# Sathyabama University 2008 B.E Civil Engineering Mechanics of Solids - I - 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 - I

Semester: I Max. Marks: 80

Sub.Code: 620PT101 (2007/2007JAN/2008 JAN) Time: 3 Hours

Date: 15-05-2008 Session: FN

PART A (10 x 2 = 20)

Answer All the Questions

1. Define the terms (i) rigidity modulus (ii) bulk modulus

2. A bar consists of two sections of lengths 200mm
and 300mm with area of cross sections 400mm^{2} and 500 mm^{2 }respectively.
It is subjected to an axial pull of 100 kN. Take Youngs modulus (E) = 200 kN/
mm^{2}. Find the total elongation.

3. Draw the shear force and bending moment diagrams for a cantilever of length L carrying a uniformly distributed load of w per metre length over its entire length.

4. State the relationship between loading, shear force and bending moment.

5. Define section modulus and state its significance.

6. What do you understand by neutral axis and moment of resistance?

7. Find the power that can be transmitted by a shaft rotating at 150 rpm under a torque of 400 N-m.

8. Define stiffness of a helical spring and write an expression for it.

9. A tensile load of 50kN is gradually applied to
a circular bar of 5cm diameter and 4m long. If the value of Youngs modulus (E)
= 2x10^{5} N/mm^{2}, determine the strain energy absorbed by
the steel rod.

10. How would you distinguish between a deficient frame and a redundant frame?

PART B (5 x 12 = 60)

Answer All the Questions

11. a. Draw stress-strain curve and explain clearly the salient points of mild steel. (8)

b. The following data relate to a bar subjected to a tensile test:

Diameter of the bar5 = 30 mm

Tensile load = 54 kN

Gauge length = 300 mm

Extension of the bar = 0.112 mm.

Change in diameter = 0.00366 mm

Calculate (i).Possions ratio (ii) Youngs modulus. (4)

(or)

12. A compound tube consists of a steel tube 170 mm
external diameter and 10 mm thickness and an outer brass tube 190 mm external
diameter and 10 mm thickness. The two tubes are of the same length. The
compound tube carries an axial load of 1 MN. Find the stresses and the load
carried by each tube and the amount by which it shortens. Length of each tube
is 0.15m. Take Youngs modulus for steel (E_{s}) = 200 GN/m^{2}
and for brass (E_{b}) = 100 GN/m^{2}

13. Draw the shear force and bending moment diagrams for the beam shown loaded in Figure. Find the maximum bending moment.

(or)

14. A beam 7.5 m long has supports 5 m apart, there being an overhang of 1 m on the left and 1.5 m on the right. There is a point load of 5kN at each free end a uniformly distributed load of 8 kN/m over the supported length and 4 kN/m over the overhanging portion on the right. Construct shear force and bending moment diagrams.

15. A hollow rectangular column is having external and internal dimensions as 120 cm deep x 80 cm wide and 90 cm deep x 50 cm wide respectively. A vertical load of 200kN is transmitted in the vertical plane bisecting 120 cm side and at an eccentricity of 10 cm from the geometric axis of the section. Calculate the maximum and minimum stresses in the section.

(or)

16. a. Sketch the shear stress distribution over a circular section (2)

b. A 400 mm X 150 mm I grider has 20 mm thick flanges and \30 mm thick web. Calculate maximum intensity of shear stress when the shear force at the cross section is 1.6 MN. Also sketch the shear stress distribution across the depth of the beam. Calculate the percentage shear force carried by the web.

17. A shaft is required to transmit 245 kW power at
240 rpm. The maximum torque may be 1.5 times the mean torque. The shear stress
is limited to 40 n/mm^{2} and twist 1 per metre
length. Determine the diameter required if (i) the shaft is solid (ii) the
shaft is hollow with external diameter twice the internal diameter. Take
modulus of rigidity = 80 kN/mm^{2}.

(or)

18. Design a close coil helical spring of stiffness
20N/mm. The maximum shear stress in the spring is not to exceed 80 N/mm^{2}
under a load of 500 N. The diameter of the coil is to be 10 times the diameter
of the wire. Take modulus of rigidity = 84 kN/mm^{2}.

19. a. Derive an expression for strain energy stored in a body when it is subjected to a tensile force. (4)

b. An unknown weight falls through a height of 10 mm
on a collar rigidly attached to the lower end of a vertical bar 500 cm long and
600 mm^{2} in section. If the maximum extension of the rod is to be 2
mm, what is the corresponding stress and magnitude of the unknown weight? Take
Youngs modulus (E) = 2 x 10^{5} N/mm^{2}. (8)

(or)

20. A truss of span 7.5 m is loaded as shown in figure. Find the reactions and forces in the members of the truss.

Earning: Approval pending. |