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7.4-18 - Problems 14-15 llll'flllgl'l LII-23 An element...

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Unformatted text preview: Problems 14-15 llll'flllgl'l LII-23 An element inplane stress is F subjected to stresses 0'1, of and TI? {see figure]. a- Using Molir's circle, detemiine [a] the prineipal stresses and J" {h} the maximum shear stresses and associated normal stresses. l Show all results on sketches of properly oriented elements. #33. [-l a; '1— —I- I T Data farT.4-1fl a: = G, a? = —22.4 MP3, r1? = —fi.fi MPa Solution LII-1E Principal stresses a: = D a? = —’22.4 MP3 1"? = —6.fi MP3 {All stresses in MP1!)- 1'9“: —n1' — 9D“ = —11DI.51° H" = —fi0.26° “219" = 90° — a: = 59.49” E": = 29.T4° Point 31: an” = —ll.1MPa rm = R = 13.12] MP5 Point 32: an” — —ll.1MPa rm = —13.D MPH R = U{11_2]3+ {6.613 = 13.1] MP3 6.6 = 31351" 11.2 or = arctan {a} PRINIIPHL 511133535 291,. = —a = —3D.51° HP. = —15.2fi° is” = 180“ — a = 14949“ HP: = 74.74“ Point P1: a1 = R — 11.2 =1.s MP3 Pm'm P3: or: = —11.2— R = —%2m ...
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