Experimental Mechanics

, Volume 1, Issue 7, pp 23–32 | Cite as

Twisting stresses in tape

The stresses induced in a thin tape by bending over pulleys, by axial tension and by twisting of the tape when running between two out-of-plane pulleys, are analyzed
  • C. Mylonas
  • D. C. Drucker
Article

Abstract

An analysis is presented of the stresses induced in a thin tape by bending over pulleys, by axial tension and by twisting of the tape when running between two out-of-plane pulleys. Analytical results are compared with some photoelastic tests on tape models made of epoxy resin. The weak retardation produced by the thin tape is multiplied by repeated light passage through the tape and is measured by a bent-beam compensator. The tests are of especial interest because the rate of rotation of the principal stresses is higher than had been encountered before. Surprisingly, the experimental results uncorrected for rotation are in good agreement with the calculated stresses.

Keywords

Epoxy Mechanical Engineer Fluid Dynamics Principal Stress Light Passage 

List of Symbols

b

tape width

b1

central width of tape equal tob/\(\sqrt 3 \).

d

tape thickness

f

depth of parabolic segment for entire widthb of tape. The units off are fringe orders

f1

depth of parabolic segment for central widthb/\(\sqrt 3 \)

FA,…,fD

fringe order at various points of the tape

m

mirror reflectivity

ri

light ray which has passedi times through specimen

w

angle of twist over a length of tape equal to its widthb. In the present reportw is always less than 0.1 π (twist of at most one revolution in a length equal to twenty widths)

wcr

critical twist at which buckling occurs

x

coordinate axis in direction of the thickness of the tape

y

coordinate axis in direction of the width of the tape

z

coordinate axis in direction of the length of the tape

A0

original light intensity

Ai

light intensity afteri passages

Ai, opt

optimum light intensity afteri passages

Cσ

stress optical coefficient, a material fringe value with units of stress per fringe for a 1 in. thickness

Cε

strain optical coefficient, strain per fringe for a 1 in. thickness

D

diameter of pulley

E

Young's modulus

F2

focal length of collector lensV2

G

shear modulus

K

principal curvature of the helix in which longitudinal fibers twist

L

arbitrary length of tape, length of untwisted fibers

L′

length of twisted fibers when the end cross sections are held a fixed distanceL apart

N

relative retardation in wave lengths (λ=5461 Å)

P

longitudinal force applied along axis of tape

R

ratio of twice the rotation of principal stresses to the relative phase retardation over a light path

S

\(\sqrt {1 + R^2 } \)

α

angle between partially reflecting mirrors

ε

normal strain

γ

shear strain

θ

angle between maximum principal stress and tape axis

ν

Poisson's ratio

σ

normal stress

σcr

critical buckling stress

σcr

longitudinal normal stress due to external pullP

σz1, ∈z1

longitudinal stress and strain when end cross sections are held at the same distance apart in the straight and the twisted tape

σzo, ∈zo

longitudinal normal stress and strain in the absence of external loading

τ

shear stress

ψ

angle of twist of tape over lengthL

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References

  1. 1.
    Timoshenko, S., “Strength of Materials,”Van Nostrand, Vol. II 3rd ed., 286–291 (1956).Google Scholar
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    Timoshenko, S., “Theory of Elastic Stability,” McGraw-Hill (1936).Google Scholar
  3. 3.
    Mindlin, R. D., andGoodman, L. E., “The Optical Equations of Three-Dimensional Photoelasticity,”Jnl. Applied Phys.,20,No. 1,89–95 (January 1949).CrossRefGoogle Scholar
  4. 4.
    Drucker, D. C., andMindlin, R. D., “Stress Analysis by Three-Dimensional Photoelastic Methods,”,11, No. 11, 724–732 (November 01940).CrossRefGoogle Scholar
  5. 5.
    Mindlin, R. D., Jnl. Applied Mech.,8,A187 (1941).Google Scholar
  6. 6.
    Post, D., “Isochromatic Fringe Sharpening and Fringe Multiplication in Photoelasticity,”Proc. SESA, XII, No. 2, 143–356 (1955).Google Scholar
  7. 7.
    Mylonas, C., “The Optical System of Polariscopes as Used in Photoelasticity,”Jnl. Sci. Instr., 25, 77–87 (March 1948).CrossRefGoogle Scholar
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    D'Agostino, J., Drucker, D. C., Liu, C. K., andMylonas, C., “Epoxy Adhesives and Casting Resins as Photoelastic Plastics,”Proc., SESA, XII No. 2, 123–128 (1955).Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 1961

Authors and Affiliations

  • C. Mylonas
    • 1
  • D. C. Drucker
    • 1
  1. 1.Division of EngineeringBrown UniversityProvidence

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