Mechanical Design: MECH3403

Tutorial 1 (T1): Week 9, Semester 1, 2013

Adam WITTEKENCM: 2.24adwit@mech.uwa.edu.au

Recall of Basic Concepts of Solid Mechanics (Mohr Circles and Principal Stresses)

Week 31, Sem. 2,

MOHR’S CIRCLE (1)• Mohr’s circle: graphical form of expressing

transformation equations for plane stress

Equation of circle in a parametric form: 2θ (parameter), σ and τ (coordinates)

MOHR’S CIRCLE (2)

A

B

MOHR’S CIRCLE (4): PRINCIPAL STRESS

A

B

Principal Stresses(shear stress zero)

1 2

DISTORTION ENERGY (VON MISES) FAILURE (YIELD) CRITERION

or in terms of 3-D stress components

In terms of principal stresses

5

Example T1 (principal stress, von Mises stress)• The rotor shaft (solid) of the helicopter drives the rotor blades

that provide the lifting aerodynamic force that supports the helicopter in the air (as schematically shown in Fig. A). As a consequence, the shaft is subjected to a combination of torsion and axial loading (as schematically shown in Fig. B).

1) Using the Mohr’s circle determine the maximum compressive and tensile stresses in the shaft.

2) Determine the maximum equivalent (von Mises stress) in the shaft. The force F=125 kN, the torque T=2.5 kNm, and the shaft diameter

(constant) d=50 mm.

(A) (B)

Solution (1)

2.5x103

2.4544x10-5

Solution (2)

Solution (3)

9

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Solution (4)