7.3: Bending and Torsional Moments
Bending and torsional moments are two fundamental concepts in structural engineering. They play an important role in understanding the behavior of materials and structures under different loading conditions.
The reaction developed in a structural element when subjected to an external force causes the element to bend. When a structural element bends upwards, it creates compressive normal forces on the top and tensile normal forces on the bottom, resulting in a couple that determines the bending moment of the element. This moment is calculated by taking into account the distance from the point of interest to the line of action of the force and the magnitude of the force.
Bending of a ruler fixed at one end is an example of a bending moment. When a force is applied downwards perpendicular to the ruler near the unsupported end, it induces bending in the ruler. The applied force creates a moment about the fixed end, resulting in the ruler bending or deforming. In this scenario, the ruler will experience both compressive and tensile forces. The top side of the ruler, facing away from the applied force, will be in tension. The bottom side, facing towards the applied force, will be in compression.
A torsional moment occurs when a twisting force is applied to a body along its transverse or longitudinal axis, causing the section to twist. This twisting force creates an internal resistance within the material, opposing the applied force. The torsional moment is calculated as the product of the twisting force and the distance from the point of interest to the line of action of the force.
When driving a screw into a material using a screwdriver or power drill, a torsional moment is applied to the screw as it rotates and encounters resistance from the material. The twisting force generated by the screwdriver or power drill causes the screw to rotate, and the resistance from the material creates an opposing force, which generates a torsional moment.
