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Influence Line Diagrams-II

Theory of Structures - I

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Contents Qualitative Influence Lines

Influence lines for Girders

Influence Lines for Trusses

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Qualitative Influence Lines In 1886, Heinrich Muller-Breslau developed a

technique for rapidly constructing influence lines.

It states“the influence line for a function (reaction, shear or moment) is to be the same scale as the deflected shape of the beam when the beam is acted upon by that function”

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In order to draw deflected shape properly, the capacity of the beam to resist the applied function must be removed so the beam can deflect when the function is applied.

A

A

Ay

Ay

xInfluence line for Ay

REACTION

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CSHEAR

Vc

Vc

Deflected Shape

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CMOMENT

Deflected Shape

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Proof: Reaction

A Ay

x

1y’

1

y

Work = Force . Displacement

= Moment . Rotational displacement

C C

'

;1

0'.1

yy

y

yyy

A

A

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C

SHEAR

Vc

Vc

'

;1

0'.1

yc

y

yyc

V

V

y’1

1

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C

MOMENT

Deflected Shape

Mc Mc

y’

1

1'

;1

0'.1

yc

yc

M

M

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Example 6-9

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12

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Practice Problems Example 6-9 to 6-12

Chapter 6

Structural Analysis by R C Hibbeler

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Influence Lines for Girders

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Unit load on the slab is transferred to the girder only at points where it is in contact with the floor beams.

A, B, C and D are panel points and the region between these points is known as panel.

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17

18BP

BP

FFVsdFdFM

1

1 )(

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Moment will depend on where the point p is located but shear will remain same in the whole panel.

Influence line for shear in floor girders are specified for panels in the girder and not specific points along the girder.

Shear is referred to panel shear.

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Since the girder is affected only by the loadings transmitted by the floor beams, the unit load is generally placed at each floor-beam location to establish the necessary data used to draw the influence line.

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Example 6-13

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x VCD

0 0.33310 020 -0.33330 0.33340 0

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Practice Problems Example 6-13 to 6-14

Chapter 6

Structural Analysis by R C Hibbeler

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top cord

deck

sway bracing

top lateralbracing

stringers

portal end post

portalbracing

panel

floor beam

bottom cord

Truss

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Example 6-15

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x FGB

0 010 0.35420 -0.70730 -0.35440 0

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Practice Problems Example 6-15 to 6-17

Chapter 6

Structural Analysis by R C Hibbeler

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