Concrete Structure Design: Identifying the False Statement

In the field of civil engineering, specifically in the design of concrete structures, it's crucial to understand the fundamental principles and code provisions. This question asks us to identify the false statement among the given options related to concrete design practices.

Slab Behavior and Support Conditions

Let's analyze the first statement: "A rectangular slab, whose length exceeds twice its width, always behave as two way slab, regardless of the support conditions."

• A slab is primarily classified as a one-way slab or a two-way slab based on how the load is distributed and carried to the supporting beams or walls.
• A slab behaves as a one-way slab if the ratio of its longer span (\(L_y\)) to its shorter span (\(L_x\)) is greater than 2 (\(L_y/L_x > 2\)) AND it is primarily supported on two opposite sides. In this case, the slab bends predominantly in the shorter direction, transferring most of the load to the supports along that direction.
• A slab behaves as a two-way slab if it is supported on all four sides AND the ratio of its longer span (\(L_y\)) to its shorter span (\(L_x\)) is less than or equal to 2 (\(L_y/L_x \le 2\)). Here, the load is distributed to all four supports, and the slab bends in both directions.
• Even if \(L_y/L_x > 2\), a slab supported on all four sides will still exhibit some degree of two-way action, but the majority of the load will be carried in the shorter direction, making it behave predominantly as a one-way slab.
• The statement claims that such a slab "always behave as two-way slab, regardless of the support conditions." This is incorrect. If a rectangular slab with \(L_y/L_x > 2\) is supported only on two opposite sides, it will clearly act as a one-way slab. Therefore, this statement is FALSE.

Linear Strain Profile Assumption in Flexure

The second statement says: "The assumption of linear strain profile in flexure is made use of in both working stress design method and limit state design method."

• Both the Working Stress Method (WSM) and the Limit State Method (LSM) are design approaches for reinforced concrete.
• A fundamental assumption in the flexural theory for reinforced concrete is that "plane sections before bending remain plane after bending." This assumption directly leads to a linear variation of strain across the depth of the cross-section.
• This principle is applied in calculating stresses and resistances in both WSM and LSM, albeit with different stress-strain relationships for concrete and steel.
• Therefore, this statement is TRUE.

Staircase Design: Dead Weight Calculation

The third statement states: "In case of staircase design, the dead weight of the steps is calculated by treating the step to be an equivalent horizontal slab of thickness equal to half of rise."

• When designing a staircase, it is necessary to account for the dead load contributed by the steps themselves (the treads and risers), in addition to the waist slab.
• A common and practical simplification for calculating the dead weight of the steps is to consider their average thickness. Each step essentially forms a triangular shape (tread as base, riser as height).
• For a series of steps, the average thickness contributed by the steps over the horizontal projection can be approximated as half of the rise (\(R/2\)).
• This equivalent thickness is then used to calculate the dead load per unit area of the horizontal projection of the stair, which is added to the dead load of the waist slab.
• Therefore, this statement is TRUE.

Torsional Reinforcement at Slab Corners

The fourth statement is: "Torsional reinforcement is not required to be provided at the corners of simply supported rectangular slabs, if the corner are free to lift up."

• Torsional reinforcement is typically required at corners of simply supported two-way slabs where two edges meeting at the corner are discontinuous and the slab is restrained from lifting. This restraint causes torsional moments at the corners, which require specific reinforcement (usually in the form of a mesh).
• However, if the corners are not restrained and are "free to lift up," then no torsional restraint is offered, and consequently, no significant torsional moments are developed at those corners.
• In such a scenario, the code provisions (like IS 456) confirm that torsional reinforcement is not necessary.
• Therefore, this statement is TRUE.

Conclusion

Based on the detailed analysis of each statement, the only false statement is the first one concerning the behavior of rectangular slabs.