Q1: If the neutral axis of a T-beam is below the slab, the relationship between the flange width B, depth of neutral axis n, thickness of the slab ds, effective depth of the beam d, gross area of tensile steel A_t and the modular ratio m may be stated as

ANS:C -

When the neutral axis of a T-beam is located below the slab, it indicates that the tensile force in the beam is resisted primarily by the tensile reinforcement (steel) rather than the concrete flange. In this case, the relationship between the various parameters can be described as follows:

1. Flange width (B): The width of the flange contributes to the overall bending capacity of the beam by providing additional compressive strength. However, if the neutral axis is below the slab, the contribution of the flange to resisting tensile stresses is negligible.
2. Depth of neutral axis (n): The depth of the neutral axis indicates the point within the beam section where the bending stress is zero. When the neutral axis is below the slab, it implies that the tensile stress is primarily carried by the tensile reinforcement rather than the concrete.
3. Thickness of the slab (ds): The slab thickness affects the distribution of loads and bending stresses in the T-beam. However, if the neutral axis is below the slab, the thickness of the slab may not directly affect the behavior of the beam in resisting bending moments.
4. Effective depth of the beam (d): The effective depth of the beam is the distance from the extreme compression fiber to the centroid of the tensile reinforcement. When the neutral axis is below the slab, the effective depth is primarily determined by the distance from the slab to the centroid of the tensile reinforcement.
5. Gross area of tensile steel (At): The area of tensile reinforcement contributes to the overall tensile capacity of the beam. When the neutral axis is below the slab, the tensile steel carries most of the tensile force, and its area influences the bending capacity of the beam.
6. Modular ratio (m): The modular ratio represents the ratio of the modulus of elasticity of concrete to that of steel. It affects the distribution of stresses in the beam and influences the position of the neutral axis.

In summary, when the neutral axis of a T-beam is below the slab, the relationship between the flange width, depth of the neutral axis, slab thickness, effective depth of the beam, gross area of tensile steel, and the modular ratio reflects the dominance of the tensile reinforcement in resisting bending stresses, while the contribution of the concrete flange is minimal.