Question

1) An element in plane strain has a 60° strain rosette that is 150 from the x axis. Use Mohr's circle to determine. E = 29,000 ksi G= 11,200 ksi &=-.0015 E, = .004 E = -0025 a) The principal strains and maximum shear strain. b) Determine the location of the principal strains. c) Determine the stresses from the strains given d) Determine the stresses from the principal strains

Answer 1

Sed from the x-axias an element in the plane stories house 60° asteain Borgette , ie,j... 15° any ebb Eo G-1 G=11200 Ksi E = 29000ks 37 = 15; 02-75° O3 = 135° EQ:-0.0015 €6:+0.004 fc:-0.0025 calculation of exand Ey estrain (by trams formation equation) ca: Extey + Ese - @y cos 2017 sy sin Bol -o-o0ls. Ezt c4 + even y cos 30° + z sey ein 30° → 1.466 Ex +0.134 ty +0.5782y =-3x10 30 ef. God they + Gewell cos (73) +0:57 veyos ?n 2(75) +0.008 = 0.134 Ex +1.866 ty +0-57dy - © (0.0023) (2) - Eset ey + Ex-Ey COS270 + 7an yorim 270 → Eset@y-7 sy = - 5x103- from solving we get . Ex Scaen3ta x103; ty = 3:17 xto '; Escy = 5x10 CamScanner

Es 117542 point 0 - Exe) -Joyle point ® Ej, Tayla esign conuention a astear ④ shear 73.194103, 5x162 on your story in 1013* (a) principal strains from mohsi ciude Emax = Radius of mohar cirde -|(63) + (y)? Csonti (2177103)+(85 4162)

major Emor = 4.037 xto3 poincipal Storain Minor principal axis "Emin = -4.037X103 = VA 317 x 18 )2 +25x10 je Maximum ashear estrain from mots circle maximum shear astrain = Radius of mots circle [rev_max =26421037 from rosto corde b) perincipal Horarin we located to distance from Begin @ 38.220) 4 141.7499 from or sy axis. = 38.280 3:0=38.269 I (2) Es 6 - by u Scanned witale 2 CamScanner

G= eletud 11200 = 0 11200 # 2/1+4) - 29000 (1+2) = 29000 alt=0.2946. - 3112x153 _ - 0 2946 X 4 29000 29000 [9:43 • Ge - 0.2946 cy] - © a = b - Home [9.93. Gy - 0.2948 6:e] - © [G =-11&s?) oy = a1 ksy] Tey = Go Joey = 11200 X 5x10 · [Tosy = 56 ksy]: 1 d) Emax 6max homin 11:073 = omax - (0-2946) (oman) scam.073.7 min - (0-2946) (max) Cam Scanner

i [cro-go itake = 90.43 ks, omin=-90.43 ksi Timax Joymax . ha 8.07 x 103 x11200 . = 90.43k309 cs Scanned with CamScanner
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