Question

Consider the given state of stress. Take X = 10 MPa and Y = 45 MPa.

60 MPa

Determine the principal planes using Mohr's circle. a) The principal planes are at −  ° and  °.

Determine the principal stresses using Mohr's circle. b)The minimum principal stress is −  MPa, and the maximum principal stress is  MPa.

Determine the orientation of the planes of maximum in-plane shearing stress using Mohr's circle. c) The orientation of the plane of maximum in-plane shearing stress in the first quadrant is  °. The orientation of the plane of maximum in-plane shearing stress in the second quadrant is  °.

Determine the maximum in-plane shearing stress using Mohr's circle. d) The maximum in-plane shearing stress is  MPa.

Determine the normal stress using Mohr's circle. e)The normal stress is  MPa.

Answer 1

Given State of stren Standard Element 45MPa Gorpa lorpa . Tx= LOMPa Ty= -45hPa ox, ty are & They tue' Тау -- бонро- 97 (+) Theox = ✓ x²x42 Gif-83.5Mpi Joy -> 60 Sous 4030 20 TH-> ve 90s 70 (-ve) o - 02 "I love 48.50MP =) = 83.5HP

6 Major Ę Mindt principle Streu o 7 ox toy t Pay oz on 100k + sleeus )* + 1-4 10-45 To +45 12 -11: St | 21^+ 65 T =) - 17.5+ 66 = 48.50 MPa 1 77.5tla G -175-66 102 31-83.5MPO From Moker's Circle also = 48.5 MPa J = -83.5 MPa oleinatation of Principal plane Tan a - 2 Try Op= - Txury Tan20p, 2X(-60) 10+45

.-120 Taul20p) = 55 2 Op =-65.37 - 32.688 qe oport Since principal Planes are Opz= -32.688 +90% [Opz = 57.312 t О - Нахімом іл- Pla fluot bом From Mokris cicle, the radius of circle is known as rase shear stress Therese J-+ Tage lang ito ng tous Tasot JC10345) ? te boje - Theox = Truy? 2 from I phythagorous theolm | Тех - 66 HPa © Ilientation of Mox shear stren Os, a Opi tus° -32-688 +45° (Os, = 12.3120 l istanadrout

Os2= Op. +45° - 57.312 + 45° [Os2 = 10233120 and quadrant © Holmeal stren= Extry Average - lo-u5 = 2 To = -17.5 MPa