DEPARTMENT OF MECHANICAL ENGINEERING

MEB 2102 SOLID MECHANICS

ASSIGNMENT -1 SUBMISSION DATE : 14 Aug 14

PART A

1. State and briefly explain hooke’s law.

2. A steel bar is 10 mm diameter and 2 m long. It is stretched with a force of 20kN and extends by 0.2 mm . calculate the stress and strain

3. A steel column is 3m long and 0.4 m diameter . It carries a load of 50 MN. Given that the modulus of elasticity is 200 Gpa. Calculate the compressive stress and strain. Determine how much the column is compressed.

4. Illustrate the principle of superposition with a sketch

5. Differentiate the terms strain and strain energy.

6. State the importance of Poisson’s ratio in calculating strain.

7. For a body of rectangular cross section with length’l’,breadth,’b’, and thickness’t’ subjected to an axial tension of ‘P’ estimate the volumetric strain. Account poisson’s ratio as ‘1/m’ and young’s modulus as ‘E’.

8. List the types of beams with their conventional representation.

9. Define shear force and bending moment of a beam.

10. Briefly explain thermal stresses and thermal strain

Part B

1. The ultimate stress for a hollow steel hollow column which carries an axial load of 1.82 MN is 473 N/ mm2 . if the external diameter of the column is 200mm. determine the internal diameter. Take factor of safety as 4.5.

2. A cast iron flat 300 mm long and 30 mm [thickness ] x 60 mm [ width ] uniform cross section is acted upon by the following forces. 30 kN tensile in the direction of length. 360 kN compression in the direction of width, 240 kN tensile in the direction of thickness. Calculate the direct strain, net strain in each direction and change in the volume of the flat. Assume the modulus of elasticity as and poisson’s ratio for cast iron as 140kN/ mm2 and 0.25 respectively

3 . A steel bar of cross section 500 mm2 is acted upon by the forces shown in Fig. Determine the total elongation of the bar. For steel, consider E = 200 GPa.

4. Two prismatic bars are rigidly fastened together and support a vertical load of 45 kN, as shown in Fig. The upper bar is steel having length 10 m and cross-sectional area 60 cm2.. The lower bar is brass having length 6 m and cross-sectional area 50 cm2 . For steel E = 200 GPa, for brass E = 100 GPa.

Determine the maximum stress in each material. specific weight for brass and steel is 84000N and 77000 N respectively.

5. A square steel bar 50 mm on a side and 1 m long is subject to an axial tensile force of 250 kN. Determine the decrease Δt in the lateral dimension due to this load. Use E = 200 GPa and poisson’s ratio as = 0.3.

6. A hollow right-circular cylinder is made of cast iron and has an outside diameter of 75 mm and an inside diameter of 60 mm. If the cylinder is loaded by an axial compressive force of 50 kN, determine the total shortening in a 600 mm length. Also determine the normal stress under this load. Take the modulus of elasticity to be 100 GPa .

7. A steel rod of 25 mm diameter an 5 m long is connected to two grips and the rod is maintained at a temperature of 86 0 C .Determine the stress and pull exerted when the temperature falls to 38 0 C, if the ends do not yield and if the ends yield by 1.1mm . Take young’s modulus as 2x10 5 MN/m 2 and co efficient of linear expansion as 14x10 -6 / 0 C.

8. A load of 2 MN is applied on a short concrete column 475 mm x 475 mm . The column is reinforced with four steel bars of 8 mm diameter one in each corner. Find the stress in the concrete and in steel bars. Take E for steel as 2x10 5 N/mm 2 and for concrete as 1.4x10 4 N/mm 2

9. A steel rod 4.8 m long and 26 mm diameter is subjected to an axial tensile load of 50kN. Determine the change in length ,diameter and volume of the rod. Take young’s modulus as 2x10 5 N/mm 2 and poisson’s ratio as 0.26

10. For the following component calculate the stress in each section and find the total extension .

Take E as 2x10 5 N/mm 2

Guidelines

1. Submission strictly on or before the submission date

2. Students should submit only in the A4 sheet neatly filed mentioning the page numbers.

3. Briefing the questions in the assignment is necessary.

4. Results / findings need to be mentioned after every answer.

5 Writing Name and RRN is mandatory.