0
2.7kviews
Design a R.C. slab for a room measuring $5m \times 8m.$ The slab is to be cast monolithically over the beams with corners held down. The width of supporting beam is $230mm.$
1 Answer
0
60views

$$\dfrac {l_y}{l_x} = \dfrac {8.23}{5.23 }=1.57 < 2 $$

$\text { It is two way slab. } \\ d=\dfrac {\text { short effective span}}{\text {S⁄D ratio ×M.F}} \\ =\dfrac {5230}{20×1.4} =186.78 ≈200mm \\ \text { Now D= d+ effective cover. } \\ D=200+25=225mm \\ \text {Load calculation } \\ D.L = D×25=0.225×25=5.625kN/m^2 \\ L.L =3kN/m^2 \\ F.F = 1 kN/m^2 \\ Total =9.625kN/m^2 \\ \text { Factored load } (w_d) =9.625×1.5=14.43kN/m \\ \dfrac {l_y}{lx}=1.57 $

enter image description here

$$M_{ux}=α_x wdlx^2$$

$ =0.106×14.43×5.23^2 \\ =41.53kNm \\ M_{uy}= α_y wdlx^2umax \\ =0.138=0.043×14.43×5.23^2 \\ =16..97kNm \\ M_{u\space max}=0.138f_{ck} bd^2 \\ =0.138×20×1000×200^2 \\ =110.4kNm \gt M_{ux} \space \& \space M_{uy} \\ Astx= \dfrac {0.5×20×1000×200}{415} ×[1-\sqrt {1-\dfrac {4.6×41.83×10^6}{20×1000×200^2 }}]\\ =619.37mm^2 \\ \text { Assume 8mm∅ bars } ∅_x=∅_y=8d_y=192 \\ Asty= \dfrac {0.5×20×1000×192}{415}×[1-\sqrt{1-\dfrac {4.6×16.97×10^6}{20×1000×190^2 }}]\\ =293.18 \\ Astmin=\dfrac {0.12}{100} b×D=270mm^2 \lt Astx \space \& \space Asty \\ \text {* Main steal in x direction (10mm) } \\ Spacing = \dfrac {b×c/s \space area}{Astx}=\dfrac {1000×\pi⁄4×10^2}{619.37}=126.8 ≈125mm \\ \text { * Main steel in y-direction(10mm∅) } spacing =\dfrac {b×c/s\space area}{Asty}=\dfrac {1000×\pi/4 ×10^2}{293.18} \\ =267.88 ≈250mm $

enter image description here

Please log in to add an answer.