Expression for the normal and tangential stresses, Mechanical Engineering

Expression for the normal and tangential stresses:

By sing Mohr's circle, derive expression for the normal and tangential stresses on a diagonal plane of material subjected to pure shear. Also state and explain the mohr's theorem for slope and deflection.

Sol.: Mohr circle is graphical method to find out stress system on any inclined plane through body.
It is circle drawn for compound stress system. The centre of circle has the coordinate  1417_Expression for the normal and tangential stresses.png 
and radius of circle is

by drawing mohr's circle of stress following 3 systems can be determined
(a) The shear stress, normal stress, and resultant stress on any plane.

(b) Principal stresses and principal planes.

(c) Maximum shearing stresses and the planes of them along with the associated normal stress.

Mohr's circle can be drawn for compound strain system.

1. Mohr's circle of stress with the reference to 2 mutually perpendicular principal stresses acting on the body considers both dike stresses.

Both the principal stresses can be considered as (a) Tensile and (b) Compressive.

Let us for tensile

That is;
 σx> σy


l. Mark OA = Sx and OB =  Sy, along  x-axis (on positive side if tensile and negative side if compressive).

2. Draw circle with BA as diameter, called as mohr's circle of stress.

3. To obtain stress on any plane ¸ as shown in the figure given below measure angle ACP = 2¸ in anti clockwise direction.
4. The normal stress on the plane is Sn = OQ

    Shear stress is τ = PQ

    Resultant stress = σr = OP

    And Angle POQ = ? is called as angle of obliquity.

2. Mohr's stress circle for a two dimensional compound stress condition shown in fig.
Let for a tensile
σx > σy


l. Mark OA = σx and OB = σy along the  x axis

[on positive side if tensile and negative side if compessive.]

2. Mark AC =  τxy

and BD =  τxy
672_Expression for the normal and tangential stresses1.png 
1249_Expression for the normal and tangential stresses2.png 

629_Expression for the normal and tangential stresses4.png 
3. Join C and D that bisects AB at E centre of Mohr's circle.

4. With E as centre, EC or ED as radius draw the circle called as Mohr's circle of stress.

5. Point P and Q at which circle cuts S axis gives principal planes OP = σ1, and OQ = σ2 gives the 2 principal stresses.

6. ∠CEP = 2θ1 and ∠CEQ = 2θ2 can be measured in counter clockwise direction.

θ1 = (1/2) ∠CEP and θ1 = (1/2) ∠CEQ indicates principal planes.

7. ER = EC =  τmax is the maximum shearing stress.

θ′1 = (1/2) ∠CER and θ′2

= (1/2) ∠CES

is measured anti-clockwise direction gives maximum shearing planes.

8. To obtain stress on any plane 'θ' measure ∠CEX = 2θ  in anticlockwise direction.

Normal stress on the plane is,

σn = OY

Shear Stress, τ = XY

Resultant Stress is σr= OX


∠XOY = ? is known as angle of obliquity.

Posted Date: 10/23/2012 3:18:41 AM | Location : United States

Related Discussions:- Expression for the normal and tangential stresses, Assignment Help, Ask Question on Expression for the normal and tangential stresses, Get Answer, Expert's Help, Expression for the normal and tangential stresses Discussions

Write discussion on Expression for the normal and tangential stresses
Your posts are moderated
Related Questions
Tungsten Inclusions Tungsten inclusion is a discontinuity found only in TIG welding. Particles of tungsten from the electrode can be embedded in a weld when improper welding proc

Question: 1.   A dump truck is shown in the figure.  The loaded container has a mass of  8000 Kg and may be modelled as a solid homogeneous block. The hydraulic cylinder applie

For an automotive component of your choice that is traditionally metallic, review how it could be re-engineered as a composite? How factors such as fibre & matrix type, fibre volum

Q. Alloy materials control? All low alloy and high alloy equipment components including fittings, flanges and sections of pipe and all welds shall be individually tested by Ven

(a) What do you understand by steering gear ? Explain with a clean sketch the working of Davis steering gear process. Also show the required equation between wheel base and distanc

How to do matlab coding for computerized relative allocation of facilities technique

An open topped tank with a base area of 1m2 contains a layer of water 0:5m deep below an oil layer 1m deep. If the densities of water and oil are 1000kg=m3 and 850kg=m3 respectivel

(a) Illustrate Torsionally Equivalent shaft. (b) Determine the natural frequencies and mode shapes for the system shown in figure I 1 = 10 Kg -m 2 I 2 = 40 Kg -m 2

Evaluate total heat of steam: 10 kg of wet saturated steam at 15 bar pressure is superheated to the temperature of 290°C at constant pressure. Find heat needed and the total