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

One-way slab:
(i) If a slab is supported only on two opposite supports, it is called a one-way slab.
(ii) If the slab is opposite on all four sides and span ratio 'l_y/l_x > 2', it is called a one-way slab.
(iii) Main reinforcement is provided along a shorter span.
(iv) Distribution reinforcement is provided along a longer span.
(v) maximum moment in the slab is along a shorter span direction.
(vi) When simply supported along two opposite edges square slab will behave as the one-way slab.
The maximum moment for the simply supported slab is given by, 
Where l_x = shorter span length 

One way slab is a slab which is supported by beams or walls or both on the two opposite sides to carry the load along one direction.
If it is supported on all four sides but the ratio of longer span (l) to shorter span (b) is equal or greater than 2 then it is also considered as one way slab.
Longer span/Shorter Span > 2
The one way slab will bend in one direction only i.e. in the direction along its shorter span, so it will deflect along the shorter span.
The amount of deflection along shorter span depends on load on slab and therefore, it is dynamic. However, along longer span deflection remains constant irrespective of load, so it is static in nature. 

As per IS 456:2000, cl. 22.5
The moments and the shear forces for a continuous beam and one-way slab can be calculated using moment coefficients and shear force coefficients respectively only when the following conditions are satisfied:

• Continuous spans should be at least three in number.
• Supports should be fairly rigid and should not themselves deflect.
• All the spans should have the same cross-sections.
• The effective length of each span should be more or less the same and at any rate, should not differ by more than 15% of the largest effective span.
• The loading on all the spans should be substantially uniformly distributed.
• No redistribution of moments is permitted.

Moment of resistance for under reinforced beam is given by:
MOR = 0.87× f_y × A_st(d - 0.42X_u)
Where, X_u = Depth of neutral axis, A_st = Area of reinforcement
Depth of neutral axis is calculated as:
Compression force = Tension force
0.36 f_ck b X_u = 0.87 f_y A_st
Calculation:
Given,
d = 100 mm,  c/c spacing between bar = 200 mm
M20 and Fe415
Taking b = 1000 mm for slab ,Calculating A_st,

We know that,
Depth of Neutral Axis (x_u):

MOR is given as:
M_u = 0.87 f_y.A_st.(d - 0.42Xu)
M_u = 0.87×415× 393 (100- 0.42 × 19.6)
M_u = 141892.65 × 91.768  = 13021204.7 N-mm
M_u = 13.0 kN-m 

Nominal Shear stress:
IS code recommends the use of nominal shear-stress for RCC structure. The nominal shear stress in beams or slabs of uniform depth is calculated as:

Where
V_u = Shear force due to design loads,
b = breadth of beam or slab,
d = effective depth
Shear stress for slabs is very low since b is large. Therefore no shear reinforcement is provided in slabs except that the alternate bars are bent up near the supports.
Bond stress (τ_bd):
Bond stress is the shear stress developed along the contact surface between the reinforcing steel and the surrounding concrete which prevents the bar from slipping out of concrete.
It depends upon the grade of concrete and type of steel only.

One-way slab:
(i) If a slab is supported only on two opposite supports, it is called a one-way slab.
(ii) If the slab is opposite on all four sides and span ratio 'l_y/l_x > 2', it is called a one-way slab.
(iii) Main reinforcement is provided along a shorter span.
(iv) Distribution reinforcement is provided along a longer span.
(v) maximum moment in the slab is along a shorter span direction.
The maximum moment for the simply supported slab is given by,

Where l_x = shorter span length 
Calculation:
Give,
Ultimate working load (w) = 9 kN/m
Shorter span length (l_x) = 4 m, Longer span length (l_y) = 9 m
l_y/l_x = 9/4 = 2.25 > 2, so it is one way slab
The maximum moment is given by, 

Design Moment = 18 kN-m

One-way slab:
(i) If a slab is supported only on two opposite supports, it is called a one-way slab.
(ii) If the slab is opposite on all four sides and span ratio 'l_y/l_x > 2', it is called a one-way slab.
(iii) Main reinforcement is provided along a shorter span.
(iv) Distribution reinforcement is provided along a longer span.
(v) maximum moment in the slab is along a shorter span direction.
(vi) When simply supported along two opposite edges square slab will behave as the one-way slab.
The maximum moment for the simply supported slab is given by,

Where l_x = shorter span length 

One-way slab:
(i) If a slab is supported only on two opposite supports, it is called a one-way slab.
(ii) If the slab is opposite on all four sides and span ratio 'l_y/l_x > 2', it is called a one-way slab.
(iii) Main reinforcement is provided along a shorter span.
(iv) Distribution reinforcement is provided along a longer span.
(v) maximum moment in the slab is along a shorter span direction.
The maximum moment for the simply supported slab is given by,

Where l_x = shorter span length 
Calculation:
Give,
Ultimate working load (w) = 9 kN/m
Shorter span length (l_x) = 4 m, Longer span length (l_y) = 9 m
l_y/l_x = 9/4 = 2.25 > 2, so it is one way slab
The maximum moment is given by, 

Design Moment = 18 kN-m

w_L= Live load
w_d = Dead load
As per Table 12 of IS-456:2000, the bending moment coefficients for dead and live load are given below:

∴ Option 1 is correct.

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 (L_y) of the slab to shorter span (L_x) of the slab.
Aspect ratio = L_y/L_x
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