Mechanical Engineering Design Notes

Design Contents

Preliminary Matters
Design Methodology
..brain storming
..evaluation matrix
Statistical Considerations
..variability in materials
..variability in dimensions
..variability in loading
..preferred sizes
Design Factor
Introduction to Failure
Failure Theories
Application of von Mises
..criterion in 2 D

Stress Concentration
..and notch sensitivity
Failure Under Combined Loading
..combined bending and torsion
Failure Under Cyclic Loading
..fracture mechanics
Instability - Buckling
Concentrically Loaded Strut
..slender columns
..Euler formula
..effective length
..short and intermediate columns
Eccentrically Loaded Strut
.. theory
Shock Loading

Failure Under Combined Load

In many engineering situations components frequently have to withstand more than one type of load. Shafts often have to withstand torque and bending moments. To solve this type of design problem the components are assumed to behave in a linear manner and superposition is used. The stresses due to each type of loading are determined in turn and then combined using appropriate equations or Mohr's circle.

If the design is to be based on the maximum shear stress theory (Tresca) then the maximum shear stress in the component (after combining the contributions due to all the loads) must be found. In some configurations it will not be obvious where the maximum combined shear stress occurs, in these cases it will be necessary to check the combined stresses at a number of locations.

For the example of a uniform solid shaft, diameter d, subject to torsion T and tension P, the maximum shear stress is constant at all points on the surface.

The direct stress due to P is = 4 P/(3.142 d2)

The max. shear stress due to T (at the surface) is = 16 T/(3.142 d3)

The maximum combined shear stress can be found from Mohr's circle to be:

max. shear stress = [(direct stress/2)2 +(shear stress)2]0.5

For a safe design the max. combined shear stress must be less than or = yield shear stress / factor of safety.

If the design is to be assessed against the distortion energy (von Mises) theory, then the von Mises stress needs to be calculated, which means the 3 principal stresses have to be determined.

In many cases of three dimensional solid components, it will often be adequate to carry out a 2D stress analysis. An example of this is in the design of most shafting, where there are no interference fits and consequently the radial stresses are usually insignificant compared to axial stresses caused by bending and / or tension / compression and shear stresses (on axial and circumferential planes) caused by torques transmitted.

Example of calculation to design a shaft against failure under combined loading. (200kb file).

This page contains Java Script to rapidly carry out the shaft design calculation shown in the above example.

David J Grieve, modified: 25th January 2014, 27th January 2010, 21st November 2006, 21st July 2004, original: 24th October 2001.

Contact the Author:
Please contact me for comments and / or corrections or to purchase the book, at: