University of Anbar
Engineering College
Civil Engineering Department
Strength of Materials
Second Classroom
Sheet No. 4 (Torsion)
Q1: A solid steel shaft of diameter (12 in) is fixed at its ends A &B and carries a disk at C.
Using  all  10 ksi , then determine the maximum safe angle of rotation that can be given to the
disk. Ans: 1o 30'
A
D=0.5"
12"
B
C
8"
Q2: A solid steel shaft of circular cross section has a length of 300 mm and is tapered from
50-mm diameter at the small end to 100-mm diameter at the large end, as shown in Figure.
The shaft is subject to a twisting moment of 1000 N.m applied at each end. For G = 80 GPa,
determine the angle of twist between the ends and the peak shearing stress.
Ans. 0.48°, 40.7 MPa
Q3: The aluminum rod AB (G=27 GPa) is bonded to the brass rod BD (G=39 GPa). Knowing
the portion CD of the brass rod I hollow and has an inner diameter (40mm), determine the
angle of twist at point (A).
Ans: 6.02o
Q4: Determine the maximum shearing stresses in the aluminum core and steel shell, where a
torque (100 N.m) applied at the free end. Use G=77.2 GPa for steel and G=27 GPa for
aluminum. Ans:  st  1.253 MPa,  al  0.328 MPa
Q5: The shaft has a radius (c) and is subjected to a uniform torque per unit length of (t o). If it
is fixed at its far end (A), determine the angle of twist  of end (B). Let shear modulus is (G).
Ans:  
to L2
c 4G
Q6: The steel shaft shown subjected to a uniform distributed torque of 60 lb.in/in. Determine
the absolute maximum shear stess in the shaft. Use Gsteel= 11x103 ksi.
Ans: 5.5 ksi.
60 lb.in/in
0.5"
1.0"
B
C
A
5"
20"
Q7: Check adequacy of the rod has a torque (T=50 N.m). Where the allowable shearing stress
in all wall points is not exceed (  allowable  4.0 MPa ).
Ans:  A  3.94 MPa, B  2.36 MPa , Adequate because   4MPa .