# Sathyabama University 2008 B.E Civil Engineering Mechanics of Solids - II - Question Paper

**SATHYABAMA****
UNIVERSITY**

**(Established under section 3 of UGC Act, 1956)**

Course & Branch: B.E - CIVIL (Part Time)

Title of the paper: Mechanics of Solids - II

Semester: II Max. Marks: 80

Sub.Code: 620PT201 (2006/2007) Time: 3 Hours

Date: 12-05-2008 Session: FN

PART A (10 x 2 = 20)

Answer All the Questions

1. What is the maximum deflection in a simply supported beam subjected to uniformly distributed load over the entire span?

2. Draw conjugate beam for a double sided over hanging beam.

3. What is crippling load? Give the length of columns when both the ends hinged and when both the ends fixed.

4. Define Slenderness ratio

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5. A cylindrical pipe of diameter 1.5m and the
thickness 1.5 cm is subjected to an internal fluid pressure of 1.2 N/mm^{2 }Determine
the longitudinal stress developed in the pipe.

6. Determine the failure of Thin cylinders t

7. State St. Venant maximum principal strain theory.

8. Briefly discuss Guests theory.

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9. What is shear centre?

10. State the reasons for unsymmetrical bending.

PART B (5 x 12 = 60)

Answer All the Questions

11. A beam 5m long simply supported at both the ends
and carries a load 6KN at a distance of 2m from one end. Determine slope at
ends and maximum deflections. E=200GPa and I=5200cm^{4 }Use Double
integration Method.

(or)

12. A beam AB of length 8m is simply supported at
its ends and carries two point loads of 50KNand 40KN at a distance of 2m and 5m
respectively from the left support A. Determine the deflection under each load,
maximum deflection and the position at which maximum deflection occurs. Take
E=200GPa and I=8500cm^{4}.

13. A 1.2 m long column has a circular cross section of 45mm diameter one of the ends of the column is fixed in direction and position and other ends is free. Taking factor of safety as 3, calculate the safe load using

(i)
Rankines formula, take yield
stress=560N/mm^{2 }and a=1/1600 for pinned ends.

(ii)
Eulers formula, Youngs modulus
for cast iron=1.2*10^{5 }N/mm^{2}

(or)

14. From the following data of a column of circular section calculate the extreme stresses on the column section. Calculate the maximum eccentricity in order that there may be no tension any where in the section.

External diameter = 200mm

Internal diameter =160mm

Length of the column =4m

Load carried by the column =200KN

Eccentricity of the load =25mm from the axis of the column.

End conditions = Both ends fixed.

Youngs modulus =94GPa.

15. A cylindrical shell 3m long which
is closed at the ends has an internal diameter of 1m and a wall thickness of
20mm. Calculate the circumferential and longitudinal stresses induced and also
change in the dimensions of the shell, if it is subjected to an internal
pressure of 2N/mm^{2 }. Take E=2*10^{5}N/mm^{2} and
1/m=0.3

(or)

16. A thin spherical shell 1m in diameter with its
wall of 12mm thickness is filled with a fluid at atmospheric pressure. What
intensity of pressure will be developed in it if 175cm^{3}more of fluid
is pumped in to it? Calculate the circumferential stress at that pressure and
the increase in diameter. Take E=200GPa and 1/m=0.3

17. A hallow mild steel shaft having 100mm external diameter and 50mm internal diameter is subjected to a twisting moment of 8KNm and bending moment of 2.5KNm. Calculate the principal stresses and find direct stress which acting alone would produce the same

(i) maximum elastic strain energy

(ii) maximum elastic shear strain energy, as that produced by the principal stresses acting together. Take 1/m=0.25

(or)

18. A bolt is subjected to an axial load of 12KN together with a transverse shear of 6KN. Determine the diameter of bolt according to

(i)maximum principal stress theory

(ii) maximum shear stress theory

(iii) maximum strain strain theory

(iv) strain energy theory

(v) shear strain energy theory.

Given the following: Elastic limit in tension=300N/mm^{2.
}Factor of safety=3. Poissons ratio=0.3

19. A beam of rectangular section 80mm wide and
120mm deep is subjected to a bending moment of 12KN-m. The trace of the plane
of loading is inclined at 45^{0} to the YY axis of the section. Locate
the neutral axis of the section and calculate the maximum bending stress
induced in the section.

(or)

20. A beam of angle section 150mm*100mm*10mm is simply supported over span of 1.6m with 150mm leg as vertical. uniformly distributed load of 10KN/m is applied throughout the span. Determine

(i) maximum bending moment

(ii) direction of neutral axis

(iii)deflection at the centre.

Earning: Approval pending. |