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

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

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

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.

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

Maximum shear stress at the section = τ1 + τ2 = 97 Maximum shear stress at the section = τ1 + τ2 = 97.6149 N/mm2 3) Bending stress due to bending moment

4) Principal stresses at c (Compressive) (Tensile) 5) Location of principal planes θp1 = 35.78˚ and θp2 = 125.78˚

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

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

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

2) Torsional stress