Calculate the Moment of inertia for the beam as shown in fig. Keeping the same cross-sectional area if the depth is made twice the width. Calculate the moment of inertia, by doing so load carrying capacity of beam increases or decreases?

1. Moment of inertia:

$(I_{NA})_I=\frac{bd^3}{12}=\frac{10*10^3}{12}=833.33mm^4$

When depth is mode twice the width,

$(I_{NA})_II=\frac{bd^3}{12}=\frac{10*20^3}{12}=6666.67$

Section of modulus=Z=$\frac{I_{NA}}{y_{max}}$

$Z\propto I_{NA}$

When $I_{NA}$ increased then section modulus increases which means increases the load carrying capacity of beam. Hence load capacity increases.