At a point in an elastic material under strain, the stresses on the three mutually perpendicular

planes are as follows:

A normal tensile stress of 60 N/mm2

and shear stress of 50 N/mm2 on one plane and a normal tensile force of 40 N/mm2 and a complimentary shear stress of 50 N/mm2 on another plane. Find the following using Mohr circle only (take 5 N/mm2 = 2 cm)

a. The principal stresses and principal planes.

b. The maximum shear stress and its plane.

c. The normal and shear stress on a plane inclined at an angle of 30°

to major principal plane

Step 1

**Given:**

Normal tensile and shear stress on one plane are 60 N/mm2 and 40 N/mm2.

Normal tensile and shear stress on another plane are 40 N/mm2 and 40 N/mm2.

Step 2

**Calculation:**

The plane stress problem is shown below:

Take 5 N/mm2 = 1 cm and draw the Mohr’s circle as shown below:

Step 3

(a)

From the above Mohr’s circle, the maximum and minimum principal stress with angles are:

F1=91.23 Mpa at angle θ =37.98°

F2=8.76 Mpa at angle θ = 128.0°

(b)

From the above Mohr’s circle, the maximum shear stress with angle is:

τmax = 91.2 Mpa at angle θ =82.98°

(c)

The normal and shear stress at 30 deg from the maximum principal stress is calculated as follows:

In triangle AOB,

sin30=AB/OA

sin30=AB/R

sin30=AB/41.231

AB==20.6155 Mpa

And,

cos30=OB/OA

cos30°=OB/R

cos30°=OB/41.231

OB=σn=35.707 Mpa

Thus, the normal and shear stresses are 35.707 Mpa and 20.6155 Mpa.