(a) Explanation Given information: The height of the section is 1.5 a . The width of the section is a . The length of the section up to straight edge is 2 a . The length of the section in sloped edge is 2 a . Calculation: Divide the section into 1 and 2. Show the section 1 and section 2 as in Figure 1. Calculate the area ( A ) of the trapezoidal plate as below: A = A 1 + A 2 = ( 2 a × a ) + ( 1 2 2 a × a ) = 3 a 2 Express the mass ( m ) as below: m = ρ t A Here, ρ is density, t thickness of the plate. Rewrite the above equation as, ρ t = m A Substitute 3 a 2 for A . ρ t = m 3 a 2 Express the mass moment of inertia ( I mass ) as below: I mass = ρ t I a r e a Substitute m 3 a 2 for ρ t . I mass = m 3 a 2 I a r e a (1) Calculate the moment of inertia of area ( I x , a r e a ) 1 about x axis for section 1 as below: ( I x , a r e a ) 1 = 1 3 ( 2 a ) ( a 3 ) = 2 3 a 4 Calculate the moment of inertia of area ( I x , a r e a ) 2 about x axis for section 2 as below: ( I x , a r e a ) 2 = 1 (b) To determine Find the mass moment of inertia ( I y , mass ) of the plate with respect to y axis.

11th Edition

ISBN: 8220102809888

Author: BEER

Publisher: YUZU

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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 9.5, Problem 9.117P

(a)

To determine

Find the mass moment of inertia (Ix,mass) of the plate with respect to x axis.

(b)

To determine

Find the mass moment of inertia (Iy,mass) of the plate with respect to y axis.

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Chapter 9.5, Problem 9.116P

Chapter 9.5, Problem 9.118P

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Find the mass moment of inertia ( I x , mass ) of the plate with respect to x axis.