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How can a vertical metal rod carry both normal stress and shear stress?

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Figure 1: The position vector x and the velocity vector v of a material point, the body force fdV acting on an element dV of volume, and the surface force TdS acting on an element dS of surface in a Cartesian coordinate system 1, 2, 3 (see text).
mechanics of solids Figure 1: The position vector x and the velocity vector v of a material point, the body force fdV acting on an element dV of volume, and the surface force TdS acting on an element dS of surface in a Cartesian coordinate system 1, 2, 3 (see text).

A vertical metal rod can simultaneously carry both normal and shear stress depending on the orientation and nature of the applied forces.

  • Normal Stress: This arises from forces applied perpendicular to the cross-sectional area of the rod. For example, if the rod is pulled lengthwise (tension) or pushed lengthwise (compression), the resulting stress is classified as normal stress.1
  • Shear Stress: This arises from forces that act parallel to the plane of the cross-sectional area. In a metal rod, this often occurs when the rod is subjected to twisting (torsion) about its longitudinal axis, such as when tightening a screw.1

In practical engineering, structural elements like rods are often analyzed by considering the combination of axial forces, bending, and twisting torques. Because the state of stress at any point within a material is defined by a stress tensor, a rod can experience a complex internal stress state where both normal and shear components coexist, depending on the specific loading conditions applied to the structure.21