The crane arm of our design illustrates the major stress analysis concepts of bending and torsion. We used a hollow triangular arm composed of a triangular truss system. Since our lifting arm was not collinear with the crane arm, the upward force exerted by the servo motor on the crane arm produced a twisting moment. The equation for calculating shear stress produced by torsion is given as: 

τ = MR/Ip

M is the twisting moment, R is the radius from the center to a point of interest, and Ip is the polar moment of inertia. The polar moment of inertia derivation shows that material farther away from the axis of the beam produce the most resistance to twisting. This motivated our hollow design in which most of the material of the crane arm is concentrated away from the axis.

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This system is also effective at reducing the bending of the crane arm. Our motor produces a bending moment and a shear stress on the crane arm which both contribute to bending. However, the truss system of the crane arm cause the force to be loaded axially due to our links, which are two force members. Aluminum is much more resistant to deformation when loaded axially because the stress is constant throughout the part. However, in bending, the stress concentrates at the top and bottom of the part, as demonstrated by the equation for bending stress:

σ = My/I

M is the bending moment, y is the distance from the neutral plane to a point of interest, and I is the second moment of inertia. From this equation, you can see as a point gets farther from the neutral plane, y increases, thus producing more stress at that point. This unequal distribution of stress causes higher concentrations in these peak areas, which cause failure earlier than if the beam had been loaded axially.