284_Mechanics Homework Mechanics of Materials Solution

# 284_Mechanics Homework Mechanics of Materials Solution -...

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Unformatted text preview: 3.C3 Shaft AB consists of n homogeneous cylindrical elements, which PROBLEM 3'C3 can be solid or hollow. Both of its ends are ﬁxed, and it is subjected to the loading showrn. The length of element 1' is denoted by L,, its outer diameter by Element " 00,, its inner diameter by ID;, its modulus of rigidity by G“ and the torque ap- plied to its right end by T,-, the magnitude T,- of this torque being assumed to be positive if T, is observed as counterclockwise from end B and negative oth- erwise. Note that ID, = 0 if the element is solid and also that T, = 0. Write a computer program that can be used to determine the reactions at A and B, the Elementl maximum shearing stress in each element, and the angle of twist of each ele« ment. Use this program (a) to solve Prob. 3.56, (b) to determine the maximum ' shearing stress in the shaft of Example 3.05. SOLUTION WE chﬁym 7w! 25/957“on H7 6’ (is fepwnﬂwr AND ﬁnal-ass 77+? #49267 M .8 Cd‘MFUTE‘ (T53 tar/7,47 'T‘gto.‘ ﬁ F02 Elia)! arms/97 Fer-r272. LL- 1 004' s (of: 52' Cjcwvvchvz? J5 is/rr/i’é’XODf ' (DZ) 0P6}??? 723/20u5 72 7+ 72 . GNP (ax/117547? For: EAM'REMEW7 774% = 7(oq/2)/JL- pﬁ/c' 1“ Tia/65% (Sm/707;: Eng: 57A/t-7/M tar?» éro QNQ 0.9%?” 75420065 “>0 £2 EW'F/Tf ei=éi+mﬁ .' %=C-9.n own THU; 2 DBL/2e? U/wr ”ff/a 7 45/6542 A392 r aezsaawvar? UNITE-'5 (a) = UNVé‘uﬁ/Z) + UNIT Fwd .S'UPé—‘fi‘l’owpmn ,cbp new was: :97 3 70 a:— 25%. 98+ 75(umrézgmy .-.~ cs . §:;%/{0/w7‘%/w)) 77”” 75.: 27701-7; £94 Ella 525/1497 : Max 5,725.9.- 7am: mat =— mpL, +7§(Um-mu,_-) AMI-F er mar: 727m. PH/é .—. PM; +7.3(UMI7PH/J) Peas/earl» 0077997 problem 3.56 TA :5: -o.290 3mm TB = -o.21o kN*m Element tau max (MPa) Angle of Twist (degrees) 1 -39.588 —1.1'78 2 31.670 1.178 Problem 3.05 TA a -51.'733 1b*ft -38.267 lb'*ft ...
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