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

Steps:

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

Steps:

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

And

∠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
Q. Procedure for calculating the wind force on vessels? The National Building Code of Canada has a similar procedure for calculating the wind force on vessels as ASCE. The bas

First we focus on the inner region fluid (0 (solid body rotation) around the z-axis. The steady incompressible velocity field is given by ur=0 utheta=rw uz= 0. The pressure at th

Compare solid shaft with the hollow: Compare solid shaft with the hollow shaft, by strength and their weight. Sol.: ( a ) Comparison by strength: Assume that both the s

#question.needs help to do my assignment.

Q. Design Storage compounds for bulk solids? Storage compounds for bulk solids, liquids and liquefied gases are normally included in a plant layout to provide short term storag

CO2 WELDING-Power Source Normally, a power source with constant potential characteristics is used for CO 2 welding as it has the ability to self regulate the welding arc. The


what are the parts of wilson hartnell governor with their designation?


hello. what is the shape of the fractur of brittle material after applied th tensil test.