Explanation Calculation: Sketch the cross section shown in Figure 1. Express the product of inertia as shown below: I ¯ x y = ( I x y ) 1 + ( I ¯ x y ) 2 + ( I ¯ x y ) 3 Here, [ ( I x y ) 1 , ( I x y ) 2 , ( I x y ) 3 ] is product of inertia of section 1,2 and 3. The centroid of the section 2 is symmetry with neutral axis. ( I ¯ x y ) 2 = 0 Applying parallel axis theorem, I x y = I x ′ y ′ + x ¯ y ¯ A I x ′ y ′ = 0 Refer to Figure 1. Find the area of rectangle section 1 as shown below: A 1 = b 1 h 1 (1) Here, b 1 is width of the rectangular section and h 1 is height of the rectangular section. Substitute 10 mm for b 1 and 80 mm for h 1 in Equation (1). A 1 = 10 × 80 = 800 mm 2 Find the area of rectangle section 3 as shown below: A 3 = b 3 h 3 (2) Here, b 3 is width of the rectangular section and h 3 is height of the rectangular section. Substitute 10 mm for b 3 and 80 mm for h 3 in Equation (1)

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Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provi…

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Chapter 9.3, Problem 9.71P

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Find the product of inertia of the area with respect to x and y axes by using parallel axis theorem.

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Chapter 9.3, Problem 9.70P

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(b) A steel 'hot rolled structural hollow section' column of length 5.75 m, has the cross-section shown in Figure Q.5(b) and supports a load of 750 kN. During service, it is subjected to axial compression loading where one end of the column is effectively restrained in position and direction (fixed) and the other is effectively held in position but not in direction (pinned). i) Given that the steel has a design strength of 275 MN/m², determine the load factor for the structural member based upon the BS5950 design approach using Datasheet Q.5(b). [11] ii) Determine the axial load that can be supported by the column using the Rankine-Gordon formula, given that the yield strength of the material is 280 MN/m² and the constant *a* is 1/30000. [6] 300 600 2-300 mm wide x 5 mm thick plates. Figure Q.5(b) L=5.75m Pinned Fixed

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Find the product of inertia of the area with respect to x and y axes by using parallel axis theorem.

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