Mohr circles | Graphical representation of stresses | Calculations of stresses

 Mohr Circle | Graphical representation of stress | calculation of stresses 

• Mohrs circle is a graphical representation of stresses in form of circle on co-ordinate axis.

• In Mohr circle, x axis is considered as principal plane on which normal stresses 

are plotted. 

• In Mohr circle, y axis is considered as shear plane on which shear stresses are plotted.

Note : on principal plane, shear stress will always remain zero

Geometrical features of Mohr circle

Radius of mohr circle

R = (σmax – σmin)/2 =  حmax

Normal stress at location of maximum shear stress

σn = (σmax + σmin)/2

 1. The diameter of Mohr circle is double of the subtraction of principal stresses.

2. The normal stress at the location of max shear stress is half of the addition of principal stress 

Principal plan

It is the angle of inclination of the on which major & minor principal stresses will exist

σn =( σx + σy )/2+ {(σx-σy)Cos2ϴ }/2+ حxysin2ϴ

Tan2ϴp = 2حxy /σx - σy 

Major principal plane

ϴp = ½ tan-1 {2حxy /σx-σy }

Minor principal plane

Other plane = ϴp + 90°

Shear plane

• It is the angle of inclination at which max shear stress will exist.

• The difference b/w shear plane & principal plane is 45°

ϴs = ϴp + 45°

ϴs-ϴp=45o°

Maximum and minimum principal stress