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# Statics: Lecture4c

## by TU Delft OpenCourseWare on Aug 29, 2011

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## Statics: Lecture4c Presentation Transcript

• Today:Area moment of Inertia: Steiner theoremMass moment of InertiaInternal forcesBook: Chapter 10.1,10.2,10.4, 7.1-7.3 + hand outs
• Steiner theorem:Allows you to calculate I x  I x  Ad 2 ymoment of inertia aboutanother axis than through I y  I y  Ad x2the centroid J 0  J 0  Ad 2
• y-asRectangle D D’ dy h/2 yCalculate Ix x-asabout B-B’ and D-D’ h/2 CCalculate Iy B B’about B-D b/2 b/2
• Example: I-beam b Calculate t h Ix & Iy about C.G. t
• Thin-walled structures:- t << h, b- all higher order terms of t may be neglected
• bExample: T-profile(thin-walled) t b 2t
• Example: Ring (thin-walled) tCalculate J0 R
• Source: R.C. Hibbeler, "Engineering Mechanics – Statics"Mass moment of InertiaDefined as the integral of the secondmoment about an axis of infinitesimalelements of mass dm composing the bodyResistance against rotational acceleration
• Source: R.C. Hibbeler, "Engineering Mechanics – Statics"Mass moment of InertiaMass moment of inertia about the z-axisis: I   r 2 dm mUnit: [kgm2]Steiner theorem: I  IG  md 2
• Source: R.C. Hibbeler, "Engineering Mechanics – Statics"Example: Discρ = 8000 kg/m3t = 10 mmCalculate IO
• Source: R.C. Hibbeler, "Engineering Mechanics – Statics"Example: Pendulummade of two identical barsof 100 kg each.
• Note:At the exam the standard area and mass momentsof inertia for circles, cylinders, rings, rectanglesand triangles (area only) as well as the location oftheir centroids are expected to be known.See last 2 pages of book
• Calculate the Internal forces internal forces in C. BA C