msi06 moments influence lines

Faculty : Civil And EnvironmentEngineering

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Department : Stucture And MeterialEngineering

Edition 2Checking No

Title :

MOMENT INFLUENCE LINES

Efective Date 11/7/05AmendmentDate

5/7/05

1.0 OBJECTIVE

1.1 Part 1 : To plot moment influence line.1.2 Part 2 : To apply the use of a moment influence on a simply supported

beam

2.0 LEARNING OUTCOMES

2.1 Application of engineering knowledge in practical application.2.2 To enhance the technical competency in civil engineering through

laboratory application.2.3 Communicate effectively in group.2.4 To identify problem, solving and finding out appropriate soltuion through

laboratory application.

3.0 INTRODUCTION

Moving loads on beams are common features of design. Many road bridges areconstructed from beam, and as such have to be designed to carry a knife edgeload, or a string of wheel loads, or a uniformly distributed load, or perhaps theworst combination of all three. To find the critical moment at a section, influenceline is used

Prepared by:Name : Ahmad Zurisman bin Mohd Ali

Signature :

Date :

1”


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6.0 THEORY

Definition: Influence line is defined as a line representing the changes in eithermoment, shear force, reaction or displacement at a section of a beam when a unitload moves on the beam.

Part 1: This experiment examines how moment varies at a cut section as a unitload moves from one end another ( see diagram 1). From the diagram,moment influence equation can be written.

For a unit load between 0 ax ,

)(1)( xaLaxLM x

…………….(1)

For a unit load between a bx ,:

)( axLxbM x )……………..….(2)

‘Cut’

x 1 (unit load) Mx

Mx

RA= (1 – x/L) RB

=x/L

a b

L

Fig.1


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Part 2: If the beam is loaded as shown below, the moment at the ‘cut’ canbe calculated using the influence line. (See diagram 2).

Moment at ‘cut’ section = 332211 yFyFyF …….. (3)

(y1 , y2 and y3 are ordinates derived from the influence line in terms

of x1, x2, x3 ,a , b and L).

Lba F1 F2 F3

a b

x1

x2x3

Moment influencey1 y2 y3 line for cut

section

Fig 2


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5.0 APPARATUS

Sketch the apparatus use in this experiment and named the essential components.

6.0 PROCEDURES

Part 1:1. Check the Digital Force Meter reads zero with no load.2. Place hanger with any mass between 150-300g at the first grooved

hanger support at the left support and record the Digital Forcereading in Table 1.

3. Repeat the procedure to the next grooved hanger until to the lastgrooved hanger at the right hand support

4. Complete the calculation in Table 1.

Part 2:1. Place three load hangers with any load between 50g to 400g on it and

place it at any position between the supports. Record the positions andthe Digital Force Display reading in Table 2.

2. Repeat the procedure with three other locations.3. Complete the calculation in Table 2.


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7.0 RESULT

Table 1

Location of loadfrom left handsupport (m)

Digital ForceDisplay

Reading (N)

Moment atcut section

(N)

ExperimentalInfluence line

value (Nm)

TheoreticalInfluencelines value

(Nm)

0.040.060.080.100.120.140.160.180.200.220.240.260.300.320.340.360.40

Notes:

1. Moment at cut section = Digital force reading x 0.1252. Experimental Influence line values = Moment ( Nm)

Load (N)3. Calculate the theoretical value using the eqution 1 for load position 40 to 260

mm and equation 2 for load position 320mm to 400mm.


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Part 2,

Table 2

Location Position of hanger from lefthand support (m)

DigitalForce

Reading(N)

Exp.Moment

(Nm)

TheoreticalMoment (Nm)

____g ____g ____g

1234

Notes:

1. Experimental Moment = Digital Force Reading x 0.1252. Theoretical Moment is calculated using Equation (3)


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9.0 DISCUSSIONS

Part 1

1. Derive equation 1 and 2.…………………………………………………………………………………………………………………………………..………………………………………………………………..………………………………………………………………..………………………………………………………………..………………………………………………………………..……………………………………………………………….

2. On the graph paper given, plot the theoretical and experimental valuesagainst distance from left hand support.Comment on the shape of the graph. What does it tell you about howmoment varies at the cut section as a load moved on the beam.

………………………………………………………………….………………………………………………………………….……………………………………………………………………………………………………………………………………

3. Comment on the experimental results and compare it to thetheoretical results.………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………


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Part 2

1. Calculate the percentage difference between experimental and theoreticalresults in Table 2. Comment on why the results differ.

…………………………………………………………………………..………………………………………………………………………….………………………………………………………………………….………………………………………………………………………….………………………………………………………………………….………………………………………………………………………….

9.0 CONCLUSIONS

What can be proved from the experiment

msi06 moments influence lines

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