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Three rolled steel beam ISWB 300 as shown in the figure are used as built-up sections for columns having Ixx = 9821.6 × 104 mm4 and Iyy = 990 × 104  mm4. The moment of inertia of the combined section Ixx is given as:

Three rolled steel beam ISWB 300 as shown in the figure are used as built-up sections for columns having Ixx = 9821.6 × 104 mm4 and Iyy = 990 × 104  mm4. The moment of inertia of the combined section Ixx is given as: Correct Answer <span style="">206.33 × </span><span style="">10<span style="line-height: 0; position: relative; vertical-align: baseline; top: -0.5em; font-size:10.5px;">6</span></span><span style=""> mm</span><span style=" line-height: 0; position: relative; vertical-align: baseline; top: -0.5em; font-size:10.5px;">4</span>

Explanation:

Let the I-section be named as I1, I2 and I3 as per the given figure.

[ alt="F5 Madhuri Engineering 22.04.2022 D2" src="//storage.googleapis.com/tb-img/production/22/04/F5_Madhuri_Engineering_22.04.2022_D2.png" style="width: 402px; height: 327px;">

The Ixx value of I1 and I3 will lie on same plane/axis for the combined Ixx as shown in the figure.

Similarly, Iyy of I2 will lie on same plan/axis for the combined Ixx as shown in the figure.

Thus combined Ixx for the three rolled steel beam will be:

IXX = (Ixx)1 + (Ixx)3 + (Iyy)2

IXX = (9821.6 × 104 + 9821.6 × 104 + 990 × 104) = 20633.2 × 104 mm4 = 206.33 × 106 mm4.

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