TORSIONAL LOADING OF SHAFTSExamples

1. For the solid shaft as shown, determine:a. Torsional shearing stress at longitudinal axis.b. Torsional shearing stress 10mm from the longitudinal

axis.c. Torsional shearing stress at the outer surface of the

shaft.d. Maximum torsional shearing stress.e. Rotational of plane B with respect to A.

2. For the hollow shaft as shown, determine:a. Maximum transverse shear on the shaft.b. Relative rotation of D wrt B.

1000 Nm

A BL = 1 m

G = 90 GPaDiameter = 40 mm

30 kNm

A C

10 kNm

2 m

B

1 m

D

Outer Dia = 100 mmInner Dia = 600 mmG = 80 GPa

16 kNm Q

1.5 m

3. For the compound shaft (G = 80 GPa) as shown, determine:a. Maximum torsional shearing stress 3 m from left end.b. Maximum torsional shearing stress for the entire shaft.c. Relative rotation of plane D wrt A.

4. A compound shaft consisting of a steel (G = 83 GPa) segment and an aluminum (28 GPa) segment is acted upon by two torques as shown.

a. Assuming all (steel) governs, what is the value of T.b. Assuming all (aluminum) governs, what is the value of T.c. Assuming max (1.5 m length) governs, what is the value of T.d. What is the maximum permissible value of T for the

compound shaft?

5. A solid compound shaft is made of three different materials and is subjected to two applied torques as shown. (A). Determine the maximum shearing stress developed in each material. (B) Find the angle of rotation of the free end of the shaft. GAL = 28 GPa, GST = 80 GPa, GBR = 35 GPa.

A B

BC = 100 mmAB = 160 mm

1.5 m1 m

D

T

0.5 m2 m

C

35 100 5 kNm20

CD = 50 mm

Aluminum

900 mm

600 mm

Steel

2TT50 mm dia

40 mm dia Allowable Stresses:torsional (steel) = 83 Mpatorsional (aluminum) = 55 Mpa

Allowable Rotation:max (1.5 m length) = 0.105 rads

A B

Steel75 mm

Aluminum100 mm

3 m

D

1.5 m2 m

C

4 kNm 1.5 kNm

Bronze75 mm