Review Questions

Review Questions, problems for practice: Stress, Strain and Deformation of Solids - Strength of Materials

REVIEW QUESTIONS

1. Derive expressions for the normal and tangential stresses on any oblique plane in a bar subjected to tensile loading in the axial direction.

2. Derive expression for the normal and tangential stresses on any oblique plane in a material subjected to two tensile stresses acting mutually perpendicular to each other.

3. Derive expression for the normal and tangential stresses on any oblique plane in material subjected to pure shear.

4. A material subjected to a normal stress along with complimentary shear stress on two mutually perpendicular directions. Deduce the expression for normal, tangential and maximum shear stress. Also derive the formulae for principal stresses and their location.

5. At a point in a strained material there are two normal stresses along with a complementary shear stress. Derive the expressions for normal, shear and maximum shear stress. Also derive the formulae for principal stresses and their direction.

6. Draw and describe the graphical method for solving the principal stress problems for various cases.

7. Draw and describe Mohr's circle of stress and prove that it may be used to represent the state of stress at a point within stressed material. Illustrate your answer by sketches.

8. Explain the detailed procedure for drawing the Mohr's circle for the following cases.

(a) A material subjected to two normal tensile stresses acting perpendicular to each other.

(b) A member subjected to a tensile and a compressive stresses acting mutually perpendicular directions.

(c) A member subjected to a tensile stress and a complementary shear stress.

(d) A member subjected to two normal tensile stresses and and a complementary shear stress.

PROBLEMS FOR PRACTICE

1. A bar of material is subjected to the uniform tensile stress of 125 N/mm2. Find the intensity of normal, tangential and resultant stress on a plane the normal to which is inclined 30° to the axis of the bar.

2. A rectangular element subjected to tensile stresses of 45 N/mm2 and 30 N/mm2 at right angles to each other. Graphically or otherwise locate the planes for which the resultant intensity stresses is inclined at 10° to the normal. State the magnitude of this intensity. Also locate the plane for which the resultant intensity has maximum inclination which is normal.

3. At a point in a strained material, the principal stresses are 100 MPa (tensile) and 35 MPa (compressive). Find fully the stresses on a plane the normal of which makes an angle of 50° with maximum principal stress.

4. At a point in a beam the bending stress is 70 MPa (tensile) and shear stress is 30 MPa. Find the normal and shear stress on a plane inclined at 30° to the bending stress. Also locate the planes for which the shear stress is zero.

5. The like (tensile) principal stresses at a point are 800 N/mm2 and 200 N/mm2. Calculate the following.

(a) Maximum shear stress.

(b) Normal and shear stress on a plane at 30° with the plane of maximum principal stress.

(c) Resultant stress on that plane.

6. A rectangular block of material is subjected to a tensile stress of 100 MPa and a compressive stress of 50 MPa on the plane at right angles to the former. Each of the above stresses is accompanied by a shear stress of 60 MPa and that associated with former tensile stress tends to rotate the block anticlockwise. Find the principal stresses and principal planes. 

7. At a point in a plate girder the intensity of vertical shear stress is 65 MPa and that of the horizontal tensile stress is 140 MPa. Find from first principles the value of principal stresses and the angles the principal planes make with the vertical. Find also the value of the maximum shear stress at the point.

8. The state of stress at a point in a material is σx = 60 N/mm2, σy = 40 N/mm2 τxy = 50 N/mm2.

Determine (a) the magnitude and angle of obliquity of the resultant stress, (b) the normal and tangential component stresses, (c) maximum shear stress. 

9. At a certain point in a piece of elastic material there are three mutually perpendicular planes on which the stresses are as follow: A normal tensile stress of 100 N/mm2 and a shearing stress of 60 N/mm2 on one plane, a normal compressive stress of 55 N/mm2 and the complementary shearing stress of 60 N/mm2 on a second plane and no stress on the third plane. Determine (a) the principal stresses at a point and the positions of the planes on which they act and (b) the positions of the passes on which there is no normal stress.

10. At a point in a strained material there are normal stresses of 40 MPa tension and 25 MPa compression on two planes at right angles to one another, together with shearing stresses of 12 MPa on the same planes. If the loading on the material is increased so that the stresses reach value of k times those given, find the maximum value of k if the maximum direct stress in the material is not to exceed 100 MPa and the maximum shearing stress is not to exceed 55 MPa. 

11. At a point in a bracket, the resultant intensity of stress across the horizontal plane is 65 MPa tensile inclined at 30° clock wise to its normal. The normal component of intensity of stress across the vertical plane is 52 MPa tensile. Locate the principal planes and find the stresses across them.