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QUESTION: 1

For cantilever beam shown in the figure, the deflection at C due to a couple M applied at Bis equal to

Solution:

Slope and deflection at B,

[As there is no moment between B and C so BC remains linear at θ_{B} slope]

QUESTION: 2

Consider the following statements.

1. Conjugate beam can be used to determine slopes and deflection in a non-prismatic beam.

2. Conjugate beam may be statically indeterminate.

3. Conjugate beam method gives absolute slope and deflection.

The correct answer is

Solution:

QUESTION: 3

Which of the foilowing statements are correct. Macaulay's method for calcuiation of slope and deflection in a beam is suitable for

1. Prismatic beams only.

2. Several concentrated loads and can be extended to uniformly distributed loads.

3. Both prismatic and Non-prismatic beams,

Solution:

Macaulay’s method is based on singularity function. It is applicable for prismatic beams only. While Mohr’s moment area method can be used for prismatic and non-prismatic beams.

QUESTION: 4

A simply supported beam of span L and depth dcarries a central load W. The ratio of maximum deflection to maximum bending stress is

Solution:

QUESTION: 5

Calculate the reaction at the roller support for the cantilever beam shown in the figure?

Solution:

Let P be the roller reaction.

Upward deflection of beam at A due to P.

Downward deflection of beam at A due to w.

QUESTION: 6

A cantilever carries a load P as shown in the given figure

The deflection at B is

Solution:

QUESTION: 7

A simply supported beam of uniform flexural rigidity is loaded as shown in the given figure. The rotation at the end A is

Solution:

The M/EI diagram of beam is,

The slope at mid span is zero.

The difference between the slope at two points is M/EI area between these points.

So slope at A,

QUESTION: 8

The maximum deflection of simply supported beam occurs at zero

Solution:

QUESTION: 9

The stepped cantilever- is subjected to moments, M as shown in the figure below. The vertical deflection at the free end ( neglecting self weight) is

Solution:

Using moment area method,

Deflection at B, wrt A

= Moment of area of M/EI diagram between A and B about B

QUESTION: 10

A simply supported beam of length CL' carries two equal unlike couples. M at the two ends. The central deflection of the beam is given by

Solution:

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