rectangular cross section 160mm by 60mm carrying point load of 40 KN at max eccentricity position along the longer axis so that no tensile stress is applied. I worked out max eccentricity as 26.66 mm from RH and LH, … 
Chemistry
One atmosphere of pressure will push a column of mercury to a height of 760 mm when the closs sectional area of the column is 1.00 cm.what would be the height of the column of mercury supported by the atmosphere if its cross sectional …