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QUESTION: 1

In figure the maximum bending moment at the fixed end of the cantilever caused by the UDL is M.

The bending moment at a section //5 from the free end is

Solution:

QUESTION: 2

The shear force along the beam shown in the figure is

Solution:

QUESTION: 3

The correct shear force diagram for the beam shown in the figure is

Solution:

QUESTION: 4

A simply supported beam of span l is loaded (as shown) with a udl of intensity w_{1} per unit length at A and w_{2} per unit length at B the shear force at the support B is given by

Solution:

QUESTION: 5

The beam shown in the given figure has a design value of bending moment of

Solution:

QUESTION: 6

A cantilever beam is subjected to moments as shown in the given figure. The BM diagram for the beam will be

Solution:

The bending moment due to 50 kNm moment would be hogging. Similarly the bending moment due to 30 kNm would be sagging. Therefore the bending moment diagram is,

QUESTION: 7

The fixed end moment M_{A} of the beam shown in the given figure is

Solution:

∑F_{V} = 0

⇒ R_{A} + R_{C} = 20

M_{B} = 0 [from right]

∴ R_{C} x 4 - 20 x 6 = 0

⇒ R_{c} x 4 = 20 x 6

M_{B} = 0 [from left]

R_{A} x 4 - M_{A} = 0

⇒ M_{A} = R_{A} x 4 = -10 x 4

= - 40 kNm

The fixed end moment at A will be in clockwise direction, opposite to the direction shown in the figure.

∴ M_{A} = -40 kNm

QUESTION: 8

A simply supported beam with equal overhang ori both sides is loaded as shown in the figure. If the bending moment at mid-span is zero, then the percentage overhang on each side will be

Solution:

Let the overhang percentage in 100p.

So overhang = pl

The shear force diagram will be,

For B.M. at mid point to be zero, area of shear force diagram under (1) should be equal to that of (2),

1/2w(pl)^{2} = 1/2w[(0.5 - P)l]^{2}

or p^{2} = (0.5 - p)^{2} = 0.25 - p + p^{2}

∴ p = 0.25 or 25%

QUESTION: 9

A propped cantilever beam shown in the figure given is having interna! hinge at its mid-span. Which one of the following is the shape of bending moment diagram for the given loading?

Solution:

Due to hinge at C the part CB of beam be have s as simply supported beam. Thus reaction at B will be in upward direction and equals half of the load in span BC.

Span CA be haves as a cantilever beam. There fore B.M.D. will be sagging in BC and hogging in AC and it will be parabolic.

For a cantiiever B.M.D. will be as shown below.

Combining all the arguments answer will be (d) which is given with BM plotted on tension side.

QUESTION: 10

In the case of l-section, the web resists mainly

Solution:

In the case of (-section, nearly 80-90% shear force, is resisted by web and only 10-20% is resisted by flanges, whereas in bending. 80-90% moment is resisted by flanges and only 10-20% by the web.

### Shear Force & Bending Moment

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### Shear Force & Bending Moment

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