Influence Lines – Moving Load

STRUCTURAL ANALYSISBFC 21403

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Introductionwww.uthm.edu.my With Wisdom, We Explore

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In designing the structure, the positions of the maximumshear force and maximum bending moment should bedetermined.

If the structure undergoes one or two moving load, theposition of the maximum shear force and maximum bendingmoment can be determined easily from the influence line.

Moving load in structural analysis involves beam, girder andtruss systems.

In this topic, we will discuss about:

1. Maximum Influence at a point due to a series of concentrated loads on beam.

2. Absolute shear and moment.

3. Influence line for truss.

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Maximum Influence at a point due to a Series ofConcentrated Loads.

Example 5.9:

Determine maximum moment at point X on the deck due tothe wheel loads of the moving car which is moving from Ato B.

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Determine reaction force, RA and RB

Construct influence line for moment

Use trial and error

Case 1: 15kN at X

Case 2: 10kN at X

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Case 1: 15kN arrive first at point X

Case 2: load 15kN move forward and load 10kN arrive at X

Max!!!

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Example 5.10:

Determine the maximum positive shear created at point Bin the beam due to wheel loads of moving truck.

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Construct the influence line for VB

Using trial and error procedure; the wheel load of 18kN willmove first

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Case 1: 18kN at point B

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Case 2: 40.5kN at point B

Case 3: 67.5 at point B

Case 4: 45kN at point B

?

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Maximum shear and moment on the beam subjected to themoving load is located on the beam’s centerline betweenthe resultant force and the nearest point.

Occurs under one of the concentrated forces series.

Applied to each load in the series and the correspondingmaximum moment is computed.

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Example 5.11:

Determine the absolute maximum moment in the simplysupported beam.

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Absolute Max. Shear and Momentwww.uthm.edu.my With Wisdom, We Explore

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Absolute Max. Shear and Momentwww.uthm.edu.my With Wisdom, We Explore

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Absolute Max. Shear and Momentwww.uthm.edu.my With Wisdom, We Explore

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Absolute Max. Shear and Momentwww.uthm.edu.my With Wisdom, We Explore

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Absolute Max. Shear and Momentwww.uthm.edu.my With Wisdom, We Explore

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Example 5.12:

Determine the absolute maximum shear subjected to theseries of concentrated load. The loads can be moved fromleft to right or opposite direction.

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Absolute Max. Shear and Momentwww.uthm.edu.my With Wisdom, We Explore

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Absolute Max. Shear and Momentwww.uthm.edu.my With Wisdom, We Explore

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Influence Line - Trusswww.uthm.edu.my With Wisdom, We Explore

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Example 5.13:

Construct the influence lines for force in member GB fromthe given problem.

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Influence Line - Trusswww.uthm.edu.my With Wisdom, We Explore

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Influence Line - Trusswww.uthm.edu.my With Wisdom, We Explore

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Influence Line - Trusswww.uthm.edu.my With Wisdom, We Explore

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Influence Line - Trusswww.uthm.edu.my With Wisdom, We Explore

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Influence Line - Trusswww.uthm.edu.my With Wisdom, We Explore

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Example 5.15:

Draw the influence line for member EF, ED and CD for thetruss which is subjected to the uniform distributed load of2kN/m. Determine the maximum compression and tensileload for the three members.

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Influence Line - Trusswww.uthm.edu.my With Wisdom, We Explore

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Influence Line - Trusswww.uthm.edu.my With Wisdom, We Explore

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Influence Line - Trusswww.uthm.edu.my With Wisdom, We Explore

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Influence Line - Trusswww.uthm.edu.my With Wisdom, We Explore

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Influence Line - Trusswww.uthm.edu.my With Wisdom, We Explore

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Influence Line - Trusswww.uthm.edu.my With Wisdom, We Explore

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