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CEN-309Structural Analysis and Design-

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Influence Line

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Influence Line

It is the diagram showing the variation in the shear, moment, reaction, stress in a truss member or any other direct function due to a unit load moving across the structure. An influence line is constructed by plotting direct under the point, where the unit load is placed. An ordinate the height of which represents to some scale the value of the particular function being studied when the load is in that position. For determinate structures influence lines are always straight lines.

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First>>> Decide how the stress is to be calculated.

Second>> Move the unit load along the span and observe the effect on the stress in question.

Third>>> Calculate the controlling ordinates on the influence line and complete the diagram.

Influence Line

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0; ,

1 0

1

B

A

A

M clockwise ve

R L L xL x xR

L L

0; ,1 0

1 1 0

BA

B

B

V upward veR R

x RL

xRL

Influence Line of Beam

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0; ,1 0

, 1

A

B

B

A

M clockwise vea R L

aRL

aand RL

0; ,0BC

BC

V upward veV R

V R

0; ,0C A

C A

V upward veV RV R

IL of VC:When load at left side of point C;

When load at right side of point C;

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0; ,

0C

B

C

BC

C

M L a

R L a

aM L aL

M clockwise ve

RM

1

0; ,0

C

C

C A

BC

a

a aM a L aL L

M clockwise veM R

M aR

IL of MC:

When load at left side of point C;

When load at right side of point C;

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Muller-Breslau Principle :The ordinates of an influence line for any force are proportional to the deflected shape of the structure produce by removing the capacity of the structure to carry the force and then introducing into the modified structure. A displacement the corresponds to the restrained removed.

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Calculation

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Calculation

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Calculation

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Calculation

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Cont’d

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Influence Line of Girder with Floor Beams

More in PDF File (Influence line of girder & Truss).

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Influence Lines of Truss

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Calculation

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Calculation (Cont’d)

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Calculation (Cont’d)

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Calculation

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Calculation (Cont’d)

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Calculation (Cont’d)

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Calculation (Cont’d)

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Calculation

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Calculation (Cont’d)

More problems in PDF File (Influence line of girder & Truss).