Use of Scientific Visual tools to analyze the stresses in a Simply loaded Cantilever beam

The loaded cantilever beam is extensively studied by undergraduate students in basic mechanics courses. The stress states in a cantilever beam depends on the position of the plane, the load position and its intensity. These stress states are often difficult to explain to students but with proper visual and multimedia tools students can grasp the concepts easily by seeing the relationships visually. A scientific visual representation of different sections of such a loaded beam should provide the ideal backup to all the analytical information we have.

When a slender member is subjected to transverse loading we say that it acts as a beam. These members resist loads applied laterally or transversely to their axis. The beam is assumed to be simply loaded, i.e., the force is concentrated at one point.

We are interested in the analysis of a Simply loaded Cantilever beam. This includes looking into the Normal and Shear stress distribution across different sections perpendicular to the axis of the beam. The load position is also a variable.

• Normal Stress, Plane Position 1
• Normal Stress, Plane Position 2
• Normal Stress, Plane Position 3
• Shear Stress, Plane Position 1
• Shear Stress, Plane Position 2
• Shear Stress, Plane Position 3

From the color code representation of the Normal and Shear stresses we note the following:

1. The normal stress is directly proportional to the distance from the point of action of the load, i.e., as the distance from the point of action of the load increases so does the normal stress. One has to keep in mind that the normal stress is zero from the point of action of the load to the free end of the beam.

2. We also observe that the normal stress is also dependent on the (perpendicular) distance from the neutral surface to the point where the stress is required. Thus at the top edge of the beam we observe maximum positive stress passing through zero at the center and then the maximum negative stress at the bottom edge.

3. Looking at the shear stress distribution we note that the shear stress is independent of the point of action of the load and is dependent only on the perpendicular distance from the neutral surface. At the top and bottom edge of the beam, the shear stress is nil and increases parabolically to a maximum value at the neutral surface from either direction. Shear stress reduces to zero beyond the point of application of the load to the free end of the beam.

Anand Kuppuswamy (anandk@vtvm1.cc.vt.edu)

Dept. of Engineering Science & Mechanics

Virginia Tech

Blacksburg, Virginia

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