Please help me with question. I need all the parts with detailed answers please. Thanks! and that for the deflection of a beam under a distributed load f per unit length:1 f Lª8 :8 EIwhere I = t/12. For a self-loaded beam f= p Ag, where p is the density of thematerial of the beam, A its cross-sectional area, and g the acceleration due to gravity.a. Show that the best material for a cantilever beam of given length L andgiven (i.e., fixed) square cross-section (t × t) that will deflect least undera given end load F is that with the largest value of the index M = E,where E is Young's modulus (neglect self-weight). (See Figure E.4(a).)b. Show that the best material choice for a cantilever beam of given a lengthL and with a given section (t × t) that will deflect least under its own self-weight is that with the largest value of M = E/p, where p is the density.(Figure E.4(b).)c. Show that the material index for the lightest cantilever beam of length L andsquare section (not given, i.e., the area is a free variable) that will not deflectby more than ô under its own weight is M = E/p² . (See Figure E.4(c).)d. Show that the lightest cantilever beam of length L and square section(area free) that will not deflect by more than ô under an end load F isthat made of the material with the largest value of M = E'/2/p (neglectself weight). (See Figure E.4(d).) E7.2 Material indices for elastic beams with differing constraints(Figure E.4) Start each of the four parts of this problem by listing thefunction, the objective, and the constraints. You will need the equations forthe deflection of a cantilever beam with a square cross-section t x t, given inAppendix B.3. The two that matter are that for the deflection & of a beam oflength L under an end load F:FL³ЗЕFixed(a)F, 8Force f per unit lengthFixed(b)Force f per unit lengthFree(c)Free(d)F, 8FIGURE E.4

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a. Show that the best material for a cantilever beam of given length L and given (i.e., fixed) square cross-section (t × t) that will deflect least under a given end load F is that with the largest value of the index M = E, where E is Young's modulus (neglect self-weight). (See Figure E.4(a).) b. Show that the best material choice for a cantilever beam of given a length L and with a given section (t x t) that will deflect least under its own self- weight is that with the largest value of M = E/p, where p is the density. (Figure E.4(b).)

a. Show that the best material for a cantilever beam of given length L and given (i.e., fixed) square cross-section (t × t) that will deflect least under a given end load F is that with the largest value of the index M = E, where E is Young's modulus (neglect self-weight). (See Figure E.4(a).) b. Show that the best material choice for a cantilever beam of given a length L and with a given section (t x t) that will deflect least under its own self- weight is that with the largest value of M = E/p, where p is the density. (Figure E.4(b).)

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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