1. Unit-5. Torsion in Shafts and Buckling of Axially Loaded Columns Lecture Number-3 Mr. M.A.Mohite Mechanical Engineering S.I.T., Lonavala

2. Stresses due to combined torsion, bending and axial load on shaft
Shafts subjected to combine torsion and bending
Shaft subjected to combine torsional moment T and bending moment M simultaneously at any cross section
i) The normal stress developed across the cross section will be
ii) Shear stress developed across the section will be

3. Both the stresses are maximum at outer surface
Thus point at outer surface can be assumed to be subjected to biaxial stress state.
The principal stresses can be found as
Maximum normal stress
Maximum shear stress

4. Ex. 1) A solid circular shaft of 20 mm dia
Ex.1) A solid circular shaft of 20 mm dia. is loaded as shown in figure. Determine
Maximum shear stress on horizontal diameter AB.
Principal stress at element C of vertical diameter.

5. Solution:
From torsion
From distribution of shear stress over a circular area

6. Maximum shear stress at the section = τ1 + τ2 = 97
Maximum shear stress at the section = τ1 + τ2 = N/mm2 3) Bending stress due to bending moment

7. 4) Principal stresses at c
(Compressive)
(Tensile)
5) Location of principal planes
θp1 = 35.78˚ and θp2 = ˚

8. Shaft subjected to combine axial force and torsion
Shaft subjected to combine torsional moment T and axial force F simultaneously at any cross section
i) The normal stress developed across the cross section will be
ii) Shear stress developed across the section will be

9. The principal stresses can be found as
Maximum normal stress
Maximum shear stress

10. Ex.2) A solid circular shaft of diameter 50 mm is subjected to axial compressive force of 30 kN and a torque of 0.75kNm. Determine principal stresses and maximum shear stress developed at a point on the surface of shaft. Solution:- 1) Normal stress

11. 2) Torsional stress