ANS:D - 1/30th of span

Assuming the width of the beam to be 1/30th of the span for an initial estimate in beam design is another commonly used approximation, especially for lightweight or less heavily loaded beams. Here's a more detailed explanation:

1. Simplification: When engineers are making initial estimates for beam designs, they often rely on simplified rules of thumb to quickly approximate the dimensions of the beam. These approximations help to provide a starting point for further detailed calculations and design iterations.
2. Conservative Approach: Assuming a smaller width relative to the span (such as 1/30th) can be a conservative approach. It tends to result in a narrower beam, which can lead to a more efficient use of materials and potentially lighter structures. However, it's crucial to ensure that this assumption aligns with the specific requirements and constraints of the project.
3. Applicability: The assumption of 1/30th of the span for the width of the beam may be more appropriate for certain types of beams, such as those with relatively low loads or spans, or for preliminary estimates of lightweight structures. It may not be suitable for all cases, particularly for heavily loaded beams or those with specific design requirements.
4. Iterative Design Process: It's important to remember that initial estimates are just the starting point in the design process. Engineers typically refine and adjust these estimates through iterative calculations, considering factors such as bending moments, shear forces, deflections, and other structural constraints. The chosen width must ultimately satisfy the structural requirements and ensure the safety and performance of the beam under the anticipated loads.

In summary, while assuming the width of the beam to be 1/30th of the span is a commonly used approximation in some cases, it's essential to verify its suitability for the specific project and to refine the design through detailed calculations and considerations of structural requirements.