21.1:
Design of Prismatic Beams for Bending
The design process for prismatic beams subjected to bending begins by determining the allowable stress for the chosen material.
The allowable stress is generally obtained from a table of material properties or design specifications. Alternatively, it can be computed by dividing the material's ultimate strength by a suitable safety factor.
Then, the shear force and the bending moment diagrams corresponding to the specified loading conditions are drawn.
Next, the maximum absolute value of the bending moment is calculated using the shear force diagram.
The minimum allowable section modulus is then calculated using the beam's absolute bending moment value and allowable stress.
When a timber beam is designed, the ratio characterizing the shape of its cross-section is usually specified. The unknown dimensions are identified using the relationship between the dimensions of the beam and the section modulus.
While designing a rolled-steel beam, a table containing properties of the rolled-steel beam is referred to, and only those beam sections with a section modulus greater than or equal to the minimum required section modulus are considered.
21.1:
Design of Prismatic Beams for Bending
The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and stress characteristics. Its value will depend on the selected material and the structure's intended use.
Next, plot shear force and bending moment diagrams to visualize load distribution and identify maximum bending stress points. This visualization is key to optimizing beam dimensions to maximize safety and efficiency of the beam.
Finally, calculate the minimum section modulus that will allow the beam to resist bending stress. Higher moduli indicate a greater resistance. For timber beams, the designer specifies a cross-section shape ratio that will produce the desired modulus. For steel beams, the designerselects from pre-existing sections, ensuring the beam's modulus exceeds the calculated minimum. This selection guarantees that the beam can withstand bending forces, maintaining structural safety and stability.
This systematic approach combines safety considerations with material and load analysis, ensuring the chosen beam upholds the structure's integrity and reliability under anticipated loads, ultimately securing long-term structural performance.