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Rapid interpretation of moiré photographs

Second-order moiré is used to determine the reinforcement and shear forces in slabs

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Abstract

The paper describes the possibilities of rapidly and conveniently obtaining results by means of the reflection moiré method.

The moiré photographs are produced with the aid of a screen provided with a finely ruled grid. The contrast of the photographs is increased by optical means. By displacement of two equal moiré photographs, moiré fringes of second order for the curvature or the twist are obtained.

It is shown how charts can be produced which indicate:

  1. (a)

    The distribution of the bending moments

  2. (b)

    The distribution of the bending moments for which the reinforcement should be designed

  3. (c)

    The distribution of the shear forces and the magnitude of the bearing reactions.

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Abbreviations

a :

distance between model and screen

D :

flexural rigidity of a plateEt 3/[12(1 -v 2)]

d :

pitch of the ruled screen

E :

modulus of elasticity

f :

focal length of lens

h :

displacement of two moiré photographs (in the direction of the subscript)

k, l, m :

integers

m x m y :

bending moments per unit length

m xy m ni :

twisting moments per unit length

\(\bar m_x ,\bar m_y \) :

moments on which the reinforcement inx resp.y direction should be designed

n :

direction which makes an angle α with thex axis

P :

single load

Q :

total shearing force

q x q y q r :

shearing force per unit length

q :

intensity of continuously distributed load

r :

direction which makes an angle β with thex axis

t :

thickness of a plate

ω:

deflection

x, y, z :

rectangular coordinates

α, β, γ, ω:

angles

φ:

slope

ν:

Poisson's ratio

Δω:

\(\partial ^2 w/\partial x^2 + \partial ^2 w/\partial y^2 \)

σ:

normal stress

τ:

shear stress

References

  1. Ligtenberg, F. K., “The Moiré Method,” {jtProc. Soc. Exp. Stress Anal., {vnXII ({sn2}) ({dy1955}).

  2. Dantu, P., “Utilisation des Réseaux pour l'Etude des Déformations,” Annales de l'Institut Technique du Bâtiment et des Travaux Publics, 121 (Jan. 1958).

  3. De Haas, H. H., and Loof, H. W., “An Optical Method to Facilitate the Interpretation of Moiré Pictures,” V.D.I. Berichte Nr. 102: Experimentelle Spannungsanalyse, Berlin (1966)

  4. Beranek, W. J., “Het rechtstreeks wapenen van platen aan de hand van moiré-foto's,”Cement, XIX, 6 1967

    Google Scholar 

  5. Heise, U., “A Moiré Method for Measuring Plate Curvature,”Experimental Mechanics,7 1 47–48 1967

    Article  MathSciNet  Google Scholar 

  6. Leitz, H., “Die Drillungsmomente bei kreuzweise bewehrten Platten,” Die Bautechnik (1925)

  7. Hageman, J. G., “Bepaling van de ligging en van de hoeveelheid wapening in een plaat bij een gegeven membraanspanningstoestand,” Report TNO-IBBC (1959)

  8. Beranek, W. J., “Het wapenen en voorspannen van platen volgens de elastische berekeningswijze,” Report TNO-IBBC BI-68-2

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Authors and Affiliations

  1. Institute TNO for Building Materials and Building Structures (IBBC), Rijswijk

    W. J. Beranek (Engineer)

Authors
  1. W. J. Beranek
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Beranek, W.J. Rapid interpretation of moiré photographs. Experimental Mechanics 8, 249–256 (1968). https://doi.org/10.1007/BF02327021

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  • DOI: https://doi.org/10.1007/BF02327021

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