Shear force & bending moment diagram - Solved Examples

Apply the method of section to a simply supported beam with two loads, derive reactions by equilibrium, and compute shear force and bending moment across key sections.

Apply the method of section to draw shear force and bending moment diagrams for a simply supported eight-meter beam under a 5 kN/m uniform load, with reactions and center-load conversion.

Compute maximum bending moment and bending stress for a simply supported beam with a 3000 N/m udl, yielding Mmax 3375 N·m and σmax 67.5 MPa for 30×100 mm cross section.

Compute reactions, draw the shear force and bending moment diagrams, and determine the maximum bending moment and maximum bending stress for a simply supported beam with point loads.

Convert a uniformly distributed load on a simply supported beam with a right overhang into a resultant, compute the reactions, and derive the SFD and BMD.

Use the moment area method on a propped cantilever with a uniform load, converting to point loads and applying triangular and parabolic centroids to determine reaction at the simple support.

Derive slope and deflection for a cantilever beam under a point load w, using boundary conditions to obtain maximum slope and deflection.

Derive the bending stress, or flexural formula, for a simply supported beam, showing how stress varies with distance from the neutral axis and relates to moment of inertia.

Explore bending stress calculations for beam configurations, including simply supported with uniform load, cantilever, and circular sections, using the flexure formula M/I = sigma/y and the section modulus.

Apply the flexural formula to a simply supported four-meter beam with a rectangular section and two 50 mm holes, to determine the uniformly distributed load for 50 MPa bending stress.

Examines bending stress in a simply supported square cross-section beam for vertical and diagonal orientations, deriving I and z, with σ_b = 6m/a^3 (vertical) and σ_b = 6√2 m/a^3 (diagonal).

Determine maximum tensile and compressive stresses in a hollow offset beam under a uniform load for cantilever and simply supported cases, using centroid calculations, neutral axis, and bending stress formulas.

Compute the maximum UDL a four-meter simply supported beam can carry under a 25 MPa bending stress, by analyzing triangular cutouts, centroids, areas, and inertia.