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In part 1, statics was applied to determine the internal forces acting on the vertical section of the bent arm. The next step is to perform stress analysis on the bent arm component to determine the worst case stress and its location. The worst case stress location will be the sole focus of the remaining fatigue analysis, thus this is an important step!!
STEP 3: Determine the worst case stress location and its resulting stress
Recall that the vertical section of the bent arm is loaded in pure bending and axially as shown in the figure below:
The two different load cases can be evaluated independently and combined using the principle of superposition to determine the worst case stress and its location. For the bending case, because the rod is in pure bending, i.e. only a moment acts on the rod, the inside or outside portion of the rod will be where the worst case stress occurs. These locations are indicated by the white square elements above. Therefore one should compare the stresses at these two locations and nothing in the middle to determine the worst case stress location. Consider the bending case.
From the figure above, it should be clear that the counterclockwise moment causes a tensile stress on the inside of the rod and a compressive stress on the outside of the rod. To calculate the stresses due to bending, the flexure formula is applied to a circular cross section. The stress calculation is performed for the inside and outside location of the beam as shown below:
The stress on the inside of the beam is in tension and the stress on the outside of the beam is in compression. Consider the Axial case:
From the figure above, it should be clear that the internal load produces a tensile stress on the inside and outside locations of the rod. This stress is equivalent to 
. Knowing the stresses for both cases, they can be combined using superposition to determine the total stress felt on the inside and outside portions of the rod. The principle of Superposition is illustrated below:
From the figure above, it should be clear that the inside portion of the rod is the worst case stress location because the bending and axial loads produce a tensile force. For the outside portion of the rod, the bending load produces a compressive stress and the axial load produces a tensile stress, hence they oppose each other. Applying the principle of superpostion, the total stress on the inside (
) portion of the rod can be calculated as shown below:
Using the principle of superposition, the worst case stress location was determined. In the next section, we will build upon this analysis to evaluate the fatigue life of the bent arm of the gondola.