# Solid and hollow shafts

by series111
Tags: hollow, shafts, solid
 P: 54 1. The problem statement, all variables and given/known data assuming that the maximum shear stress and torsion are the same in both shafts design a hollow shaft to replace the solid one . the ratio diameters is to be 0.6 for the maximum shear stress i calculated 79.95 x 10 ^6 mn/m2 and for the torsion i calculated 122.78x10^3 in the previous question. 2. Relevant equations (T) torque/ (J) polar second moment of area and (t) shear stress/ ( r) radius polar second moment of area = pie (d4-d4)/32 radius = D/2 3. The attempt at a solution (j)= pie ((0.6)4-d4)/32 = 0.08545 d4 (r) = 0.6/2 = 0.3 solid shaft = j/r = 152.41x10^6 / 99.25 x 10 ^-3 = 1.535 x 10^-3values from previous question hollow shaft = j/r = 0.08545/0.3 = 284.83 x 10^ -3 d 3 square root with 1.535 x 10^-3/284.83 x 10^-3 under it = 175.32 x 10^-3 D= 0.6 x D = 0.6 x 175.32 x 10^-3 = 105.19 x 10^-3 therefore the dimensions are 175mm and 105mm i think these values are wrong as the solid shaft is 198.5mm and i always thought the hollow shaft would be larger in diameter please help as i dont no what i have done wrong..
HW Helper
PF Gold
P: 6,038
 Quote by series111 1. The problem statement, all variables and given/known data assuming that the maximum shear stress and torsion are the same in both shafts design a hollow shaft to replace the solid one . the ratio diameters is to be 0.6 for the maximum shear stress i calculated 79.95 x 10 ^6 mn/m2 and for the torsion i calculated 122.78x10^3 in the previous question. 2. Relevant equations (T) torque/ (J) polar second moment of area and (t) shear stress/ ( r) radius polar second moment of area = pie (d4-d4)/32
that's pie(d_o^4 - d_i^4)/32