If the ratio of long and short spans of a two way slab with corners held down is r, the actual reduction of B.M. is given by
A. $$\frac{5}{6}\left( {\frac{{\text{r}}}{{1 + {{\text{r}}^2}}}} \right){\text{M}}$$
B. $$\frac{5}{6}\left( {\frac{{{{\text{r}}^2}}}{{1 + {{\text{r}}^2}}}} \right){\text{M}}$$
C. $$\frac{5}{6}\left( {\frac{{{{\text{r}}^2}}}{{1 + {{\text{r}}^3}}}} \right){\text{M}}$$
D. $$\frac{5}{6}\left( {\frac{{{{\text{r}}^2}}}{{1 + {{\text{r}}^4}}}} \right){\text{M}}$$
Answer: Option B
Solution (By Examveda Team)
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.
This Question Belongs to Civil Engineering >> RCC Structures Design
Correct option B