Question

Two carbon steel balls, each 30 mm in diameter, are pressed together by a force F. Find the maximum values of the principal stress and the maximum shear stress if F = 50 N, $ u$ = 0.3, and E = 207 GPa. $sigma_1 = sigma_2 = sigma_x = sigma_y = -P_{ ext{max}} left[ left( 1 - frac{z}{a} an^{-1} left| frac{1}{z/a} ight| ight) (1 + u) - frac{1}{2 left[ 1 + (z/a)^2 ight]} ight]$ $sigma_3 = sigma_z = -frac{P_{ ext{max}}}{1 + (z/a)^2}$ $ au_{12} = au_{xy} = 0$ $ au_{ ext{max}} = au_{13} = au_{23} = au_{yz} = au_{xz} = frac{1}{2} (sigma_1 - sigma_3) = frac{1}{2} (sigma_2 - sigma_3)$

          Two carbon steel balls, each 30 mm in diameter, are
pressed together by a force F. Find the maximum values
of the principal stress and the maximum shear stress if F
= 50 N, $
u$ = 0.3, and E = 207 GPa.
$sigma_1 = sigma_2 = sigma_x = sigma_y = -P_{	ext{max}} left[ left( 1 - frac{z}{a} 	an^{-1} left| frac{1}{z/a} 
ight| 
ight) (1 + 
u) - frac{1}{2 left[ 1 + (z/a)^2 
ight]} 
ight]$
$sigma_3 = sigma_z = -frac{P_{	ext{max}}}{1 + (z/a)^2}$
$	au_{12} = 	au_{xy} = 0$
$	au_{	ext{max}} = 	au_{13} = 	au_{23} = 	au_{yz} = 	au_{xz} = frac{1}{2} (sigma_1 - sigma_3) = frac{1}{2} (sigma_2 - sigma_3)$

$Two carbon steel balls, each 30 mm in diameter, are pressed together by a force F. Find the maximum values of the principal stress and the maximum shear stress if F = 50 N, u = 0.3, and E = 207 GPa. sigma1 = sigma2 = sigmax = sigmay = -P extmax left[ left( 1 - fracza an^-1 left| frac1z/a ight| ight) (1 + u) - frac12 left[ 1 + (z/a)^2 ight] ight] sigma3 = sigmaz = -fracP extmax1 + (z/a)^2 au12 = auxy = 0 au extmax = au13 = au23 = auyz = auxz = frac12 (sigma1 - sigma3) = frac12 (sigma2 - sigma3)$

Added by Kelly J.

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