Determine the maximum permissible eccentricity of the load, Mechanical Engineering

Determine the maximum permissible eccentricity of the load:

A small hollow cylindrical column carries a compressive force of 400 kN. The external diameter of the column is 200 mm & the internal diameter is 120 mm. Determine the maximum permissible eccentricity of the load, if the permissible stresses are 60 N/mm2 in compression & 25 N/mm2 in tension.

Solution

External diameter, D = 200 mm

Internal diameter, d = 120 mm

Area of the section,

A = (π/4) (D2  - d 2 ) = (π/4) (2002  - 1202 ) = 2.01 × 104  mm2

Applied load, P = 400 kN = 4 × 105  N

Direct stress, f0= P /  A=        4 × 105 /2.01 × 104=  19.9 N/mm2  (compressive)

Let the eccentricity of the load = e mm.

Bending moment, M = P × e = (400 × 105 × e) N-mm

Section modulus,

z =  (π /64) (D4  - d 4 ) × (  2/d)

=  (π/32) ((200 4  - 1204 )/200) = 68.36 × 104   mm

Bending stress, f b   =± M/ Z

=± (4× 105 × e) /(68.36 × 10 4)

= ± 0.585 × e

Resultant stress at extreme fibres = f0  ± fb  = 19.90 ± 0.585 e

∴          Maximum compressive stress = (19.90 + 0.585 e) ----------- (a)

Minimum compressive stress = (19.90 - 0.585 e)

or         Maximum tensile stress = (0.585 e - 19.90)    ------- (b)

Therefore, (19.90 + 0.585 e) ≤ 60 N/mm2 (allowable compressive stress)

                              ∴ e ≤ 68.55 mm ---------------(c)

                 (0.585 e - 19.90) ≤ 25 N/mm2 (allowable tensile stress)

∴          e ≤ 8.72 mm                 ---------- (d)

 From these two conditions, the allowable maximum eccentricity = 8.72 mm from the centre of the section.

Posted Date: 1/21/2013 7:04:25 AM | Location : United States







Related Discussions:- Determine the maximum permissible eccentricity of the load, Assignment Help, Ask Question on Determine the maximum permissible eccentricity of the load, Get Answer, Expert's Help, Determine the maximum permissible eccentricity of the load Discussions

Write discussion on Determine the maximum permissible eccentricity of the load
Your posts are moderated
Related Questions
Explain the Base of radial drilling machine The base of the drilling machine handles the entire machine and when bolted to the floor, gives for vibration-free operation and bes


what is tool cost?

State of motion of body change with force: A body on contact with the surface is being pulled along it with the increasing force from zero. How does the state of motion of bo

Illustrate throttling process and free expansion process in details? A fluid is confined in a cylinder by a spring loaded frictionless piston so that pressure in the fluid is a

The Nissan leaf has a battery size of 24 kWh and autonomy of 84 miles.

Q. Ultrasonic Examination? Ultrasonic examination, UT and the acceptance criteria shall be in accordance with the Code and performed in accordance with written procedures. W

Tunnels: Tunnels become unavoidable for negotiating hills, where detours are costly. The tunnels in rock are not lined, but those in loose strata require a lining of cement c

What is STEP The STEP (Standard for External Representation of Product Data) project is supported by the ISO workgroup TC 184/SC4. it is also sometimes called Standard for Exch

Discover the increase in pressure: A copper tube of 50 mm diameter and 1200 mm length contains a thickness of 1.2 mm along closed ends. This is filled with water at atmospheri