Before start with Mohr's circle we will go through some basics , and importance to study Mohr's circle.
STRESS IN 1-D SYSTEM
When stress acts in one direction its called 1-D stress system,
ex-
*Stress will be maximum when cross-section area would be minimum (for constant resisting force)
*cross-section area will be minimum in vertical plane only , so we can conclude that material will fail at vertical plane when the applied load exceed the ultimate tensile/shear/compressive strength of material.
STRESS IN 2-D SYSTEM
When stress acts in more than one direction its called 2-D stress system.
ex-
COMPLEX STRESS
When stress acts in more than one direction and its difficult to say from which plane material will fail.
PRINCIPAL STRESS
Principal stresses are defined as the maximum and minimum normal stresses that acts on a body.
PRINCIPAL PLANE
Plane at which principal stresses acts.There are 2 principal plane
1-MAJOR PRINCIPAL PLANE
Plane at which normal stress is maximum.
2-MINOR PRINCIPAL PLANE
Plane at which normal stress is minimum.
SHEAR PLANE
Plane at which maximum shear stress acts.
*There are 2 methods to determine principal stress, principal plane, max shear stress and shear plane.
1-ANALYTICAL METHOD
2-GRAPHICAL METHOD
Mohr's is based on the second method.
MOHR'S CIRCLE
*It is a graphical way to determine principal stress,principal plane,shear stress and shear plane.
*We can also calculate shear stress and normal stress for a particular plane.
*We can also calculate the angle at which principal plane will occur with respect to the vertical or horizontal plane.
NOTES
*Any point on mohr's circle will have 2 co-ordinates,normal stress and shear stress.
*Radius mo mohr's circle represent plane in the material also radius represents the max shear stress value.
*All the angle taken in the material will be double in mohr's circle.
*Principal plane are separated by an angle of 90 degree.
*Shear stress is zero at principal plane.
*Normal stress is not zero at shear plane.
*There are 2 shear plane and shear plane are separated by an angle of 90 degree.
*Angle between principal plane and shear plane is 45 degree.
We discuss all these notes in analytical method in another blog.
WE WILL DRAW MOHR'S CIRCLE FOR THE GIVEN PROBLEM:
*Plot a graph taking normal stress in x-axis and shear stress in y-axis.
*Mark the value of normal stress and shear stress in X and Y axis respectively.
sign convention
*tensile stress is taken as positive where as compressive stress is taken as negative.
*Shear stress which tends generate a clock wise moment taken as positive, and shear stress which tends to generate anti clock wise moment is taken as negative.
*Join the 2 points and named the intersection point as p.
*Draw the circle taking the join line as diameter and point p as center.
*In vertical place sigma x and tao x,y are acting similarly in horizontal plane sigma y and tao x,y are acting. As per the notes each radius of mohr's circle represent a plane.
* Find in which plane in mohr's circle sigma x and tao x,y are acting and name them as vertical plane(v.p) and same way name the horizontal plane(h.p).And name all points.
*XA- represent magnitude of major principal stress.
*XB- represent magnitude of minor principal stress.
*PA- represent major principal plane.
*PB-represent major principal plane.
*XY-represent magnitude of maximum shear stress.
*PY-represent major shear plane.
*PT-represent vertical plane.
*PG-represent horizontal plane.
*XF-represent magnitude of normal stress at angle 2 แ from v.p.
*XE-represent magnitude of shear stress at angle 2 แ from v.p.
In this way we can draw mohr's circle for various case and can determine various parameters.
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