The propeller shaft of a large ship has outside diameter 18

The propeller shaft of a large ship has outside diameter 18 in. and inside diameter 10 in., as shown in the figure. The shaft is rated for a maximum shear stress of 4200 psi. 18 in. 200 rpm 10 in. 18 in (a) If the shaft is turning at 200 rpm., what is the maximum horsepower that can be transmitted without exceeding the allowable stress? Round your answer to the nearest whole hp (b) If the rotational speed of the shaft is increased in 3 times but the power requirements remain unchanged, what happens to the shear stress in the shaft? Shear stress l -in imes.

Solution

Solution:-

(1)   (shear stress) = T * D₀/2/(/32*(D₀⁴ – D_i⁴))

      4200 = T * 18/2*/(/32*(18⁴ – 10⁴ ))

T = 4.35 *10⁶ pound – inch

T (torque) = 362.5 * 10³ pound – foot

Power (H) = T * N/(5252)

                  = 362.5 * 10³ * 200/(5252)

                  = 13766.18 hp    Answer

(2) When N= 3* 200 =600 rpm

Then

Power = T * N/5252

13766.18 = T * 600/5252

T = 120.4999 *10³ pound –foot

= 1.44599*10⁶ pound - inch

Shear stress = T *D₀/2*/(/32 *(D₀⁴ – D_i⁴ )

                      = 1.44599*10⁶ *18/2*/(/32 *(18⁴ – 10⁴ ))

                     = 1395.7 psi     Answer

Times initial shear stress = 1395.7/4200 =0.332 times    Answer