2.7. The principal stresses at a given point are o1 =10 MPa, ơ2=-100 MPa. Sketch Mohr's circle for this state of stress and determine the normal stress on a plane in- clined at an angle 0 to the principal plane 1. Hence find the range of values of 0 for which the normal stress is tensile.

2.7. The principal stresses at a given point are o1 =10 MPa, ơ2=-100 MPa. Sketch Mohr's circle for this state of stress and determine the normal stress on a plane in- clined at an angle 0 to the principal plane 1. Hence find the range of values of 0 for which the normal stress is tensile.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.2.21P: An clement m plane stress from the frame of a racing car is oriented at a known angle 8 (sec...

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Concept explainers

Stress transformation

The term stress indicates the measure of internal forces that develop due to an external force's application on an object. When a specific external force is applied to an object, internal stress generates in the material. The value of stress can obtain by taking the ratio of the externally applied force and cross-sectional area of the object. There are different types of stress depending on the type of external force.

Question

2.7. The principal stresses at a given point are ơj =10 MPa, ơ2=-100 MPa. Sketch
Mohr's circle for this state of stress and determine the normal stress on a plane in-
clined at an angle 0 to the principal plane 1. Hence find the range of values of 0 for
which the normal stress is tensile.

Expert Solution

Step 1

Given data:

The positive principal stress, $σ_{1} = 10 MPa$ .
The negative principal stress, $σ_{2} = - 100 MPa$ .

The center of Mohr's circle is given as, $(σ_{a v g}, 0)$ .

Calculate the average stress as follows:

$\begin{array}{rcl} σ_{a v g} & = & \frac{σ_{1} + σ_{2}}{2} \\ = & \frac{10 MPa + (- 100 MPa)}{2} \\ = & - 45 MPa \end{array}$

So the center of the Mohr's circle lies at $(- 45 MPa, 0)$ .

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