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A built-up section is made by joining two equal I-sections at the flanges at their outer faces so that the composite consists of one I-section above the other. The moment of inertia of each section through a centroidal axis parallel to the web is Iyy. The moment of inertia of the composite built-up section about a similar axis is:

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  1. \(\frac{I_{yy}}{2}\)
  2. 2Iyy
  3. 4Iyy
  4. Iyy

Answer (Detailed Solution Below)

Option 2 : 2Iyy
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Detailed Solution

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Concept:

A built-up section formed by placing two equal I-sections one above the other has its moment of inertia about an axis parallel to the web calculated by summing the individual moments of inertia of the sections (when the axis remains unchanged).

Given:

  • Each section has a moment of inertia = Iyy
  • Axis of interest is parallel to the web (horizontal)

Calculation:

Since the axis is at the same level and passes through the centroid of each I-section in the same direction:

\( I_{\text{total}} = I_{yy} + I_{yy} = 2I_{yy} \)

 

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More Moment of Inertia and Centroid Questions

Q1.For a symmetrical T-section, the moment of inertia through centroidal axes in its plane parallel to the flange Ixx = 2 × 107 mm4, and perpendicular to the flange is Iyy = 1.5 × 107mm4. The moment of inertia about the centroidal axis normal to the planar area works out to (in mm4):
Q2.A symmetrical I-section has a moment of inertia about the centroidal axis in its plane perpendicular to the web, of 22.34 × 104 mm4. The moment of inertia of the full rectangular area occupied by the I-beam cross section about this axis is 65 × 104 mm4. The two empty spaces on either side of the web are square. What is the height of the web?
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Q6.A symmetrical planar built-up section consists of two channel sections joined together at the tips of their flanges to form a closed rectangular area. The total width of each flange is ‘B’. Each web is ‘w’ units deep inside, ‘D’ units deep at its outside (longer) face, and ‘b' units thick. The moment of inertia of the composite section about its centroidal axis perpendicular to the webs is given by:
Q7.A symmetrical T-section has its flange horizontal on top. Its dimensions are: Flange: Width = 100 mm, thickness = 24 mm; Web: Height = 84 mm, thickness = 20 mm. Its moment of inertia about a vertical axis through its centroid parallel to the web is (in mm4):
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More Engineering Mechanics Questions

Q1.What is a characteristic of a coplanar parallel force system?
Q2.Which of the following options best describes non-coplanar concurrent forces?
Q3.For a symmetrical T-section, the moment of inertia through centroidal axes in its plane parallel to the flange Ixx = 2 × 107 mm4, and perpendicular to the flange is Iyy = 1.5 × 107mm4. The moment of inertia about the centroidal axis normal to the planar area works out to (in mm4):
Q4.Which of the following happens when two equal and opposite forces are applied at a point on a rigid body?
Q5.A symmetrical I-section has a moment of inertia about the centroidal axis in its plane perpendicular to the web, of 22.34 × 104 mm4. The moment of inertia of the full rectangular area occupied by the I-beam cross section about this axis is 65 × 104 mm4. The two empty spaces on either side of the web are square. What is the height of the web?
Q6.When two equal forces F act at an angle θ, the resultant force is given by which of the following expressions?
Q7.A beam with a symmetrical T section has a top flange 50 mm wide and 20 mm thick, and a web 40 mm high and 10 mm thick. An additional plate, 10 mm thick and 60 mm wide, is welded above the flange. The moment of inertia of this symmetrical planar cross- section about an axis in its plane normal to the web and in line with the upper face of the 10 mm thick plate works out to 1506,666.66 mm4. The centroidal axis of the combined area is 21.5 mm below this axis, normal to the web. The moment of inertia of this built-up area about the centroidal axis is (in mm4):
Q8.Which of the following beams is classified as a statically determinate beam?
Q9.The radius of gyration about the polar axis of a circular lamina of radius 0.2 m is:
Q10.How is the resultant force calculated if two forces act along the same straight line but in opposite directions?
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