CED. UET. Taxila 1

Influence Line Diagrams-II

Theory of Structures - I

CED, UET, Taxila 2

Contents

Qualitative Influence Lines

Influence lines for Girders

Influence Lines for Trusses

CED, UET, Taxila 3

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”

CED, UET, Taxila 4

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

x

Influence line for Ay

REACTION

CED, UET, Taxila 5

CSHEAR

Vc

Vc

Deflected Shape

CED, UET, Taxila 6

CMOMENT

Deflected Shape

CED, UET, Taxila 7

Proof: Reaction

A Ay

x

1y’

1

y

Work = Force . Displacement

= Moment . Rotational displacement

C C

'

;1

0'.1

yy

y

yyy

A

A

CED, UET, Taxila 8

C

SHEAR

Vc

Vc

'

;1

0'.1

yc

y

yyc

V

V

y’

1

1

CED, UET, Taxila 9

C

MOMENT

Deflected Shape

Mc Mc

y’

1

1'

;1

0'.1

yc

yc

M

M

CED, UET, Taxila 10

Example 6-9

CED, UET, Taxila 11

CED, UET, Taxila 12

CED, UET, Taxila 13

Practice Problems

Example 6-9 to 6-12

Chapter 6

Structural Analysis by R C Hibbeler

CED, UET, Taxila 14

Influence Lines for Girders

CED, UET, Taxila 15

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.

CED, UET, Taxila 16

CED, UET, Taxila 17

CED, UET, Taxila 18BP

BP

FFV

sdFdFM

1

1 )(

CED, UET, Taxila 19

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.

CED, UET, Taxila 20

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.

CED, UET, Taxila 21

Example 6-13

CED, UET, Taxila 22

CED, UET, Taxila 23

x VCD

0 0.333

10 0

20 -0.333

30 0.333

40 0

CED, UET, Taxila 24

Practice Problems

Example 6-13 to 6-14

Chapter 6

Structural Analysis by R C Hibbeler

CED, UET, Taxila 25

top cord

deck

sway bracing

top lateralbracing

stringers

portal end post

portalbracing

panel

floor beam

bottom cord

Truss

CED, UET, Taxila 26

Example 6-15

CED, UET, Taxila 27

CED, UET, Taxila 28

x FGB

0 0

10 0.354

20 -0.707

30 -0.354

40 0

CED, UET, Taxila 29

Practice Problems

Example 6-15 to 6-17

Chapter 6

Structural Analysis by R C Hibbeler

CED, UET, Taxila 30