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

## Mechanics of Solids - Jun 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.**Explain about elasticity and plasticity.

**1.b.**Explain the strain energy and deduce the expression due to gradual loading.

**1.c.**draw the S.F.D and B.M.D of cantilever carrying couple (M) at the free end.

**1.d.**write the relation between load, shear force and bending moment.

**1.e.**What is bending stress? Write pure bending equation.

**1.f.**Draw the shear stress distribution for regular, hollow, circular, cross section.

**1.g.**what is mohr'scircle of stresses?

**1.h.**Discuss in brief various prominent theories of failure.

**1.i.**Explain about thin spherical shells?

**1.j.**Drive the equations of longitudinal and circumferential stress.

PART - B (50MARKS)

**2.**Drive an expression for strain energy stored in body when the load is applied with an impact.

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**3.a.**The shear stress in a material at a point is given as 50N/mm². Determine the local strain energy per unit volume stored in material due to shear stress. Take modulus of rigidity as 8*10⁴ N/mm².

**3.b.**A load 'P' is suspended from two roads as shown in figure 1. The rod AC is of Steel, having a circular c/s 30 mm in daimeter, and an allowable stress of 16MN/m², the road BC is aluminium having diameter 40 mm and allowable stress of 60MN/m². What is the maximum load p which can be suspended from these rods?

**4.**A horizontal beam 10 m long carries u.d.l of 180N/m over its entire span and it adding concentrated load of 200N at the left end. The beam is supported at two points 7m apart, so choose and that each support carries half the total load. Draw S.F.D and B.M.D

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**5.**Calculate the reaction in the beam shown in the figure2. Draw the SFD and BMD. Determine the location of maximum bending moment and mark it clearly on each of the diagram.

**6.a.**What are the design criteria according to the building and relation between bending moment and section modulus?

**6.b.**What is bending stress? What are difference between bending stress and direct stress?

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**7.**A T-section beam shown in the figure 3 is subjected to a shear force of 9KN at a section. Determine the amount of maximum intensity of shear stress and draw the distribution of the shear Street acrod depth of the section.

**8.**At a point in a strained material the principal stress are 210 N/mm² (tensile) and 120N/mm² (compressive). Determine the following stress on an oblique section incliend at 40° with the axis of the minor principal stress: a) Normal stress b) Shear stress c) Resultant stress (magnitude only) d) Max. shear stress.

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**9.**A certain type of Steel has yield strength of 270N/mm². At a point in a strained region the principal stresses are +120, +80 and -30N/mm². Determine the factor of safety as per the max. Principal strain theory. Take poisson's ratio is 0.285.

**10.**Determine the diameter of a solid shaft which will transmit 300 KW at 250 rpm. The max shear stress should not exceed 30N/mm² and twist should not be more than 1° in a shaft length of 2.0m. Take modulus of rigidity = 1*10 raise to 5 N/mm².

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**11.**Drive the equation for the circumferential and longitudinal stress included in the thin spherical shells.

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