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answer key to stress homework 2

answer key to stress homework 2 - GEOL 3071 Structural...

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GE OL 3 071 : S tru ct u ra l G eo l ogy Stress Homework 2 1 . Stra i g ht o u tt a F i g ur e 3 .10 in yo ur b ook : E s tim ate th e n or m a l a nd s h ear s tr e s ses on t h e s i x pla n es [ i n (a)] by ap pl y i ng th e Mo hr cir c l e cons tr uct i o n [ i n ( b )]. P r in c i pa l stresses a nd a n g l es 8 a r e g i ve n in (a) . Yo u ca n c h eck yo u r es tim ates by u s in g E qu a t io n s 3 . 7 a nd 3. 10 f r o m yo ur b oo k , bu t will o nly r ece iv e f ull m a rks if y o u s h o w t h e compl e te M o hr ci rc l e . (' 1 1 00 MP a I I I 8 0 i : + - -_ .. j I I ~- f - I i I 6 0 ! i I 4 0 I r ~ ! P2 i - I 20 i I il - i i 1 / - \ I -- ~ i bo ll 1 ;( ,; 0 I n . n 120 1 0 0 8 0 60 4 0 20 2 0 J 4 0 80 80 dO l 1 20 I ! \ J I 20 ~ - - I , / - - I -- ._- . - _ ~ . .. . . L +: :: - I I 4 0 I ! I ! i t " t n ! ; I - rt - - _._- - I -- ~ - -- ~ 60 · - - ~ - r -- - y -- - - I -- f - - - I - f = - r - 1 - - I -~ ~ + t . ~ J-l - -- + - - - + -- i - I - ++ . + I -- H - +- + - - - - 1- - 8 0 I I I . ~ G ",,= . \{ )O " "Po ., Q s : : . o M f a - f ~~ ~ 252 M f ~ \ G : : ' 3 oW\P~ 6> Mp 6{ = - 35 MP~ 2 . Co n s i de r t h e st r ess a t a p o in t . T h e pri n c ipa l s t resses are 01 = 50 MPa a nd 0 3 = 30 MP a . G ive n th a t th e p o l e to t h e pl a n e P i s o ri ente d 45 ° f r o m t h e axis o f th e 0\ pri n cipa l s tr e ss ( i .e ., 8 = 45 ° ) ,
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