Q1: In a doubly-reinforced beam if c and t are stresses in concrete and tension reinforcement, d is the effective depth and n is depth of critical neutral axis n, the following relationship holds good

ANS:A -

In a doubly-reinforced beam, where both concrete and tension reinforcement are present, the stress in the concrete (c) and the stress in the tension reinforcement (t) contribute to the overall behavior of the beam. The effective depth of the beam (d) and the depth of the critical neutral axis (n) are important parameters in analyzing the stress distribution within the beam. The relationship between these parameters can be expressed through the equation for equilibrium of forces in the beam's cross-section. One common relationship that holds true for doubly-reinforced beams is based on the stress equilibrium condition. This relationship can be stated as: c×Area of concrete above neutral axis=t×Area of tension reinforcement This equation represents the balance of forces between the compressive stress in the concrete above the neutral axis and the tensile stress in the reinforcement below the neutral axis. It ensures that the internal forces in the beam are in equilibrium, considering the flexural behavior of the structure. In addition to this relationship, other equations and principles may also apply depending on the specific design and analysis requirements of the doubly-reinforced beam, such as compatibility of strains, moment equilibrium, and stress-strain relationships for concrete and steel. Therefore, the following relationship holds good for a doubly-reinforced beam: c×Area of concrete above neutral axis=t×Area of tension reinforcement