Question

The one-way simply-supported slab for a room of plan dimensions 9 m x 4 m carries ultimate working load of 9 kN/m. The design moment for the slab should be
1. 12.00 kN.m
2. 18.00 kN.m
3. 9.00 kN.m
4. 27.00 kN.m

Answer 1

Correct Answer - Option 2 : 18.00 kN.m

Concept:

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,

\({M_x} = \frac{{wl_x^2}}{8}\)

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, \({M_x} = \frac{{wl_x^2}}{8}\)

⇒ \({M_x} = \frac{{9\; × \;{4^2}}}{8} = 18\ kN - m\)

Design Moment = 18 kN-m