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490_Mechanics Homework Mechanics of Materials Solution

490_Mechanics Homework Mechanics of Materials Solution -...

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Unformatted text preview: 4.07 The machine element of Prob. 4.204 is to be redesigned by re- moving part of the triangular cross section. it is believed that the removal of a small triangular area of width at will lower the maximum stress in the element. 2in. ~—31n.——l In order to verify this design concept, write a computer program to calculate B—Ir the maximum stress in the element for values of a from 0 to 1 in. using 0.1- PROBLEM 4.07 p in. increments. Using appropriate smaller Increments, determine the distance a 2 51“ for which the maximum stress is as small as possible and the corresponding . I I i value of the maximum stress. SOLUTION 32:4: Fa; 4*. 79 Pegs“ 2.9? #261,701 13:5,}. b2=2.§;n Abe 61:0 70 /.o 47' 0.! #51752va W 5r.2+a_ a a mam» ARM: 2(6, 7"42)( 15/2) y m. [it 5/;(5/3)+J-.621{25//]/912M fw 9-01-72) 252(6,7L4162) R... FEM/'7' FWD PERM?» EWﬂé/eﬁM 0117' PDT 1 a R sigma!) sigma]! 1:1 in . in . kli 1:51 0.00 3.855 -8.5071 2.1014 0.00 4.00 0.145 0.10 3.858 ~7.7736 2.1197 0.08 4.00 0.144 0.20 3.869 -7.2700 2.1689 0.17 4.01 0.140 0.30 3.884 -6.9260 2.2438 0.25 4.02 0.134 0.40 3.904 -6.7004 2.3423 0.33 4.03 0.127 0.50 3.928 -6.5683 2.4641 0.42 4.05 0.119 0.60 3.956 -6.5143 2.6102 0.50 4.07 0.111 .70 3.985 -6.5296 2.7828 0.58 4.09 0.103 .80 4.018 -6.6098 2.9852 0.67 4.11 0.094 .90 4.052 -6.7541 3.2220 0.75 4.14 0.086 Determination of the maximum co ressive stress that is as small as possible a R sigmaD ‘s gmaB b1 rbar e in . in . ksi ksi 0.620 3.961 —6.51198 2.6425 0.52 4.07 0.109 0.625 3.963 -6.51185 2.6507 0.52 4.07 0.109 0.630 3.964 -6.51188 2.6591 0.52 4.07 0.109 ANSWER: When a r: 625 in. the compressive stress is 6.51 ksi ...
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