File:Kt arbre epaule torsion.svg

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Summary

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Description
Français : Abaque de facteurs de concentration de contrainte (Kt) dans le cas d'un arbre épaulé en torsion.
English: Stress concentration factors (Kt) chart for a shaft with shoulder fillet in torsion.
Date
Source Own work, from Pilkey, Walter D., Peterson's Stress Concentration Factors 2nd ed., Wiley & sons (1997), ISBN 97-0-471-53849-3, p. 166
Author Cdang
 
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Calculation
t is the fillet height, t = (D - d)/2
Coefficient for the calculation of Kt
β = t/r 0,25 ≤ β ≤ 4,0
C1
C2
C3
C4

Scilab source

// ********************
// Initialisation
// ********************

clear;
clc;

// ********************
// Fonctions
// ********************

// Saisie des paramètres géométriques

function [A]=param_geo()
    A(1) = input("grand diamètre : D = ");
    A(2) = input("petit diamètre : d = ");
    A(3) = input("rayon : r = ");
endfunction

// Calcul en torsion

function [Kt] = Kt_torsion(Alpha, Beta)
    coefs = [0.905, 0.783, -0.075;
        -0.437, -1.969, 0.553;
        1.557, 1.073, -0.578;
        -1.061, 0.171, 0.086];
    C = coefs(:,1) + coefs(:,2)*sqrt(Beta) + coefs(:,3)*Beta;
    polynome = poly(C', "x", "c") ;
    Kt = horner(polynome, Alpha);
endfunction

// ********************
// Programme principal
// ********************

// Accueil

disp("Facteurs de concentration de contrainte d''un arbre épaulé")
disp("W. D. Pilkey, Peterson''s Stress Concentration factors, Wiley & sons (1997)")

// A(1) = D ; A(2) = d ; A(3) = r

A = param_geo();
t = 0.5*(A(1) - A(2)); // hauteur de filet
Beta = t/A(3); // t/r
Alpha = 2*t/A(1);

Kt_to = Kt_torsion(Alpha, Beta);

if (Beta < 0.25) | (Beta > 4) then
    disp("Torsion : attention, valeur extrapolée");
end
disp('Kt torsion = '+string(Kt_to));

Licensing

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I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

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Date/TimeThumbnailDimensionsUserComment
current09:46, 24 April 2013Thumbnail for version as of 09:46, 24 April 2013672 × 751 (192 KB)Cdang (talk | contribs)Missing edges in sketch
09:33, 24 April 2013Thumbnail for version as of 09:33, 24 April 2013672 × 751 (192 KB)Cdang (talk | contribs)User created page with UploadWizard

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