Prismatic Beams: Problem Solving

In the design of a supported timber beam subjected to a distributed load, both the beam's physical dimensions and the timber's characteristics, such as its grade and species, are critical. These factors determine the allowable stress values, which are crucial for calculating the necessary beam depth to ensure structural integrity and safety.

The design begins with analyzing the beam as a free body to identify moments and force balances, thereby determining support reactions. Next, the designer creates shear force and bending moment diagrams which highlight that the maximum bending moment for a uniformly distributed load typically occurs at the beam's midpoint.

Key to the design is calculating the maximum bending moment from the shear diagram, and then determining the minimum section modulus needed, by dividing this moment by the allowable stress. The timber's grade and species significantly influence this allowable stress, emphasizing the importance of material selection in design calculations.

The final step in the design process is calculating the beam's minimum depth. This step ensures the beam can carry the applied loads without exceeding allowable stress or deflection limits. This step requires careful consideration of the beam's geometry and its calculated section modulus. Through this systematic approach, the design ensures the timber beam meets all required structural criteria.