www.mechdiploma.com Moment​ ​of​ ​Inertia

List​ ​of​ ​types 1.​ ​Problems​ ​on​ ​Parallel​ ​and​ ​Perpendicular​ ​axis​ ​theorem. 2.​ ​Problems​ ​on​ ​Composite​ ​standard​ ​sections ​ ​ ​ ​ ​( Angle, C − channel, I − section, T − section ) 3.​ ​Problems​ ​on​ ​Composite​ ​sections ​ ​ ​ ​ ​ ​(​ ​involving​ ​rectangle,triangle,semicircles​ ​and​ ​quarter​ ​circles)

  ​ ​Developed​ ​By​ ​:​ ​Shaikh​ ​sir’s​ ​Reliance​ ​Academy,​ ​Near​ ​Malabar​ ​Hotel,​ ​Station​ ​road,​ ​Kolhapur​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Contact​ ​:[email protected]

www.mechdiploma.com ​ ​Type​ ​1.​ ​Problems​ ​on​ ​Parallel/Perpendicular​ ​axis​ ​theorem. 1.Determine​ ​the​ ​MI​ ​of​ ​a​ ​triangular​ ​section​ ​having​ ​base​ ​5​ ​cm​ ​and​ ​6​ ​cm​ ​height​ ​about​ ​its​ ​base. {Ans:​ ​ I base = 900 × 103 mm4 } 2.A​ ​triangular​ ​section​ ​has​ ​base​ ​100​ ​mm​ ​and​ ​300​ ​mm​ ​height​ ​determine​ ​moment​ ​of​ ​inertia​ ​about the​ ​centroidal​ ​axis​ ​parallel​ ​to​ ​axis​ ​1)MI​ ​about​ ​axiz​ ​passing​ ​through​ ​base​ ​2)MI​ ​about​ ​axis​ ​passing through​ ​apex​ ​3)​ ​MI​ ​about​ ​axis​ ​passing​ ​through​ ​apex. {Ans:​ ​ I base = 225 × 106 mm4 , I gg = 75 × 106 mm4 , I apex = 675 × 106 mm4 } 3.Find​ ​the​ ​moment​ ​of​ ​inertial​ ​of​ ​a​ ​hollow​ ​circular​ ​section​ ​having​ ​external​ ​diameter​ ​100​ ​mm​ ​and internal​ ​diameter​ ​80mm​ ​about, 1)​ ​Axis​ ​passing​ ​through​ ​center​ ​2)​ ​About​ ​tangent​ ​to​ ​the​ ​outer​ ​circle​ ​and​ ​parallel​ ​to​ ​xx​ ​axis. { I xx = 2.89 × 106 mm4 , I pq = 9.94 × 106 mm4 } 4.Find​ ​the​ ​moment​ ​of​ ​inertia​ ​of​ ​a​ ​hollow​ ​rectangular​ ​section​ ​about​ ​its​ ​centre​ ​of​ ​gravity,​ ​if​ ​the external​ ​dimensions​ ​are​ ​40​ ​mm​ ​deep​ ​and​ ​30​ ​mm​ ​wide​ ​and​ ​internal​ ​diamension​ ​ar​ ​e25​ ​mm​ ​jand​ ​15 mm​ ​wide. { I xx = 140470 mm4 , I yy = 82970 mm4 } 5.​ ​An​ ​isosceles​ ​triangular​ ​section​ ​ABC​ ​has​ ​base​ ​width​ ​80​ ​mm​ ​and​ ​height​ ​60mm.​ ​Determine​ ​the moment​ ​of​ ​inertia​ ​of​ ​the​ ​section​ ​about​ ​the​ ​centre​ ​of​ ​gravity​ ​of​ ​the​ ​section​ ​and​ ​the​ ​base​ ​BC. { I xx = 480 × 103 mm4 , I pq = 1440 × 103 mm4 } 6.A​ ​hollow​ ​C.I.​ ​pipe​ ​with​ ​external​ ​diameter​ ​100​ ​mm​ ​and​ ​thickness​ ​of​ ​metal​ ​10​ ​mm​ ​is​ ​used​ ​as​ ​a strut.​ ​Calculate​ ​the​ ​moment​ ​of​ ​inertia​ ​and​ ​radius​ ​of​ ​gyration​ ​about​ ​its​ ​diameter. { I xx = 2.89 × 106 mm4 , K xx = 32.017 mm } 7.A​ ​circular​ ​disc​ ​has​ ​M.I.​ ​about​ ​its​ ​any​ ​tangent​ ​is​ ​ 6.283 × 105 mm4 .​ ​Find​ ​the​ ​diameter​ ​of​ ​the​ ​disc. { d = 40 mm}

8.An​ ​equilateral​ ​triangle​ ​has​ ​a​ ​side​ ​of​ ​150​ ​mm.​ ​Find​ ​the​ ​moment​ ​of​ ​inertia​ ​about​ ​any​ ​of​ ​its​ ​sides. { I pq = 27.404 × 106 mm4 } 9.Find​ ​MI​ ​of​ ​and​ ​equilateral​ ​triangle​ ​of​ ​side​ ​2m​ ​about​ ​its​ ​base. { I pq = mm4 } 10.A​ ​semicircular​ ​lamina​ ​has​ ​a​ ​base​ ​diameter​ ​140mm.​ ​Calculate​ ​the​ ​moment​ ​of​ ​inertia ​ ​ ​ ​1)​ ​about​ ​centroidal​ ​axis​ ​ ​2)​ ​about​ ​base. { I xx = 2.64 × 106 mm4 , I pq = 9.428 × 106 mm4 } 11.Calculate​ ​Polar​ ​MI​ ​of​ ​a​ ​square​ ​section​ ​having​ ​200mm​ ​as​ ​side. {​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​} 12.Calculate​ ​polar​ ​moment​ ​of​ ​inertia​ ​for​ ​a​ ​circle​ ​having​ ​diameter​ ​250​ ​mm. { ​ ​} ​ ​Developed​ ​By​ ​:​ ​Shaikh​ ​sir’s​ ​Reliance​ ​Academy,​ ​Near​ ​Malabar​ ​Hotel,​ ​Station​ ​road,​ ​Kolhapur​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Contact​ ​:[email protected]

www.mechdiploma.com ​ ​Type​ ​2.​ ​Problems​ ​on​ ​composite​ ​standard​ ​section.

1.​ ​Find​ ​MI​ ​of​ ​a​ ​“T”​ ​section​ ​about​ ​its​ ​centroidal​ ​axis​ ​having​ ​following​ ​dimensions, ​ ​ ​ ​ ​ ​1)​ ​Flange=200​ ​mm​ ​ × 40​ ​mm​ ​ ​ ​ ​ ​2)​ ​Web=​ ​ ​200​ ​mm​ ​ × ​ ​40​ ​mm { I xx = 85.33 × 106 mm4 , I yy = 27.733 × 106 mm4 }

2)​ ​Find​ ​Ixx​ ​and​ ​Iyy​ ​for​ ​an​ ​unequal​ ​angle​ ​100​ ​ × ​ ​80 × 10​ ​mm.​ ​100​ ​mm​ ​leg​ ​is​ ​horizontal. { I xx = 0.952 × 106 mm4 , I yy = 1.672 × 106 mm4 }

3)​ ​Find​ ​MI​ ​of​ ​a​ ​T​ ​section​ ​200​ ​ × ​ ​20​ ​mm​ ​flange​ ​and​ ​180 × ​ ​20​ ​mm​ ​web​ ​about​ ​x​ ​axis. { I xx =

mm4 }

4}A​ ​symmetrical​ ​I​ ​section​ ​has​ ​the​ ​following​ ​dimensions, ​ ​ ​ ​Flanges=100mm​ ​ × ​ ​10mm,​ ​ ​Web=10​ ​mm​ ​ × ​ ​100​ ​mm.​ ​Calculate​ ​Polar​ ​MI​ ​of​ ​the​ ​section. { I P = 8.575 × 106 mm4 }

5)Calculate​ ​Ixx​ ​and​ ​Iyy​ ​for​ ​an​ ​unequal​ ​angle​ ​section​ ​70​ ​ × ​ ​50 × 10​ ​mm.​ ​Take​ ​70​ ​mm​ ​leg​ ​vertical { I xx = 0.952 × 106 mm4 , I yy = 1.672 × 106 mm4 }

6)Determine​ ​Momento​ ​of​ ​inertia​ ​about​ ​xx​ ​and​ ​yy​ ​axis​ ​of​ ​I​ ​section​ ​having​ ​following​ ​dimensions ​ ​ ​ ​ ​Top​ ​flange​ ​:​ ​20​ ​ × ​ ​80​ ​mm,​ ​ ​ ​ ​ ​Web​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​:​ ​10​ ​ × ​ ​280​ ​ ​mm,​ ​ ​ ​ ​Bottom​ ​Flange​ ​ ​:​ ​120​ ​ × ​ ​20​ ​mm {Ixx=106.4​ ​ × 106 mm4 ,​ ​Iyy​ ​=​ ​3.756​ ​ × 106 mm4 ​ ​}

7)​ ​A​ ​c​ ​Channel​ ​is​ ​shown​ ​below​ ​find​ ​its​ ​Moment​ ​of​ ​inertia​ ​about​ ​xx​ ​and​ ​yy​ ​axis.

{Ixx​ ​=​ ​4.4733​ ​ × 106 mm4 ,​ ​Iyy​ ​=​ ​0.7097​ ​ × 106 mm4 }

8.​ ​Find​ ​the​ ​radius​ ​of​ ​gyration​ ​of​ ​the​ ​channel​ ​section​ ​about​ ​the​ ​centroidal​ ​axis​ ​as​ ​shown​ ​below

{Ixx=327.05​ ​ × 103 mm4 } ​ ​Developed​ ​By​ ​:​ ​Shaikh​ ​sir’s​ ​Reliance​ ​Academy,​ ​Near​ ​Malabar​ ​Hotel,​ ​Station​ ​road,​ ​Kolhapur​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Contact​ ​:[email protected]

www.mechdiploma.com TYPE​ ​3​ ​ ​:​ ​Problems​ ​on​ ​Composite​ ​sections ​ ​ ​ ​ ​ ​(​ ​involving​ ​rectangle,triangle,semicircles​ ​and​ ​quarter​ ​circles)

​ ​Developed​ ​By​ ​:​ ​Shaikh​ ​sir’s​ ​Reliance​ ​Academy,​ ​Near​ ​Malabar​ ​Hotel,​ ​Station​ ​road,​ ​Kolhapur​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Contact​ ​:[email protected]

section.

the​ ​centroidal​ ​axis​ ​parallel​ ​to​ ​axis​ ​1)MI​ ​about​ ​axiz​ ​passing​ ​through​ ​base​ ​2)MI​ ​about​ ​axis​ ​passing through​ ...
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