The bending moment in strength of materials refers to the internal moment or torque that causes a structural element, such as a beam, to bend or undergo deformation. It is a measure of the bending effect induced by external forces or loads applied to the structure. Bending moments play a crucial role in structural analysis […]

When a point load P is applied to a beam or structure, it induces reaction forces at the supports. For a simply supported beam (supported at both ends) with a point load at the midpoint, the reaction forces at each support are equal and half of the applied load: ​ where: R = Reaction force

Shear force in strength of materials refers to the internal force that acts parallel to the cross-section of a structural element, such as a beam, and tends to cause deformation by sliding one part of the element past another, The shear force V at the location of the point load can be calculated using the

The bending moment M at the location of the point load can be calculated for different beam configurations. For a simply supported beam with a point load at the center, the bending moment is: ​ where: M = Bending moment at the point load location (in newton-meters, N·m) P = Applied point load (in newtons,

Bending stress is the stress developed in a beam due to bending moments. It is calculated based on the bending moment and the moment of inertia of the beam’s cross-sectional area. The formula for bending stress in a cantilever beam is given by: ​ where: σb​ = Bending stress (in pascals, Pa or N/m²) M

Torsional stress is the stress experienced by a material or structural component when subjected to twisting or torsional loads, The formula for calculating torsional stress depends on the geometry of the component and the applied torque. For a circular shaft or rod with radius r and subjected to a torque T, the formula for torsional

The polar moment of inertia J is a property of the shaft’s cross-sectional area and is needed to calculate torsional stress. For a circular shaft with radius r, the polar moment of inertia J is given by: ​ where: J = Polar moment of inertia (in meters to the fourth power, m⁴) r = Radius

For a circular cross-section with radius r, the moment of inertia I about an axis perpendicular to the plane of the circle and passing through its center is given by: where: I = Moment of inertia (in meters to the fourth power, m⁴) r = Radius of the circular cross-section (in meters, m)

For a rectangular cross-section with width b and height h, the moment of inertia I about an axis perpendicular to the base and passing through the centroid is given by: where: I = Moment of inertia (in meters to the fourth power, m⁴) b = Width of the rectangular cross-section (in meters, m) h =