JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III Year STRUCTURAL ENGINEERING - I (RCC) Previous Question Paper (February - 2022 - R18)

In the Limit State Method (LSM) of design, the behavior of a reinforced concrete section under flexure is classified based on the relative strain development in the concrete and the steel reinforcement at the point of failure. The classification depends on the relationship between the actual depth of the neutral axis (x_u) and the limiting depth of the neutral axis (x_u,max).

• Under-Reinforced Section: In this section, the area of steel provided is less than the area required for a balanced section. Consequently, the steel reaches its yield strain (ε_st ≥ 0.002 + 0.87f_y/E_s) before the concrete reaches its ultimate compressive strain (ε_cu = 0.0035). This leads to a ductile failure, characterized by significant deflection and cracking, providing ample warning before collapse. Here, x_u < x_u,max.
• Balanced Section: This is a theoretical state where both the concrete and the steel reach their respective ultimate strains simultaneously. It represents the transition between ductile and brittle failure. In practice, this is rarely used as it does not provide sufficient warning of failure. Here, x_u = x_u,max.
• Over-Reinforced Section: In this section, the area of steel provided is greater than that required for a balanced section. The concrete reaches its ultimate strain (ε_cu = 0.0035) while the steel is still in the elastic range (ε_st < yield strain). This results in a sudden, brittle failure without warning, which is dangerous in structural engineering. Consequently, IS 456:2000 prohibits the design of over-reinforced sections. Here, x_u > x_u,max.

Regarding sketches, visualize a rectangular cross-section with a neutral axis line. For an under-reinforced section, the strain diagram shows the steel strain line extending beyond the yield point while the concrete strain remains at 0.0035 at the extreme fiber. For the over-reinforced section, the strain diagram shows the concrete reaching 0.0035 while the steel strain is significantly lower than the yield strain, indicating the concrete is the limiting factor.

To design a simply supported T-beam, we follow the limit state method as per IS 456:2000.

1. Design Constants and Loads:

• Concrete: M25 (fck = 25 N/mm²), Steel: Fe415 (fy = 415 N/mm²)
• Span (L) = 6 m, Spacing (s) = 2.5 m
• Slab thickness (Df) = 120 mm
• Live Load (LL) = 4 kN/m²
• Load from slab = 4 × 2.5 = 10 kN/m
• Self-weight of slab = 0.12 × 2.5 × 25 = 7.5 kN/m
• Assume beam web size 300 mm × 500 mm (overall depth). Self-weight of rib = 0.3 × (0.5 - 0.12) × 25 = 2.85 kN/m
• Total Load (w) = 10 + 7.5 + 2.85 = 20.35 kN/m
• Factored Load (wu) = 1.5 × 20.35 = 30.53 kN/m
• Factored Bending Moment (Mu) = (wu × L²) / 8 = (30.53 × 6²) / 8 = 137.39 kNm

2. Effective Flange Width (bf):

Since 1620 mm < 2500 mm (spacing), use bf = 1620 mm.

3. Depth of Neutral Axis and Reinforcement:

Assuming neutral axis lies within the flange (xu ≤ Df):

Assuming effective depth d = 450 mm, solving for Ast:

• Ast ≈ 950 mm². Provide 3 bars of 20mm diameter (Ast = 942 mm²).

4. Shear Reinforcement:

Factored Shear Force (Vu) = (wu × L) / 2 = 91.59 kN. Provide 8mm diameter 2-legged stirrups at 200 mm c/c spacing.

5. Reinforcement Sketch Details:

• Main reinforcement: 3-20mm bars at bottom, 2-12mm hanger bars at top.
• Stirrups: 8mm diameter 2-legged links @ 200mm c/c.
• Ensure proper development length and anchorage at supports.