Answered: 100 mm y' 400 mm Op, = 57.1° 100 mm Өр,…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Determine the principal moments of inertia for the beam’s cross-sectional
the area is shown in Figure with respect to an axis passing through the centroid C.

100 mm
y'
400 mm
Op, = 57.1°
100 mm
Өр,
= -32.9°
400 mm
100 mm
600 mm

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Step 2

Moment of Inertia,

$I_{x x} = (I$ _xx)1+(I_xx)2+(Ixx)3 mm4Ixx=(100X300312+(100X300)(-250)2)+(600X100312)+(100X300312+(100X300)(250)2) mm4Ixx=0.00425 m4 ....(1) Iyy=(Iyy)1+(Iyy)2+(Iyy)3 mm4 Iyy=(300X100312+(300X100)(200)2)+(100X600312)+(300X100312+(100X300)(-200)2) mm4Iyy=0.00665 m4

$I_{x y} = (I$ _xy)1+(I_xy)2+(Ixy)3 mm4Ixy=(I_xy+axy)1+(I_xy+axy)2+(I_xy+axy)3 mm4Ixy=(0+100X300X(-250)X200)+(0+(100X600X0X0) + (0+100X300X250X(-200)) mm4Ixy=0.003 m4....(3)

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