Assignment in Principal Stresses

Question Bank: S.M.2,Unit -1

Short Answer questions

1. Define the term obliquity and explain about Normal and tangential stresses on an inclined plane. 

2. Define the terms principal planes and principal stresses  

3. Find the principal stresses and the principal planes at a point, if Normal stresses are acting in X and Y axis along with shear stress. 

4. Explain graphical method for locating principal axes.

5. Define and explain maximum strain energy theory. 

6. Discuss briefly the maximum principal stress theory

7 Discuss in brief various prominent theories of failure

Short Answer questions - Mohr's circle of stresses

1.If the element is subjected only normal stresses equal and opposite in nature the Mhor's circle is shown in figure.  In this case pure shear stresses are exit in a plane of 45 degrees to normal stress plane and equal to normal stress.

2.If the element is subjected only normal stresses unequal and same in nature the Mohr's circle is shown in figure.

1

3.If the element is subjected only normal stresses unequal and opposite in nature the Mohr's circle is shown in figure.

4.If the element is subjected only normal stresses equal and same in nature the Mohr's circle is a point as shown in figure.

5.If the element is subjected only shear stresses the center of  Mohr's circle is located at the origin with a radius of shear stress  shown in figure.

6. The sum of the mutually perpendicular stressess in any plane is constant.

sx + sy = sx1 + sy1   = s1 + s2 =  constant

Long Answer questions

1. For a given loading conditions the state of stress in the wall of a cylinder is subjected to normal stresses 85 MN/m2 tensile,in x- direction and 25 MN/m2 tensile in y- direction,along with Shear stresses of 60 MN/m2 on the planes on which the stresses are act a)Calculate the principal stresses and the planes on which they act. 

b)What would be the effect on these results if owing to a change of loading if the 85MN/m2 becomes compressive while other stresses are remain unchanged.

2. At a point with in a body is subjected to two mutually perpendicular stresses are shown in fig. Determine the normal , shear and resultant stress on an oblique plane inclined at angle of 300 axis of minor tensile stress. Also Calculate the principal stresses and the planes on which they act. 

3. Direct stresses of 120 N/mm2 (tensile) and 90 N/mm2 (compressive) exist on two perpendicular. planes at a certain point in a body. They are also accompanied by shear stress on the planes. The greatest principal stress at the point due to these is 150 N/mm2. a) What must be the magnitude of the shearing stresses on the two planes?

b) What will be the maximum shearing stress at the point?

4 A rectangular block of 1200 mm2 cross-sectional area is subjected to stresses as shown in fig. If the block is cut by an oblique plane making an angle of 300 with normal section of the block. Determine: 

(i)Normal stress on the oblique plane 

(ii)Tangential stress along the oblique plane, and 

(iii) Resultant stress on the oblique plane. 

(iv) the principal stresses and the planes on which they act 

(v) the maximum shearing stress at the point

5. At a point the stresses in two mutually perpendicular planes are 120 N/mm2 and 200N/mm2 both tensile and shear stress across both planes are 140N/mm2 Using Mhor’s circle find the principal stresses and maximum shearing stress at the point. Also find the resultant stress on the planes of maximum shear stress. 

6. A solid circula shaft is subject to bendin moment 80kN-m and torque 120kN-m. In a uniaxial tensile test the shaft material have modulus of elasticity 2x105N/mm2 , stress at yield point is 300N/mm2 and poission’s ratio is 0.3 Estimate the least diameter of shaft with a factor of safety 3 and by using a) Maximum principal stress theory (b) Maximum Shear stress theory c) Maximum Strain energy theory (d) Maximum Shear strain energy theory

7. At a point with in a body there are two mutually perpendicular stresses of 80 N/mm2 and 40 N/mm2 of tensile in nature. Each stress is accompanied by a shear stress of 60 N/mm2 . Determine the normal, shear and resultant stress on an oblique plane at an angle of 45° with the axis of the major principal stress

8. A material is subjected to two mutually perpendicular direct stresses of 80 Mpa tensile and 50 MPa compressive, together with a shear stress of 30 MPa. The shear couple acting on planes carrying the 80MPa stress is clockwise in effect. Find by using of Mohr circle
(i) principal stresses (ii) the maximum shear stress (iii) the normal stresses on the plane of maximum shear (iv) the stresses on a plane at 20° counter clockwise to the plane on which the 50 MPa stress acts.