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5.1 INTRODUCTION

Members supporting perpendicular

loadings (transverse) are called beams

Beams are classified on loading basis:

simply supported beams

cantilever beams

overhanging beams, and etc.

Beams are in buildings, aircraft wings,

bridges, etc.

Beams developed internal shear and

moment

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SIGN CONVENTION

Distributed load

Upward is positive

Shear

If the internal shear rotates the segment

cw, the shear is then positive.

Moment

If the internal moment causes

compression on the top surface

(holding the water), the moment is then

positive

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5.2 SHEAR AND BENDING MOMENT DIAGRAMS

Example:

Draw the shear and the

moment diagram.

4

V is positive

then, slope M is

positive

V is negative

then, slope M is

negative

Slope V is constant

then, M is linear

5

Example: Draw the shear and moment diagram.

6

V is positive

then, slope M is

positive

V is negative

then, slope M is

negative Slope V is negative;

then, M is concave down

7

Example: Draw the shear and the

moment diagram.

8

w is negative

Then, slope V is negative.

Slope w is negative

Then, V is concave down

V is positive

Then, slope M is positive.

Slope V is negative

Then, M is concave down

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46 kN

14 kN

26 kN

50 kN

B

D

max

max

Example :

R

R

V

M

10

V (kN)

11

V

M

Example: Draw the shear and the

moment diagram.

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5.3 RELATIONS AMONG LOAD, SHEAR AND

BENDING MOMENT

( )

( )

( )

dw x

dx

d

dx

w x dx

x dx

V

MV

V

M V

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Example:

Draw the shear and

the moment diagram.

14

Example:

Draw the shear and

the moment diagram.

15

Example:

Draw the shear and the moment diagram.

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END OF CHAPTER FIVE

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