Question

There is one force element in xy-axes, with Sigma (x) = 30 MPa, Sigma (y) = 60 MPa, and Tao (xy) = 40 MPa. (Sigma for normal stress and Tao for shear stress) (1) Draw a force element with all above stresses labeled in xy-axes and translate the information on a Mohr's circle; (2) Rotate the force element 30 degree (counterclockwise). Use Mohr's circle to derive the stresses in this new element; (3) Use Mohr's circle to determine the principal stress and maximum shear stress. Draw corresponding force elements. Note: I need solutions using Mohr's circle. All other approaches using equations will be discarded.

Answer 1

- Son Ciren. 6x = 80 Ma . ( Normal s}xep h 4- đire thôn ) ty = 60 MPa (Noomal stress in y-cincinion) y = 4ompa (shear stress in my plane), Dziewing the state of stress on the element, o . 40 mpa ↑ Ey = 60 MPa. y = 30MPa one = Bompa 7 Caryn Llompa, y = 60 MPa. => Clockwise Shear streis is the Dreaving the Mohr circle (You can also draw it Con grapban Dapper with suitable scale and calculabing the required Cs. Scanned with

Data. MC80,40) musel - - * Eny -40% . 11 --- - A boy 69.1440 El que Iox +30 I by to .; 447-40 ..to B (60; 40) centre of Mohr circle = c( Eat by no) CS Scanned with c (45,0) CamScanner

- ® Any angle on element is half of the angle of Mohr circle. so on moho cirle o → 20 80° Go' Counter clock wise ) State of stress at this element is given by point D. which is at an angle 9.44. careeyaled by: angle with a or 6 axis. axis. ant 2o . for calculating To=30° OC- CD Logs 9.49' - 45 - (Radius ces g.yy. Scanned witle cantos e Buner

Torso = 45- (Azpiec? les pinay =.45 - 5 4027152 casquery 150-30 52.85851 mPa. To 30 = Les CD sin 9.44 = Radis) sin9.44. = AE2+ EC2 singung T=3 7.0067 mPa. s o primeiple stsemes. are given by. Major Minor Mojet i principle stes. Bonuple shren 5 = OH = OC 7C14 = Olt Pachiw. 67 = '06 = GC - OC = ladies -06 -VAE2EC2 – 45 = $4024152 - 45 = 45+ TAE2+EC2 2457 4024152 67 - - 2:27 MPa. Ccompresion) G : 87,72 mpa. ( Teorsion) Elemental Representation. 152= -2.27 mPa. 6 = 87.72 MA Scanned with CamScanner

Maximum sheas shen is ginon by. Tomar a Radius of Mohr cirlo. - LAERTEC2 4024 152 Tmax = 42:72 ppa, Elemental Repomerintanoon. Tmax = 42.72 Mpai CS Scanned with CamScanner

Here I have tried my best to explain you each and every step please forgive for any calculation mistake and do comment for any queries.

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