$25410222$:$OB$

Due to symmetry:$-$

$($entroid $($C$)$ : $(50\mathrm{.}8mm,127mm)$

$A_A=690\mathrm{.}9m{m}^2$

$A_B=1370\mathrm{.}9m{m}^2$

$A_L=690\mathrm{.}9m{m}^2$

$A=2752\mathrm{.}2m{m}^2$

a$)$

$I_{}={}_{A,B,C}{I}_{}+{}_{A,B,C}A(y^{\text{'}}{)}^2$

$I_{}=(\frac{101\mathrm{.}6{6\mathrm{.}8}^3}{12})2+(\frac{5\mathrm{.}7{240\mathrm{.}4}^3}{12})+690\mathrm{.}9(123\mathrm{.}6{)}^2$

$+1370\mathrm{.}4(0{)}^2+690\mathrm{.}9(-123\mathrm{.}6{)}^2$

$I_{}=27714314m{m}^4=2771\mathrm{.}4c{m}^4$The standard section tables give the following dimensions for a $254\backslash$times $102\backslash$times $22$ UB: D $=254\mathrm{.}0$ mm$,$ B $=101\mathrm{.}6$ mm$,$ t $=5\mathrm{.}7$ mm and T $=6\mathrm{.}8$ mm where the symbols are defined in the diagram shown below.

The tabulated value for Ixx is $2841$ cm$4,$ try to explain the discrepancy. $($Hint you should have a look at the standard section tables for UBs$)$