Design of Prismatic Beams for Bending

Allowable stress is obtained from material properties tables or design specifications. Alternatively, calculate it by dividing the material's ultimate strength by a suitable safety factor. This safety factor accommodates uncertainties and varies depending on the material—timber, steel, or concrete—and the structure's intended use.

These diagrams visualize load distribution across the beam and identify maximum bending stress points. By plotting shear force and bending moment diagrams, designers locate the maximum absolute value of bending moment, which is critical for calculating the minimum section modulus required to safely resist bending forces.

The section modulus is a geometric property that indicates a beam's resistance to bending stress. The minimum allowable section modulus is calculated using the beam's absolute bending moment value and allowable stress. Higher section moduli indicate greater resistance to bending, ensuring the beam can withstand applied loads safely.

For timber beams, the designer specifies a cross-section shape ratio that produces the desired section modulus. Unknown dimensions are identified using the mathematical relationship between the beam's dimensions and the required section modulus. This approach ensures the timber beam achieves the calculated minimum section modulus.

Designers refer to a table containing properties of rolled-steel beam sections. Only beam sections with a section modulus greater than or equal to the minimum required section modulus are considered. This selection method ensures the chosen steel beam can withstand bending forces while maintaining structural safety and stability.

The first step is determining the allowable stress for the chosen material. This value is either obtained from material properties tables or computed by dividing the material's ultimate strength by a safety factor. Establishing allowable stress ensures the design accommodates material uncertainties and maintains structural integrity.

Timber beam design involves specifying a cross-section shape ratio and calculating unknown dimensions from the section modulus relationship. Steel beam design uses pre-existing rolled sections from property tables, selecting only those with adequate section modulus. Both approaches ensure the beam resists bending stress while optimizing safety and efficiency.