ANS:A - 4.5 m

When designing continuous slabs, engineers aim to distribute loads and moments evenly across the entire structure to achieve efficient and effective load-bearing capacity. The length of the end span, which refers to the portion of the slab adjacent to a support (such as a column or a wall) at the end of a continuous system, is a critical aspect of this design process. Several factors influence the determination of the length of the end span:

1. Structural Behavior: The length of the end span affects the distribution of moments and shear forces within the slab. Longer end spans typically result in higher moments and deflections at the support, while shorter end spans can lead to increased moment redistribution along the continuous system. Engineers must consider the desired structural behavior and performance criteria when selecting the length of the end span.
2. Deflection Control: Controlling deflections is essential to ensure serviceability and prevent excessive cracking or deformation in the slab. Longer end spans may result in higher deflections, especially near the supports. Engineers may adjust the length of the end span to limit deflections within acceptable limits according to design codes and standards.
3. Construction Considerations: The length of the end span can influence construction sequencing, formwork requirements, and construction joints. Longer end spans may pose challenges during construction, such as increased formwork complexity or difficulties in achieving proper consolidation of concrete. Engineers may opt for shorter end spans to simplify construction processes and reduce associated costs and risks.
4. Aesthetic and Functional Requirements: Architectural and functional considerations may also influence the determination of the end span length. For example, longer end spans may be preferred to create uninterrupted floor areas or accommodate specific architectural features. Conversely, shorter end spans may be chosen to enhance the visual appearance or functionality of the space.
5. Code Requirements: Design codes and standards provide guidelines and limitations on span lengths based on structural performance, safety, and serviceability criteria. Engineers must ensure that the selected end span length complies with relevant code provisions and meets the required design objectives.

In summary, the determination of the length of the end span in continuous slab design involves careful consideration of structural behavior, deflection control, construction requirements, aesthetic preferences, and code compliance. Engineers must evaluate these factors holistically to select an appropriate end span length that optimizes the performance, efficiency, and safety of the slab structure.