1. The essence of the science of strength of material. Concept of bars, plates and shells

The polar moment of inertia of a section is a measure of the section's resistance to torsion. It is equal to the sum of the moments of inertia about two perpendicular axes.

Concentrated forces are forces that are applied at a single point on a structure, while distributed forces are forces that are applied over a length or area. Examples of concentrated forces include point loads and reactions, while distributed forces include uniform loads and varying loads.

Construction of internal force diagrams in tension and compression involves determining the magnitude and direction of the internal forces (normal, shear, and bending) at different locations within the structure. These diagrams can be used to analyze the behavior of the structure under different loading conditions and to design the structure for optimal strength and stiffness.

Construction of internal force diagrams in torsion: In torsion, internal forces are represented by shear stresses that act perpendicular to the longitudinal axis of the shaft or member. The distribution of these stresses can be determined using a shear stress formula and are represented graphically by a shear stress diagram. The maximum shear stress occurs at the outermost layer of the shaft, and the shear stress varies linearly with radial distance from the center.

Construction of internal force diagrams in bending: In bending, the internal forces are represented by normal stresses that act perpendicular to the longitudinal axis of the beam or member. The distribution of these stresses can be determined using bending moment formula and are represented graphically by a bending moment diagram. The maximum normal stress occurs at the top and bottom of the beam and is directly proportional to the distance from the neutral axis. The neutral axis is the location where the normal stress is zero, and it passes through the centroid of the cross-sectional area.