UNIT IV CODE: 101402 STRENGTH OF MATERIALS IMPORTANT QUESTIONS

Applicable for Civil Engineering 4th Semester
ANNA UNIVERSITY OF TECHNOLOGY

CODE: 101402 STRENGTH OF MATERIALS

UNIT IV

BEAM DEFLECTION

PART-A (2 Marks)
1. What are the advantages of Macaulay method over the double integration method, for finding the slope and deflections of beams?
2. State the limitations of Euler’s formula.
3. Define crippling load.
4. State Mohr’s theorem.
5. State any three assumption made in Euler’s column theory.
6. What are the different modes of failures of a column?
7. Write down the Rankine formula for columns.
8. What is effective or equivalent length of column?
9. Define Slenderness Ratio.
10. Define the terms column and strut.

PART- B (16 Marks)
1. A simply supported beam of 10 m span carries a uniformly distributed load of 1 kN/m over the entire span. Using Castigliano’s theorem, find the slope at the ends. EI = 30,000 kN/m2. (16)
2. A 2m long cantilever made of steel tube of section 150 mm external diameter and10mm thick is loaded. If E=200 GN/m2 calculate (1) The value of W so that the maximum bending stress is 150 MN/m (2) The maximum deflection for the loading (16)
3. A beam of length of 10 m is simply supported at its ends and carries two point loads of 100 KN and 60 KN at a distance of 2 m and 5 m respectively from the left support.
Calculate the deflections under each load. Find also the maximum deflection.
Take I = 18 X 108 mm4 and E = 2 X 105. (16)
4. i) A column of solid circular section, 12 cm diameter, 3.6 m long is hinged at both ends. Rankine’s constant is 1 / 1600 and c = 54 KN/cm2. Find the buckling load.
ii) If another column of the same length, end conditions and rankine constant but of
12 cm X 12 cm square cross-section, and different material, has the same buckling load, find the value of c of its material. (16)
5. A beam of length of 6 m is simply supported at its ends. It carries a uniformly distributed load of 10 KN/m as shown in figure. Determine the deflection of the beam at its mid-point and also the position and the maximum deflection. Take EI=4.5 X 108 N/mm2. (16)
6. An overhanging beam ABC is loaded as shown is figure. Determine the deflection of the beam at point C. Take I = 5 X 108 mm4 and E = 2 X 105 N/mm2. (16)

7. A cantilever of length 2 m carries a uniformly distributed load of 2.5 KN/m run for a length of 1.25 m from the fixed end and a point load of 1 KN at the free end. Find the deflection at the free end if the section is rectangular 12 cm wide and 24 cm deep and E=1 X 104 N/mm2 (16)
8. A cantilever of length 2m carries a uniformly distributed load 2 KN/m over a length of 1m from the free end, and a point load of 1 KN at the free end. Find the slope and deflection at the free end if E = 2.1 X 105 N/mm2 and I = 6.667 X 107 mm4 . (16)
9. Determine the section of a hollow C.I. cylindrical column 5 m long with ends firmly built in. The column has to carry an axial compressive load of 588.6 KN. The internal diameter of the column is 0.75 times the external diameter. Use Rankine’s constants.
a = 1 / 1600, c = 57.58 KN/cm2 and F.O.S = 6. (16)