## Strength of Materials - Dec 2013

### Mechanical Engineering (Semester 3)

TOTAL MARKS: 80

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Assume data if required.

(4) Figures to the right indicate full marks.

### Solve any Four

**1 (a)** write a short note on Macaulays Method(5 marks)
**1 (b)** What are the characteristics of bending Moment and What do you mean by point of contraflexure(5 marks)
**1 (c) ** Prove that $$ \dfrac {f_{b}}{y}=\dfrac{M}{t}=\dfrac {E}{R} $$(5 marks)
**1 (d) ** What is the equivalent length of column? Give the ratio of equivalent length and actual length of column with various end condition(5 marks)
**1 (e) ** What is the length of 5 mm diameter without aluminium wire so that it can be twisted thorugh one complete revolution without exceeding shear stress of 42 MN/m^{2} Modulus of ragidity G=27 GN/m^{2}(5 marks)
**1 (f) ** Derive an expression for elongation due to self weight of bar(5 marks)
**2 (a)** A draw SFD, BMD and AFD for the following beam and also the point of contraflexure if any.

(12 marks)
**2 (b) ** Find the Euler crushing load for a hollow cylinder cast iron column 200 mm external diameter and 25 mm thick, if it 6 m long hinged at both ends. Take E= 1.2 × 10^{5} N/mm^{2}. Compare the load with the crushing load as given by Rankine formula, taking f_{c}=550 N/mm^{2} and α=1/1600(8 marks)
**3 (a) ** A cast iron bracket subjected bending banding has a C/S of I shape with unequal flages. If the section is subjected to shear force of 120 KN. Draw shear force distribution diagram over the depth of section

(10 marks)
**3 (b)** A hollow shaft with diameter ratio of 3/8 is required to transmit 500 K W at 100 RPM, the maximum torque being 20% greater than mean. The maximum shear stress is not exceed 60 N/mm^{2} and the twist in the length of 3 is not exceed 1.4. calculate the minimum diameter required for the shaft C=84 N/mm^{2}(10 marks)
**4 (a)** A wooden beam 250 mm × 150 mm has a steel strap 10 mm × 150 mm fixed at the top and the bottom. The beam is subjected to bending moment of 5KN-m around the horizontal axis. Determine the stress in the steel and wood. Es=200 Gpa, Ew=20 Gpa(10 marks)
**4 (b)** A steel bolt of 20 mm diaeter passes centrally through a copper tube of internal diameter 25 mm and thickness 10 mm. the tube is 600 mm long and is closed by rigid washer of negligible thickeness and fastened by nuts is tightened by the one quarter of the turn relative to other. the pitch of the thread is 2 mm. Take E_{s}=200 GPa and E_{c}=100 GPa

(10 marks)
**5 (a)** Determine the strain energy of prismatic beam AB for the loading as shown in fig take E=200 Gpa

(7 marks)
**5 (b)** A horizontal beam is loaded and supported as shown in fig. determine (i) Slope at A (ii) Deflection and Slope at B (iii) Slope at D

(13 marks)
**6 (a)** The composite bar consisting of steel and aluminium components shown in fig is connected to two grip at a tempreture of 60°C. find the stresses in the two rods, when the temperature, falls to 20°C

(i) If the ends does not yield

(ii) If the ends yeild by 0.25 mm

Take - E_{s}=2 × 10^{5} N/mm^{2} , E_{A}=0.70 × 10^{5} N/mm^{2}

α_{s}=1.17 × 10^{5} per °C α^{A}=2.34 × 10^{5} per ° C

(10 marks)
**6 (b)** A cylindrical shell 800 mm in diameter and 3 m long is having 10 mm metal thickness. If the shell is subjected to an internal pressure of 2.5 N/mm^{2}

Determine (i) The change in diameter

(ii) The change in length

(iii) The change in volume

Assume the modulus of elasticity and poissions ration of the material of the shell as 200 KN/mm^{2} and 0.25 respectively.(10 marks)