Transcript
Bridge EngineeringBridge Engineering(SE(SE--507)507)
Lecture 4
Department of Civil EngineeringUniversity of Engineering and Technology
Lahore, Pakistan
Lecture 4Dr. AzharSpring 2012
Influence LinesInfluence Lines
Influence lines are graphical representations of the effect of moving loads (live loads) in structural systems. They are represented by a unit load of variable position at a given point in the structural system,. These diagrams are used
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the structural system,. These diagrams are used to compute the maximum response at a given section in the structures.
Influence lines play a primery role in structures subjected to moving load, such as bridges, industrial crane rails, and systems where loads move across spans.
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Influence Line for Vertical Reaction AInfluence Line for Vertical Reaction Ayy
� Apply unit-load at an arbitrary position x
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ILD of Ay
Influence Line for Shear at 0.25LInfluence Line for Shear at 0.25L
� Apply unit-load along the beam and compute shear just before and after 0.25L
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Before 0.25 L After 0.25 L
0.25L0 ≤≤ x
L1Ay
x
−=
L1AV yc
x
−=−=
L0.25L ≤≤ x
L1Ay
x
−=
L1AV yc
x
−==
Influence Line for Shear at 0.25LInfluence Line for Shear at 0.25L
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L1
x
−
x
5
L
x
−
1.0x
Influence Line for Moment at 0.5LInfluence Line for Moment at 0.5L
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22
L.1
2
L.
L1MD
x
x
x
=
−−
−= ( )x
xx
−=−=
−= L
2
1
22
L
2
L.
L1MD
( )x−L2
12
x
x
L25.0
Loading Maximum EffectsLoading Maximum Effects
After developing the influence line for a specific effect (reation, shear or moment), the maximum effect can be found by positioning the live load on the beam which will yield the maximum value of the function.
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the function.
Concentrated Load
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Ay = Load x ordinate of influence line
Ay is max. with P at x = 0, = P x 1 = P
−=
L1P.Ay
x
Loading Maximum EffectsLoading Maximum Effects
Uniform Load
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In case of a distributed load, the maximum effect is obtained by multiplying the area under the influence line by intensity of the uniform load.
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