Unit - IV

1. List any four methods of determining slope and deflections of a loaded beam.

Ans: a) double integration method

b) Macaulays method

c) Moment area theorem method

d) Conjugate beam method

2. State the two theorems in the moment of area method.

Ans: Theorem 1: The change of slope between any two points is equal to the net

area of bending moment diagram between these points divided by EI.

Theorem 2: The total deflection between any two points is equal to the

moment of area of bending moment diagram between these two points about the last point

divided by EI.

3. State the expression for slope and deflection at the free end of a cantilever beam of length

L subjected to a uniformly distributed load of w per unit length.

Ans: Slope at the free end,

Deflection at the free end ,

4. write the relationship between slope, deflection and radius of curvature of beam?

Ans:

5. A cantilever beam of span 2 m is carrying a point load of 20kN at its free end. Calculate

the slope at the free end. Assume EI = 12x103 kN/m

2.

Ans: Slope at the free end,

= 0.0033 rad

6. In a SSB of 3m span carrying uniformly distributed load throughout the length, the slope

at the supports is 10. What is the maximum deflection in the beam.

Ans: Slope ,

Deflection

7. Calculate the maximum deflection of a simply supported beam carrying a point load of

100kN at mid span. Span = 6m and EI = 20000 kN/m2.

Ans: Deflection

8. Differentiate a Column and a strut. Ans: In column, the member of structure is vertical and both of its ends are rigidly

fixed. Eg: piller

In strut, the member of structure is not vertical and one or both of its ends are

hinged or pin jointed. Eg: piston rod, connecting rod.

9. State two assumptions made in the Eulers columns theory. Ans: i) The cross section of the column is uniform throughout its length.

ii) The material of the column is perfectly elastic homogeneous and obeys

hookes law. 10. State slenderness ratio.

Ans: The ratio between actual length and the least radius of gyration of the column is

known as slenderness ratio

11. Define equivalent length of a column. Ans: The equivalent length or effective length of the column can be defined as the

length the length of an equivalent pin ended column having the same load carrying

capacity as the member under consideration

12. State Eulers formula for crippling load. Ans: the crippling load or critical load for any type of end condition of given column is

given by

Where, L = l both ends are hinged L = 2l one end is fixed and other end is free L = l/2- both ends are fixed

L = l/ 2 - one end is fixed and other end is hinged

13. What are the limitations of Eulers formula? Ans: Eulers formula gives the value of crippling stress greater than crushing stress when the slenderness ratio is less than a certain limit.

14. Define crippling load. Ans: The load at which the column just buckles is known as crippling or buckling

load.

15. State Rankines formula for crippling load.

Where - crushing stress , A cross sectional area, a Rankines constant, L equivalent length and k least radius of gyration.

16. What is the expression for crippling load when both the ends of the column are hinged and fixed?

Columns with both ends are hinged =

Columns with both ends are fixed =

Find the critical load of an Eulers column having 4m length 50mm x 100mm cross section and hinged at both ends. E = 200 kN/mm

2.

17. The actual length of column is 10 m . determine its effective length if both the ends of the column are rigidly fixed.

Ans: Effective length for both ends are fixed L = l/2, then L = 5

18. State the parameters influencing Buckling load of a long column. Ans: Bending stiffness and slenderness ratio

19. Define Short column, Medium sized column, Long columns. Ans: A column is considered to be short when the ratio of its effective length to its least

lateral dimension does not exceed12.

If the ratio of the the effective length to its least lateral dimension exceeds12 the column

is considered to be a long column

20. Write the equivalent length of a column for a column with

a) one end is fixed and other end is free L = 2l

b) both ends are fixed L = l/2

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