Question

Given the stress element below: 1. Draw Mohr Circle for the stress element shown below. Use proper scale and draw neatly. 2. Show and label the principal and max shear stress on the circle. 3. On the Mohr circle indicate the angles form the X-axis of Mohr circle to the o axis and Tmax axis. 4. Draw stress elements for initial, principal, maximum shear in their proper orientation. Mark all points on Mohr Circle and corresponding points on stress elements with A, B, C, D, E and F. у 200 MPa (T) A-100 MPa (CCW) B -150 MPa (C) A

Answer 1

Solution:

1)Fig 1 represents the required Mohr circle for the given state of stress,

300.0 Max shear = 2016 250.0 (-150.0, 100.0) 2000 (-150.0, 100.0) 150.0 100.0 X 50.0 Min prin = -176.6 (25.00, 0.0) 100.0 -400.0 -300.0 -200.0 - 100.0 200.0 500.0 010 -50.0 300.0 400.0 Max prin = 226.6 - 100.0 - 150.0 (200.0, -100.0) (200.0, -100.0) -200.0 -250.0 Min shear = -201.6 -300.0

Fig 1: Mohr circle for the given state of stress

2)

Please refer to fig 1 for the labelled representation of principal and max shear stress state.

3)

Please refer to table 1 to find the required values.

Results

	Value	Angle [deg]
Rotated Element, Normal Stress X	-150.0	0.000°
Rotated Element, Normal Stress Y	200.0	90.00°
Rotated Element, Shear Stress	-100.0	---
Max Principal Stress	226.6	-75.13°
Min Principal Stress	-176.6	14.87°
Max Extreme Shear Stress	201.6	-30.13°
Min Extreme Shear Stress	-201.6	59.87°

Table 1 : Mohr circle result

4) Please find the following figures for initial state, principal stress state and shear state stress

Unrotated Element(Black Line in Mohr's Circle) o.y = 200.0 T= -100.0 у 1966% Ľ х O.X = -150.0 T = 100.0 T= -100.0 o.y = 200.0

Rotated Element (0.000 deg) O.y = 200.0 T= -100.0 10964 Ľ х X = -150.0 T = 100.0 T= -100.0 O.y = 200.0

Element Rotated to Max Principal Stress (-75.13 deg) 0.X = 226.6 T = 0.000 O.y = -176.6 0.000 O.y = -176.6 T+0.000 T = 0.000 0.X = 226.6

Element Rotated to Max Shear Stress (-30.13 deg) O.y = 25.00 T = 201.6 0.X = 25.00 T=-2016 у X 0.X = 25.00 T = 201.6 0.y = 25.00 T=-2016

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