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
Find out the angle of force: Q: A uniform wheel having 60 cm diameter weighing 1000 N rests against rectangular obstacle   15 cm high. Find least force required which when ac

what is relation between tool life and cutting speed?


Effect of the parameters in spot welding The passage of more current than what is required causes the following defects. I. Weld expulsion ii. Cavitations iii. Weld cracking

Working of a Four-stroke Engine: To understand the working of a four-stroke motorcycle engine, the whole operation can be divided into four parts, known as strokes. The strokes ar

eXPLAIN THE GRAPHICAL IMPLEMENTATION OF TOOL PATH GENERATION

Gradual Engagement : The clutch should positively take the drive gradually without the occurrence of sudden jerks.


Find the maximum torque - I-section: An I-section 150 × 80 mm has flanges 6 mm thick and web 4 mm thick. Discover the maximum torque that may be safely applied if the shear st

a) Describe Quality. What are various quality measures. b) A steel chairs manufacturer is also the quality inspector in his manufacturing unit this parameter of a chair being de