Test: Two Way Slab - Civil Engineering (CE) MCQ

The following points should be remembered for reinforcement detailing in the two-way slab  as per IS 456-2000:

• Slabs are considered as divided in each direction into middle and end strips. Minimum steel can be provided in the edge strip
• 50% of the tension reinforcement provided at midspan in the middle strip shall extend in the lower part of the slab to within 0.25l of a continuous edge or 0.15l of a discontinuous edge and the remaining 50% shall extend into support.
• 50% of tension reinforcement at top of a continuous edge shall be extended for a distance of 0.15L on each side from the support and at least 50% shall be provided for a distance of 0.3l on each face from the support.
• At the discontinuous edge, the negative moment may arise, so 50% of mid-span steel shall be extended into the span for a distance of 0.1L at the top.
• Tension steel shall be provided at corners in the form of a grid (in two directions) at the top and bottom of the slab where the slab is discontinuous at both the edges. This area of steel in each layer in each direction shall be equal to ¾ the area required for maximum mid-span moment. This steel shall extend from the edges for a distance of L/5.

Slabs:
Slabs are considered as plane element or plate elements which are classified based on aspect ratio.
Aspect ratio:
It is defined as ratio between longer span (Ly) of the slab to shorter span (Lx) of the slab.

Types of slab based on aspect ratio 

• One way slab:
  Slab spanning in one direction
  
• Two way slab:
  Slab spanning in both the direction
  

Explanation:
The ratio of the long to short dimension of the slab is greater than X
By comparing to Aspect ratio of one way slab

We get X = 2

One-way slab:

• Rectangular slabs which are supported only on two opposite sides by unyielding supports and are uniformly loaded along the direction parallel(not multiple directions, option 1 is saying) to the supports are one-way slabs.
• The span ratio 'l_y / l_x > 2'.
• In one way slab, the load is carried in one direction perpendicular to the supporting beam.
• The main reinforcement is provided along a shorter span.
• The distribution reinforcement is provided along a longer span.
• The maximum moment in the slab is along a shorter span direction.

Two-way slab:

• The two-way slab is supported by the beam on all four sides.
• The span ratio 'l_y / l_x ≤ 2'.
• The two-way slab is bent in both spanning side directions while load transfer.
• In a two-way slab, the load is carried in both directions.
• In a two-way slab, both twisting and bending moments are generated.

Torsion reinforcement shall be provided at any corners in a two-way slab which is simply supported on both edges meeting at the corner.

• It shall consist of top and bottom reinforcement, each with layers of bars placed parallel to the side of the slab and extending from the edges a minimum distance of 1/5th of the shorter span.

Torsional reinforcement need not be provided at any corner where both edges are continuous.

• Torsional reinforcement of 50 % of three-quarters of the area required for maximum mid-span moment in the slab shall be provided at a corner contained by edges over only one of which the slab is continuous.

CI. 24.4 of IS 456:2000 recommends for designing two way slabs by any acceptable theory. IS 456:2000 describes the procedure for the following types of two way slabs:
(i) Simply supported slabs whose corners are not restrained from lifting up (CI. D-2 of IS 456:2000)
(ii) Torsionally restrained slabs whose corners are restrained from lifting up and whose edges may be continuous or discontinuous (CI. D-1 of IS 456:2000)
Uniformly Loaded and otherwise simply supported Rectangular slab (Torsionally Unrestrained slab):
(i) CI. D-2 of IS 456:2000 describes moment coefficients in order to assess the maximum moments in the short and long span directions considering unit width of the slab. These moment coefficients are based on Rankine Grasshoff theory.
Uniformly loaded Restrained Rectangular slab:
(i) CI. D-1 of IS 456:2000 defines restrained slabs are the slab whose corners are prevented from getting lifted up and are of provided with suitable reinforcement to resist torsion and are called as restrained slab.
(ii) Corner restrained in the slab reduce the bending moment and deflection in the middle of slab just like fixed beams which reduce the mid-span moment and deflections as comapred to simply supported beams.
(iii) The expression for the design moment coefficient for both continuous (fixed) and discontinuous edges of the slab are given by many authors based on elastic analysis and also based on approximate solutions out of which some of them are;
(a) Marcus method
(b) Pegeaud's method
(c) IS code method 

• As per IS 456 CI. D-1, Restrained slab is the slab whose corners are prevented from getting lifted up and are provided with suitable reinforcement to resist torsion and are called a restrained slab.
• All the four edges of the slab are assumed to be rigidly tied with the beams or walls underneath and the edges may be either continuous (Fixed) or discontinuous.
• Corner restrained in the slab reduces the bending moment and deflection in the middle of the slab just like fixed beam which reduces the mid-span moment and deflection as compared to simply supported beams. 

Important Points
As per IS 456 (B 1.8, B 1.9, B 1.10) Torsion reinforcement provided as:

• B 1.8: Torsion reinforcement is required at the corner where both edges are discontinuous 
  • Reinforcement provided in 4 layers.
  • size of mesh = l_x/5
  • Area of steel in each layer = (3/4) × A_st(+ve)
• B 1.9: Torsion reinforcement is required where at least one edge is discontinuous
  • Provided in 4 layers
  • size of mesh = l_x/5
  • Area of steel in each layer = (3/8) × A_st(+ve)
• B 1.10: Where both edges are continuous no need to provide torsional reinforcement.

Moment coefficient: 
As per IS code method of two-way slab design with continuous edges, the positive moment coefficient is  ¾  times of corresponding negative moment coefficient.
As per IS code method of two-way slab design with discontinuous edges, the negative moment coefficient is 0.  
Note:
Coefficient Method for design of two–way slab
The coefficient method employs tables of moment coefficients for different slab edge conditions. The conditions are based on elastic analysis but inelastic redistribution is accounted for as well.
According to the coefficient approach, the slab is divided into the middle strip and column strip in each direction. The width of the latter is equal to one-quarter of the panel width whereas the width of the former is one-half the panel width.
Calculation:
Given data
The positive moment coefficient = 0.3
As per IS code method of two-way slab design with continuous edges, the positive moment coefficient is  ¾  times of corresponding negative moment coefficient.
The negative moment coefficient

Hence, according to the given options, the correct answer is 0.45.
Important Points
As per Table 12 of IS-456:2000, the bending moment coefficients for dead and live load are given below:

Slabs are generally of two types.

• One way slab 
• Two slabs slab

The difference is shown below to understand it better-


Explanation:
According to IS Code,
As per Cl. D. 1.2 of IS 456, slop are considered as divided in each direction, into middle strips end strips such that.

Width of middle strip = 3/4 (width of slab)
Important Points

• Width of end strip at each end = 1/8 ( width of the slab) 

Torsional Reinforcement Detailing in slab:
Torsional reinforcement is provided in the form of a grid or mesh both at the top and bottom of the slab.
CI. D-1.8 of IS 456:2000 recommends that the torsional reinforcement grid/mesh should extend beyond the edge for a distance not less than 20% of shorter span
i.e. l_x/5.

The total area of torsional steel provided in each of the four layers should not be less than:
(i) 0.75 Ast_x(+ve) If both the meeting edges are discontinuous i.e. edge 1.
(ii) 0.375 Ast_x(+ve) If one of the two meeting edges, one is continuous and the other discontinuous i.e. edge 2 and 3.
(iii) As per CI D-1.10 of IS 456:2000, No torsional reinforcement is required if both the meeting edges are continuous i.e. edge 4 
Here,
Ast_x(+ve) denotes the area of flexural steel required for maximum mid-span moment in the short direction.

One-way slab:

• Rectangular slabs which are supported only on two opposite sides by unyielding supports and are uniformly loaded along the direction parallel(not multiple directions, option 1 is saying) to the supports are one-way slabs.
• The span ratio 'l_y/l_x > 2'.
• In one way slab, the load is carried in one direction perpendicular to the supporting beam.
• The main reinforcement is provided along a shorter span.
• The distribution reinforcement is provided along a longer span.
• The maximum moment in the slab is along a shorter span direction.

Two-way slab:

• The two-way slab is supported by the beam on all four sides.
• The span ratio 'l_y/l_x ≤ 2'.
• The two-way slab is bent in both spanning side directions while load transfer.
• In a two-way slab, the load is carried in both directions.
• In a two-way slab, both twisting and bending moments are generated.

Torsion reinforcement shall be provided at any corners in a two-way slab which is simply supported on both edges meeting at the corner.

• It shall consist of top and bottom reinforcement, each with layers of bars placed parallel to the side of the slab and extending from the edges a minimum distance of 1/5th of the shorter span.

Torsional reinforcement need not be provided at any corner where both edges are continuous.

• Torsional reinforcement of 50 % of three-quarters of the area required for maximum mid-span moment in the slab shall be provided at a corner contained by edges over only one of which the slab is continuous.

CI. 24.4 of IS 456:2000 recommends for designing two way slabs by any acceptable theory. IS 456:2000 describes the procedure for the following types of two way slabs:
(i) Simply supported slabs whose corners are not restrained from lifting up (CI. D-2 of IS 456:2000)
(ii) Torsionally restrained slabs whose corners are restrained from lifting up and whose edges may be continuous or discontinuous (CI. D-1 of IS 456:2000)
Uniformly Loaded and otherwise simply supported Rectangular slab (Torsionally Unrestrained slab):
(i) CI. D-2 of IS 456:2000 describes moment coefficients in order to assess the maximum moments in the short and long span directions considering unit width of the slab. These moment coefficients are based on Rankine Grasshoff theory.
Uniformly loaded Restrained Rectangular slab:
(i) CI. D-1 of IS 456:2000 defines restrained slabs are the slab whose corners are prevented from getting lifted up and are of provided with suitable reinforcement to resist torsion and are called as restrained slab.
(ii) Corner restrained in the slab reduce the bending moment and deflection in the middle of slab just like fixed beams which reduce the mid-span moment and deflections as comapred to simply supported beams.
(iii) The expression for the design moment coefficient for both continuous (fixed) and discontinuous edges of the slab are given by many authors based on elastic analysis and also based on approximate solutions out of which some of them are;
(a) Marcus method
(b) Pegeaud's method
(c) IS code method