Question

Qustion : An L diameter rod with L length is supported by one end. F1 and F2 affect the forces welded to the free end of the rod. In this case, examine the stress state of point A of the section in the middle of the rod and find the values and directions of the prime stresses by drawing the mohr circle. given: L = 20 cm, d = 3 cm, a = 25 cm, F1 = 200 N, F2 = 500 N. -

question

Answer 1

W The force Fo creates a clockwise torque on the rod TI • Fixa - 200 * (25x10-2) N-m [ Clockwise torque -stre? Anti u - ve] The force F₂ creates anticlockwise torque on the rod T₂= Fexa --500 * (25*10-2) = - 125 N Total torque T= Titt, + 500-125 =-75 N-m [ Anti clockwise Total force on the rod F Fit +Ę 700 N - Bending moment at the section of point a FX4 20x10-2 = F x 2 70 N-m Poler moment of inertia of the rod cross section about neutral axis through the center J- TT 32 D4 17 12 (3x10=274 mi = 7.952 X10-8 Aren moment of inentin of the cross section about neutral axis. 3 1 3.976 x 10-8 my

The nexttal axis of the rod is equivalent to centroidial axis, because the rod is proper circut a Distance of point A from the to centroidia neutral axis 3x10-2 YA 2 1.55 X10-> Tensile bending moment stress at a MX YA ra 70x1.5x18-2 3.976X 18-8 I = 26.41 x lot N/m = 26.41 MPa A Sher stress due to the torque ZA TX YA X YA 75*1.5*10-2 7.952 710-8 ZA 14 15 x 106 Hlmm -14.15 MPa * The negetive sign indicates the and clockwise sherr stress in the section. . The stress element of point A 26.41 MPa 14.15 >X Mea

As per the co-ordinate system drown beside Tx TA = 26.41 MPa Ty=0 Zxy = ZA = -14.15 MPa .: The center of the Mohor's circle C = 10,0) Ty try 26.nl to c = 13.205 MP 2 2 The center point location C = (13.205,0) The radius of the Mohs's circle r [ (5-03) + zay]' [(26.41–0)7 (-14-15)]" .: r 19. 354 MPa : The Mohr's circle is az (MPa) (0,0) r (MPN) (5210) (1,0)

From the Mohrs circle the principle prime stresses awe = Ctr =+32.550 MP * the sign indicates tensile stress directed outward and Tz Cars -6.149 MPa -re sign indicales compressive stress directed in wada. @ If you have any confirsion with the solution, please ask me in the comments.