## Strength of Materials - December 2016

### MU Mechanical Engineering (Semester 3)

Total marks: --

Total time: --
INSTRUCTIONS

(1) Assume appropriate data and state your reasons

(2) Marks are given to the right of every question

(3) Draw neat diagrams wherever necessary

### Write a short note any four Q1.(a,b,c,d,e)

**1(a)**Draw stress strain curve for ductile and brittle material also Explain factor of saftely with the help of stress-strain diagram of both. 5 marks

**1(b)** Define Hoop stress and Longitudinal stress stress in thin cylinder. Derive their formula.
5 marks

**1(c)** For a rectangular cross section of beam, show that the maximum shear stress is 1.5 times the average shear stress. Also draw shear stress distribution diagram.
5 marks

**1(d)** State Torision Formula and explain the terms involved in it. Give assumptions in the analysis of pure torsion.
5 marks

**1(e)** Establish the relationship between shear force, bending moment and rate of loading in beam.
5 marks

**2(a)** A stepped bar ABCD has the following dimensions:

Portion AB: Length 1200 mm and diameter 40 mm

Portion BC: length 800 mm, diameter 20mm.

Portion CD: Length 1000 mm, diameter 30 mm. It is subjected to four point loads as shown in Figure 1. Find the Value of 'P' for equilibrium and then find the change in length of the bar. Assume E=200Gpa.

!mage
5 marks

**2(b)** A steel stock 360mm ×80mm × 160 mm is subjected to the following forces

i) A tensile force of 1280KN on the 160mm×80mm faces (take as a X- direction)

ii) A tensile force 3456 KN the 360mm×80mm faces( take as a Y-direction) and

iii) A compressive force of 5184KN on the 160mm×360mm faces ( take as a Z-direction) Find the changes in the dimensions of the block and also the change in volume. Take E=2×10^{5}N/mm^{2} and 1/m=0.25
5 marks

**3(a)** A beam 8.5 m long rests on the supports 5 m apart, the beam carries load as shown in Figure 2. Draw SFD and BMD showing all the important points.

!mage
5 marks

**3(b)** A steel bar consists of two eaual portions each 1 meter long, the respective diameters of each portion being 30mm and 50 mm. Find he total strain energy of the bar when it is subjected to an axial pull 150 KN. Take E=200×10^{3} N/mm^{2} for steel.
5 marks

**4(a)** A symmetrical I-section with flanges 250mm×20mm has a web 160mm×10mm. If the shear force acting on the section is 80KN, find maximum shear stress developed in the section and draw shear stress distribution diagram.
5 marks

**4(b)** A cylindrical shell 3 meter long closed at the ends having 1 meter internal diameter is subjected to an internal pressure. 1.5MPa. If the thickness of the shell wall is 15 mm, find the circumferential, longitudinal stresses and Maximum shear stress. Find also the change in diameter, Length and volume of the shell. E=2×10^{5}N/mm^{2}, 1/m=0.3
5 marks

**5(a)** Determine the diameter of a soild shaft, which will transmit 300KW at 250 rpm and the working conditions to be satisfied are:

The twist should not be more than 1° in a shaft of length 2 meter and The maximum shear stress should not exceed 30N/mm^{2}

Take, Modulus of rigidity = 1×10^{5}N/mm^{2}
5 marks

**5(b)** Find Euler's crippling load for hollow cylindrical column of 50 mm external diameter and 5 mm thick. Both ends of column are hinged and length of column is 2.5 meter. Take E=2×10^{5}N/mm^{2}. Also determine Rankine's crippling load for the same column. Take fc=350 Mpa and α=1/7500.
5 marks

**6(a)** A 4 m long steel bar of square cross section of 40 mm side, is heated through 75°C with its ends clamped before heating. Calculate the thrust exerted by the bar on clamps:

i) if the clamps do not yield

ii) if the clamps yield by 0.6 mm. Take, E=210GPa and α=11.5×10^{-6}/°C.
5 marks

**6(b)** Find slope and deflection equation for the beam as shown in figure given below. Determine the deflection at a point where couple 50KNm is acting (Figure 3) Take, EI = 2×10^{4}KN/m^{2}

!mage
5 marks