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MPSC AE CE Mains 2019 Official (Paper 1)

Option 1 : Flexural strength of the plate

ST 1: Building Construction and Materials

1095

20 Questions
40 Marks
24 Mins

It is assumed that the maximum bending moment occurs at the edge of the column. As a slab tends to bend simultaneously about the two principal axes, the stress caused by bending about one axis is influenced by stress due to bending about other axes. The Poisson ratio of 0.3 is used to account for this effect.

\({M_{x,net}} = \frac{{w{a^2}}}{2} - 0.3\frac{{w{b^2}}}{2} = \frac{w}{2}\left( {{a^2} - 0.3{b^2}} \right)\) ----- (1)

Moment capacity of plate = 1.2 f_{y}Z_{e}

\(= 1.2{f_y} \times 1 \times \frac{{t_s^2}}{6}\) ---- (2)

Equating (1) and (2)

\(\frac{{1.2{f_y}t_s^2}}{6} = \frac{w}{2}\left( {{a^2} - 0.3{b^2}} \right)\)

Applying partial factor of safety = γ_{m0}

\(\begin{array}{l} \frac{{1.2{f_y}t_s^2}}{{6{\gamma _{mo}}}} = \frac{w}{2}\left( {{a^2} - 0.3{b^2}} \right)\\ {t_s} = \sqrt {\frac{{2.5w\left( {{a^2} - 0.3{b^2}} \right){\gamma _{mo}}}}{{{f_y}}}} \end{array}\)