Question Paper: Mechanics of Solids Question Paper - Dec 18 - Mechanical Engineering (Semester 3) - Jawaharlal Nehru Technological University (JNTUH)

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## Mechanics of Solids - Dec 18

### Mechanical Engineering (Semester 3)

Total marks: 80

Total time: 3 Hours
INSTRUCTIONS

(1) Question 1 is compulsory.

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

(3) Draw neat diagrams wherever necessary.

PART - A (25MARKS)

**1.a.**Define the principle of superposition. What is its utility?

**1.b.**State hooke's law. Sketch the stress - again diagram for ductile material like the mild Steel tested under tension up to destruction marketing the salient points on it.

**1.c.**Bring out the difference between statically determine beam and statically interminate beam?

**1.d.**What is the relation between shear force and loading, bending moment and shear force in a beam?

**1.e.**Define moment of resistance of a beam?

**1.f.**sketch the bending stress as well as shear stress distribution for a beam of rectangular cross section.

**1.g.**What do you mean by phase plane and principal stress?

**1.h.**define the term of obliquity and how it is determined?

**1.i.**Distinguish between thin cylinder and thic cylinder what are the application?

**1.j.**State the assumptions of shear stress in a circular shaft subjected to torsion. TYPE_QUESTION_HERE

PART - B (50 MARKS)

**2.a.**Drive an expression between modulus have electricity and models of rigidity.

**2.b.**The extension in a rectangular Steel bar of length 800 mm and the thickness 20 mm to be 0.25 mm, The bir tapers and unformally in the width of 80 mm to 40 mm. If E the bar is 2 into 10 raise to 5N/mm², determine the axial tensile load on the bar.

OR

**3.a.**What is the procedure to finding thermal stress in a composite bar?

**3.b.**A bar of 15 mm diameter get stretched by 4 mm under a steady load of 8000 N. What stress would be produced in the same bar by a weight of 800 N, which falls vertically through a distance of 10 cm on the rigid Collar attached at the end? The bar is initially unstressed.Take E=2*10 raise to 5 N/mm².

**4.**A beam of length 10 m a simply supported and carries points load at 5 knN each at a distance of 3 m and 7 m from Left support and also uniformly distributed load of 5 kN/m between the point loads. Draw the S.F and B.M diagram for the beam

OR

**5.a.**What do you mean by point of contra flexure? Is the point of contra flexure and point of inflexion different?

**5.b.**A cantilever beam of 2m long is loaded with an uniformly distributed load of 3 kN/m run over a length of 1 m from the end. It also carries a point load of 5 kN at a distance of 1.5 m from the free end, Draw the S.F and B.M.

**6.a.**What do you mean by simply bending? What are the assumption ls made in theory of simple bending?

**6.b.**show from first principle that if a beam of rectangular section is subjected to a transverse shearing force, the maximum shear stress as a cross - section of 1.5 times the mean shear stress.

OR

**7.a.**prove that the relation between M/1=σ /y= E/R.

**7.b.**An I-section beam consists of two flanger 160 mm * 25 mm and a web of 320 mm x 12 mm. Find the magnitude of maximum shear stress when it is subjected to a shear force of 60 kN.

**8.a.**Explain with the reason with theory of failure is best suited for i) Ductile material and ii) brittle material.

**8.b.**A point in a strained material is subjected to matually perpendicular stresses of 40Nmm² (tensile) and 20 N/mm² (compressive). It is also subjected to a shear stress of 20 N/mm² . Draw mohr's circle and find the principal stress and maximum shear stress.

OR

**9.a.**Drive and expression for the stresses on an oblique plan of rectangular body, when the body is subjected to a simple shear stress.

**9.b.**drive and expression for the dish torsion energy per unit volume when a body is subjected to principal stresses σ1,σ2 σ3.

**10.a.**A cylindrical shell is subjected to internal fluid pressure. Find an expression for change in diameter and change in length of the cylinder?

**10.b.**A hollow shaft has transmit 337.5 KW at 100 RPM. If the shear stress is not exceed 65N/mm² and the internal diameter is 0.6 of the external diameter. Find the external and internal diameter assuming that maximum torque is 1.3 times mean. TYPE_QUESTION_HERE

**11.a.**Define the term polar modulus. Find the expression for polar modulus of a solid stuff and for a hollow shaft.

**11.b.**A spherical shell of 1.5 m diameter is subjected to an internal pressure of 1.45N/mm². Taking the maximum allowable stress as 110 N/mm², find the necessary thickness of plate. Take the joint efficiency at 71%.