Mechanics of Materials Laboratory
Dr. M. E. Barkey
Department of Aerospace Engineering and Mechanics
The University of Alabama
Stress State from Combined Loading
M. E. Barkey
A. Introduction and Objective
The objectives of this experiment are to compute a stress state for combined loading and
the principal stresses that result from this stress state; measure strains experimentally with
a strain gage rosette; calculate stresses from the measured strains and compute the
principal stresses from the experimental data.
1.0 Stress State from Combined Loading
We have studied states of stress from varies types of loads as they are applied
independently on a structure. The formulas for the stresses are summarized below:
(axial normal stress)
(longitudinal bending stress)
(pressure vessel stresses)
(transverse shearing stress)
(torsional shearing stress).
For a state of combined loading, the stress states from these individual loads can be
superimposed to determine the combined loading stress state. The principle of
superposition can be applied as long as the system that you are analyzing remains
linear—for our purposes in this class, that means that the material cannot have
yielded—i.e. when load is applied and removed, the strains return to nearly the same
M. E. Barkey
The following steps should be taken to determine the stress state at the point of
interest on your structure:
1) Make a free-body-diagram to determine the reactions (loads and moments) that
act at the point of interest in the structure.
2) Determine how each reaction contributes to the stress state at the point of interest.
Before these two steps, you can also use statics to simplify the structure by removing
various loading arms and replacing them with a statically equivalent force-moment
system. Note that forces and moments must be resolved to the centroid of the crosssection of the bar on which you are determining the stress state.
Figure 1: Structure subjected to combined loading.