Rcc Structures Design — Part 1 MCQs with Explanations

Shear stress distribution in a rectangular cross-section of a beam is not uniform across the depth. The intensity of shear stress is zero at the extreme top and bottom fibers and maximum at the neutral axis (center of the depth). This distribution follows a parabolic curve, where the shape of the curve resembles a parabola with the vertex at the neutral axis. This is derived from the shear stress formula in bending: τ = VQ / Ib, where τ is shear stress, V is shear force, Q is the first moment of area, I is the moment of inertia, and b is the width. Hence, for rectangular sections, the resulting variation of τ across the depth is parabolic in nature. Therefore, the correct answer is Option C: A parabolic curve .

The question is about two-way slabs in Reinforced Cement Concrete (RCC) structures. Two-way slabs are supported on all four sides and the load is carried in both directions (length and width). The ratio 'r' refers to the ratio of the longer span to the shorter span of the slab. When the corners of a two-way slab are held down (meaning they are prevented from lifting), it changes how the slab bends (its bending moment, or B.M.). Because the corners are held down, the bending moment is reduced . The question asks which formula correctly represents this reduction in bending moment. The correct formula, representing the reduction, is: $$\frac{5}{6}\left( {\frac{{{{\text{r}}^2}}}{{1 + {{\text{r}}^2}}}} \right){\text{M}}$$ , where M is the original bending moment. So, the answer is Option B.

1. Definition of Clear Cover: The clear cover is the distance between the outer surface of the reinforcement and the exposed surface of the concrete. 2. Importance of Clear Cover in RCC Columns: It provides protection to reinforcement against corrosion and fire exposure. Ensures proper bond strength between concrete and reinforcement. 3. Standard Requirement: As per IS 456:2000, the minimum clear cover for RCC columns should be the greater of 40 mm or the diameter of the bar used in reinforcement. This ensures sufficient durability and structural integrity under various environmental conditions. Conclusion: The correct answer is Option A: Greater of 40 mm or diameter , as per standard RCC design guidelines.

The maximum value is 275 KN/mm 2 and used for 200 KN/mm 2 .

The correct answer is Option A: Fixed end Here's why: A cantilever beam is a beam that's fixed at one end (the fixed end ) and free at the other end (the free end ). Think about it like a diving board. The part attached to the pool deck is the fixed end, and the end you jump off is the free end. When a load is applied to a cantilever beam, the maximum bending moment (the force that causes bending) and shear force (the force that causes sliding) occur at the fixed end. Therefore, the design of a reinforced concrete cantilever beam (R.C.C.) is primarily based on these maximum forces at the fixed end to ensure it can withstand the load without failing. * Free end: The bending moment and shear force are typically zero at the free end. * Mid span: The bending moment and shear force are present at the mid-span, but they're not the maximum values that the beam needs to be designed for. * Mid span and fixed support: While both locations experience forces, the fixed support is where the maximum forces are concentrated.

Reason: As per standard RCC detailing practice (IS 2502/IS 456), a hooked bar must have a straight extension beyond the hook to ensure adequate anchorage and prevent slip. Minimum requirement: The straight portion beyond the end of the hook should be at least 4ϕ , where ϕ is the bar diameter. Why 4ϕ? This length ensures the bearing and bond developed by the hook is effectively transferred into the concrete without premature pull-out or cracking at the bend.

M150 grade concrete refers to a mix ratio of 1:2:4 (Cement : Sand : Aggregate), where the characteristic compressive strength (fck) is 15 N/mm² . The moment of resistance factor (R) , also known as the limiting moment of resistance per unit width and square of effective depth, is a design parameter used in the limit state method for RCC beam design. According to standard design aids and tables based on IS 456:2000, for M15 grade concrete , the commonly referred value of the moment of resistance factor is approximately 8.50 . Option A: 0.87 is incorrect, as it usually refers to the partial safety factor or percentage of steel yield stress, not the moment of resistance. Option C: 7.50 and Option D: 5.80 are not the correct standard values for M150/M15 grade concrete. Therefore, the correct answer is Option B: 8.50 .

In RCC design, plain concrete columns are allowed only when the column is short and not subjected to significant bending . According to standard design guidelines, a column can be made of plain concrete if its unsupported length does not exceed three times its least lateral dimension . This limitation ensures that the column behaves primarily under axial compression and avoids buckling or instability . If the length exceeds this limit, reinforcement becomes necessary to provide additional strength and stability. Therefore, the correct condition is three times the least lateral dimension.

Given: Diameter of R.C.C. column D = 30 cm; 6 bars of 12 mm (1.2 cm) diameter; Axial load P = 40,000 kg Gross area of column (A g ): (π/4)D 2 = (π/4)(30) 2 = 706.86 cm 2 Area of one bar: (π/4)d 2 = (π/4)(1.2) 2 = 1.131 cm 2 (approx.) Total steel area (A s ): 6 × 1.131 = 6.786 cm 2 Net concrete area (A c ): A g − A s = 706.86 − 6.786 = 700.07 cm 2 Assume modular ratio (m): 15 (typical for RCC working stress method) Transformed area carrying load: A c + mA s = 700.07 + 15×6.786 = 801.86 cm 2 Concrete stress (working): σ c = P / (A c + mA s ) = 40,000 / 801.86 = 49.9 kg/cm 2 Therefore, the stress is 49.9 kg/cm 2 ⇒ Option A.

Permissible compressive stress in concrete (σ cbc ) = 50 kg/cm 2 Permissible tensile stress in steel (σ st ) = 1400 kg/cm 2 Modular ratio (m) = 18 To find the depth of the neutral axis (X c ): X c = (m × σ cbc ) / (m × σ cbc + σ st ) × d = (18 × 50) / (18 × 50 + 1400) × d = 900 / (900 + 1400) × d = 900 / 2300 × d = 0.3913d ≈ 0.39d From moment of resistance equation: 0.5 × b × n 2 = m × A st × (d - n) Divide both sides by b × d 2 to get percentage reinforcement: A st / (b × d) = 0.692% Therefore, the required percentage area of steel A st is: 0.692% Correct Option: C) 0.696% (Note: The small rounding difference from 0.692% to 0.696% is acceptable in multiple-choice exams.)

In RCC design, the span to depth ratio is used to control deflection in structural members. For a cantilever slab , the structure is more prone to deflection because one end is fixed and the other is free. According to standard guidelines (such as IS 456), the maximum span to effective depth ratio for a cantilever is generally taken as 10 . This limit ensures that the slab remains safe and serviceable without excessive bending or deflection. Higher ratios like 12 or 16 would lead to excessive deflection , making the structure unsafe. Therefore, the correct maximum ratio is 10 .

In reinforced cement concrete (RCC) design, beams are classified as shallow or deep based on the ratio of their effective span to overall depth. A deep beam is one in which the span is relatively short compared to its depth, leading to significant shear deformation and nonlinear strain distribution. According to IS 456:2000 (Indian Standard for RCC design), a continuous beam is considered a deep beam if the ratio of effective span to overall depth is less than 2.5 . This classification affects how the beam is analyzed and designed, as deep beams do not follow conventional beam theory and require special design considerations. Therefore, the correct answer is: Less than 2.5 (Option D).

On an absolutely rigid foundation base: The pressure distribution is uniform because the foundation remains undeformed under the applied load. Detailed Reasoning: 1. Definition of a Rigid Foundation: A rigid foundation is an idealized structure that does not bend, flex, or deform when subjected to loads. It is assumed to transfer the applied load uniformly to the underlying soil or base material. 2. Uniform Pressure Distribution: When a rigid foundation is placed on a base, the rigidity ensures that every point along the base moves together as a single unit. As a result, the pressure is distributed evenly across the foundation area. This uniformity occurs because there is no differential settlement or bending that would otherwise alter the pressure distribution. 3. Practical Assumption : The concept of uniform pressure on a rigid foundation is an idealization used in structural design. It simplifies analysis and is valid when the subsoil is homogenous, and the load is symmetrical. Deviations from this condition can cause non-uniform pressures, but these are generally analyzed using more complex methods. 4. Contrast with Flexible Foundations : In flexible foundations, deformation or bending occurs due to the applied load. This deformation causes variations in pressure, often leading to higher pressures at certain points, such as the edges or the center, depending on the load distribution and soil properties. Key Assumption: The uniform pressure distribution is based on the idealization that the foundation is perfectly rigid and the soil is homogenous and linearly elastic.

In RCC stair design , the waist is the minimum thickness of the inclined slab measured perpendicular to the soffit of the stair. For stairs spanning horizontally , the slab behaves like a reinforced concrete slab and must have sufficient thickness to safely resist bending moments and shear forces . As per standard RCC design practice, a minimum waist thickness of 12 cm is required to ensure adequate strength, stiffness, and durability . Providing a waist thickness less than this may lead to excessive deflection and structural inadequacy . Therefore, the correct answer is Option D – 12 cm .

Reason: As per IS 456:2000, the basic span-to-effective depth ratio for a simply supported slab spanning in two directions is 35 when mild steel reinforcement (Fe 250) is used. For HYSD bars: The value is multiplied by a modification factor of 0.8 , giving 0.8 × 35 = 28 . Purpose: This limit controls deflection and ensures adequate stiffness of the slab under service loads.

Understanding Doubly Reinforced Beams and Neutral Axis Let's break down this question step-by-step to understand what it's asking. Key Concepts: * Doubly Reinforced Beam: This is a beam that has steel reinforcement in both the tension zone (bottom) and compression zone (top). * Neutral Axis (NA): This is the line within the beam where there is neither tensile nor compressive stress. It's the point where the stress changes from compression to tension. * Actual Neutral Axis: The actual position of the neutral axis in a real beam under load. It's determined by the equilibrium of forces. * Critical Neutral Axis: This is a theoretical position of the neutral axis. It's the depth where the concrete and steel reach their maximum allowable stresses simultaneously. Maximum Stress: Think of 'maximum stress' as the point where the material (concrete or steel) starts to yield or fail. Explanation of Options: * Option A: "Is greater than the depth of critical neutral axis, the concrete attains its maximum stress earlier" * If the actual neutral axis is *deeper* than the critical neutral axis, it means the compression zone is larger. * A larger compression zone implies the concrete is experiencing higher compressive stresses. * Therefore, the concrete reaches its maximum stress (and potentially fails) before the steel reaches its maximum tensile stress. * Option B: "Is less than the depth of critical neutral axis, the steel in the tensile zone attains its maximum stress earlier" * If the actual neutral axis is *shallower* than the critical neutral axis, it means the tension zone is larger. * A larger tension zone means the steel is experiencing higher tensile stresses. * Therefore, the steel reaches its maximum stress (and potentially yields) before the concrete reaches its maximum compressive stress. * Option C: "Is equal to the depth of critical neutral axis; the concrete and steel attain their maximum stresses simultaneously" * This is the definition of the *critical* neutral axis. * When the actual neutral axis matches the critical neutral axis, both the concrete and steel reach their maximum allowable stresses at the *same time* . This is the ideal balanced design. * Option D: All the above * Since options A, B, and C are all correct under their respective conditions, this is the correct answer. Therefore, the correct answer is D: All the above.

All the above is the correct answer to “If the shear stress in a R.C.C. beam is”. This question is standard in competitive examination syllabi for Rcc Structures Design.

High strength concrete and high tensile steel is the correct answer to “In a pre-stressed member it is advisable to use”. This question is standard in competitive examination syllabi for Rcc Structures Design.

$${\frac{1}{7}^{{\text{th}}}}$$ of the span is the correct answer to “In a simply supported slab, alternate bars are curtailed at”. This question is standard in competitive examination syllabi for Rcc Structures Design.

$$\frac{{\text{L}}}{2}\left( {1 - \frac{5}{{{{\text{q}}_{\max }}}}} \right)$$ is the correct answer to “If L is the effective span of a R.C.C. beam which is subjected to maximum shear q max at the ends, the distance from either end over which stirrups for the shear, are provided, is”. This question is standard in competitive examination syllabi for Rcc Structures Design.

$$\frac{{\text{h}}}{3}$$ is the correct answer to “Total pressure on the vertical face of a retaining wall of height h acts parallel to free surface and from the base at a distance of”. This question is standard in competitive examination syllabi for Rcc Structures Design.

W - 2P sinθ is the correct answer to “In a pre-stressed beam carrying an external load W with a bent tendon is having angle of inclination θ and pre-stressed load P. The net downward load at the centre is”. This question is standard in competitive examination syllabi for Rcc Structures Design.

Safe in shear is the correct answer to “An R.C.C beam of 25 cm width has a clear span of 5 metres and carries a U.D.L. of 2000 kg/m inclusive of its self weight. If the lever arm of the section is 45 cm., the beam is”. This question is standard in competitive examination syllabi for Rcc Structures Design.

$$\frac{{{\text{Shear force}}}}{{{\text{Lever arm}} \times {\text{Width}}}}$$ is the correct answer to “The maximum shear stress (q) in concrete of a reinforced cement concrete beam is”. This question is standard in competitive examination syllabi for Rcc Structures Design.

4.5 m is the correct answer to “If the length of an intermediate span of a continuous slab is 5 m, the length of the end span is kept”. This question is standard in competitive examination syllabi for Rcc Structures Design.

Is decreased by $$\frac{{{\text{Pe}}}}{{\text{Z}}}$$ is the correct answer to “If the tendon is placed at an eccentricity e below the centroidal axis of the longitudinal axis of a rectangular beam (sectional modulus Z and stressed load P in tendon) the stress at the extreme top edge”. This question is standard in competitive examination syllabi for Rcc Structures Design.

Equal to its width is the correct answer to “A foundation is called shallow if its depth, is”. This question is standard in competitive examination syllabi for Rcc Structures Design.

0.5 is the correct answer to “If the sides of a slab simply supported on edges and spanning in two directions are equal, the maximum bending moment is multiplied by”. This question is standard in competitive examination syllabi for Rcc Structures Design.

Remains within the flange is the correct answer to “A T-beam behaves as a rectangular beam of a width equal to its flange if its neutral axis”. This question is standard in competitive examination syllabi for Rcc Structures Design.

Needs revision of section is the correct answer to “An R.C.C. beam of 6 m span is 30 cm wide and has a lever arm of 55 cm. If it carries a U.D.L. of 12 t per m and allowable shear stress is 5 kg/cm 2 , the beam”. This question is standard in competitive examination syllabi for Rcc Structures Design.

$$\frac{{{\text{WL}}}}{{3{\text{P}}}}$$ is the correct answer to “A pre-stressed rectangular beam which carries two concentrated loads W at $$\frac{{\text{L}}}{3}$$ from either end, is provided with a bent tendon with tension P such that central one-third portion of the tendon remains parallel to the longitudinal axis, the maximum dip h is”. This question is standard in competitive examination syllabi for Rcc Structures Design.

Three-fourth of the width of the slab is the correct answer to “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”. This question is standard in competitive examination syllabi for Rcc Structures Design.

2800/3C is the correct answer to “If the permissible compressive stress for a concrete in bending is C kg/m 2 , the modular ratio is”. This question is standard in competitive examination syllabi for Rcc Structures Design.

A point of zero shear force is the correct answer to “In a combined footing for two columns carrying unequal loads, the maximum hogging bending moment occurs at”. This question is standard in competitive examination syllabi for Rcc Structures Design.

120 cm is the correct answer to “On piles, the drop must be at least”. This question is standard in competitive examination syllabi for Rcc Structures Design.

$$\frac{{{\text{WL}}}}{{4{\text{P}}}}$$ is the correct answer to “If a bent tendon is required to balance a concentrated load W at the centre of the span L, the central dip h must be at least”. This question is standard in competitive examination syllabi for Rcc Structures Design.

30 cm is the correct answer to “A singly reinforced concrete beam of 25 cm width and 70 cm effective depth is provided with 18.75 cm 2 steel. If the modular ratio (m) is 15, the depth of the neutral axis, is”. This question is standard in competitive examination syllabi for Rcc Structures Design.

0.8% and not more than 8% of cross-sectional area is the correct answer to “As per IS : 456, the reinforcement in a column should not be less than”. This question is standard in competitive examination syllabi for Rcc Structures Design.

6 mm is the correct answer to “If the diameter of longitudinal bars of a square column is 16 mm, the diameter of lateral ties should not be less than”. This question is standard in competitive examination syllabi for Rcc Structures Design.

12 mm is the correct answer to “The diameter of main bars in R.C.C. columns, shall not be less than”. This question is standard in competitive examination syllabi for Rcc Structures Design.