According to I.S. : 456, slabs which span in two directions with corners held down, are assumed to be divided in each direction into middle strips and edge strips such that the width of the middle strip, is

ANS:C - three-fourth of the width of the slab

1. Load Distribution: In two-way spanning slabs with corners held down, the load from the supported structure is transferred to the slab. The corners being held down restrict the rotation of the slab, causing the load to be distributed over a larger area compared to slabs with simply supported edges. As a result, the middle strip, which carries the central portion of the load, typically occupies a significant portion of the slab width.
2. Behavior of Slabs: Two-way spanning slabs distribute the applied loads in both directions, resulting in bending moments and shear forces being transferred to the slab in multiple directions. The middle strip is subjected to bending moments from both directions, necessitating a wider strip to effectively distribute and resist these moments.
3. Design Assumptions: The assumption that the middle strip occupies three-fourths of the width of the slab is based on engineering judgment and typical structural behavior observed in practice. This assumption provides a conservative estimate for the design of two-way spanning slabs, ensuring that the slab can adequately carry the applied loads and meet safety requirements.
4. Practical Considerations: A wider middle strip allows for more efficient distribution of reinforcement and provides better resistance against bending and shear stresses. Additionally, it simplifies the design and construction process by allowing for uniformity in detailing and reinforcement layout.

Overall, assuming the width of the middle strip to be three-fourths of the width of the slab in two-way spanning slabs with corners held down is a practical and conservative approach that ensures structural integrity and performance while simplifying design and construction processes.