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Experimental Mechanics

, Volume 26, Issue 1, pp 28–33 | Cite as

Determination of loads applied perpendicularly to the outer boundary of a ring using coefficients of influence

  • AJ Durelli
  • YH Lin
Article
  • 66 Downloads

Abstract

A procedure is explained to determined the amount of several pairs of diametrical loads applied to the outside boundary of a ring when stresses at selected points of the inside or outside boundaries are known. Coefficients of influence are used, following an approach similar to the one presented in a previous paper. Examples of application are given and the possible increase in precision is shown when the number of points of measurements is larger than the number of loads to be determined.

Keywords

Mechanical Engineer Fluid Dynamics Outer Boundary Diametrical Load 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

a

normalizing factora=P′/πRo=P/tπRo lb/in.2 or kg/cm2

f

photoelastic material fringe value psi.-in/fringe or kg/cm/fringe

F

photoelastic model fringe value:Ft=f

gij

fringe order at pointi when loadP'j=1; in/lb or cm/kg

K

normalized stress or stress factor, dimensionless (pure number)

Kij

stress factor for pointi produced by force at pointj

m

number of applied loads

n

number of points at which measurements are taken

n

fringe order

P

load applied to the ring

P′j

load per unit thickness, applied to the ring at one or several positionsj

r

residual

Ri

inside radius of the ring

Ro

outside radius of the ring

s2

residual variance

t

thickness of the ring

α

ID/OD

ε

direct or ‘normal’ strain

σ1, σ2

principal stresses σ1 > σ2 algebraically

σr

normal stress in direction perpendicular to the boundary

σθ, σ

normal stress in direction tangential to the boundary

σθij, σij

normal stress tangential to the boundary at positioni produced by the force applied at pointj. Stress locationi and load locationj variable

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References

  1. 1.
    Durelli, A.J. and Lin, Y.H., “Stresses and Displacements on the Boundaries of Circular Rings Diametrically Loaded,” to be published in the J. Appl. Mech.Google Scholar
  2. 2.
    Durelli, A.J. andWu, D., “Use of Coefficients of Influence to Solve Some Inverse Problems in Plane Elasticity,”J. Appl. Mech.,50 (2),288–296 (June1983).Google Scholar
  3. 3.
    Roark, R., Formulas for Stress and Strain, McGraw-Hill, New York, 156–159 (1954).Google Scholar
  4. 4.
    Ripperger, E.A., and David, N., “Critical Stresses in a Circular Ring,” Proc. ASCE (Feb. 1946).Google Scholar
  5. 5.
    Nelson, C.W., “Stresses and Displacements in a Hollow Circular Ring,” Thesis at Univ. of Mich. (Ann Arbor), (1939).Google Scholar
  6. 6.
    Frocht, M., Photoelasticity, John Wiley and Sons, New York (1941).Google Scholar
  7. 7.
    Bell, George, “Theorie and Versuche ueber einige Faelle von Spannungsverteilung in ringfoermingen Koerpern—Zeitschrift fuer angew,”Math und Mech.,10 (1),52–73 (Feb.1930).MATHGoogle Scholar
  8. 8.
    Durelli, A.J. andParks, V.J., Moire Analysis of Strain, Prentice Hall, Englewood Cliffs, NJ (1970).Google Scholar
  9. 9.
    Wonnacott, R.J. and Wonnacott, T.H., Econometrics, John Wiley and Sons (1966).Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 1986

Authors and Affiliations

  • AJ Durelli
    • 1
  • YH Lin
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of MarylandCollege Park

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