shear force and moment

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1.0 INTRODUCTION

Influence line is an important application especially in designing structures that

can resist large live loads, whether the load acted upon a certain locations only, or

moving from a location to another.

An influence line represents the variation in the reactions, shear, moment or

deflection at specific points in a structure or truss as a concentrated force moves over the

structure. After the line has been constructed, we will know whether the load placement

is suitable or not.

2.0 OBJECTIVE

- Part 1: o plot shear force influence lines.

- Part !: o verify the use of a shear force influence line on a simply supported

beam.

3.0 THEORY

"efinition: #hear influence line is defined as a line representing the changes in

shear force at a section of a beam when a unit load moves on the beam.

Part 1 : his e$periment e$amines how shear force varies at the cut section as a unit load

moves from one end to another. %rom the diagram, shear force influence line e&uation

can be written.

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%igure !

7

%1

%!

%0

x1

x!

x0


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4.0 APPARATUS

he sketch for the apparatus used I this e$periment is in the following figure.

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5.0 PROCEDURES

Part 1

1. he "igital %orce 9eter is checked to make sure that the reading is ero with no

load.

!. 5eplace the hanger with any mass range between 1''g to 0''g at the first

grooved hanger support at the left support and make sure record the "igital %orce

reading in able 1.

0. 5epeat again the procedure to the ne$t grooved hanger until to the last grooved

hanger at the right hand support.

7. he calculation must be complete in able 1.

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Part 2

1. Place the three load hanger with 1''g, !''g and 0''g mass respectively at any

position between the supports. hen record the positions and the "igital %orce

"isplay reading in able !.

!. And then repeat the procedure with other three locations.

0. he calculation in able ! must be complete.


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6.0 RESULT & ANALYSIS

6.1 Part 1

1. #hear force at cut section is the same value given by "igital force

reading. Add negative sign to the value for positions 0!'mm to

0='mm.

!. >$perimental Influence line values *+oad-?.

-?.%orce#hear

0. 3alculate the theoretical value using e&uation 1 for load position 7' to

!;' mm and e&uation ! for load position 0!'mm to !='mm.

Ta !" 1

6.2 Part 2

1. heoretical #hear %orce is calculated using >&uation 0.

Ta !" 2

L#$at%# #' !#a(

'r#) !"'t *a (

+,--#rt )/

D% %ta! #r$"

D%+-!a R"a(%

N/

S*"ar #r$" at

$,t +"$t%# N/

E -"r%)" ta!

I '!," $" !% "

a!,"

T*"#r"t%$a!

I '!," $" !% "

a!,"'.'7 '.1 -'.1 -'.';< -'.'@1

'.'; '.! -'.! -'.100 -'.10;

'.'= '.0 -'.0 -'.!'' -'.1=!

'.1' '.7 -'.7 -'.!;< -'.!!=

'.1! '.7 -'.7 -'.!;< -'.!

'.17 '.8 -'.8 -'.000 -'.01=

'.1; '.; -'.; -'.7'' -'.0;7

'.1= '.; -'.; -'.7'' -'.7'@

'.!' '.< -'.< -'.7;< -'.788

'.!! '.= -'.= -'.800 -'.8''

'.!7 '.@ -'.@ -'.;'' -'.878

'.!; '.@ -'.@ -'.;'' -'.8@1

'.07 -'.7 '.7 '.!;< '.!!2

%1S1 /%!S!/%0S0 * '.@=1$'.'0! / 1.@;!$'.'8< / !.@70$'.'=' 9 0.3>5 N)

8.0 DISCUSSIONS

Part 1

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1. %e#i&e equation 1 an' 2

E %$ *'

E %y *5 A / 5 6 F 1 * '

5 A / 5 6 * 1 --------------1

5 A + F 1 +-$ * '

5 A + * 1 + - $

5 A * 1 + F $ --------! +

5 6 * 1 F 1 F $H+ * $H+ --------0

E9 * 5 A + - b F 1 a - $ * ' * 1 F $H+ a - 1 a F $ * 1 ; / a 7 1 a ; / -------7 e&uation 1

L

E9 * - 5 6 b F 1 a - $ * - 5 6 b F a - $

* 5 6 b F a / $* 7 7 a / ------------8 e&uation !

L

2. On the graph paper, plot the theoreti al and e!perimental values against distan e

"rom le"t hand support. $omment on the shape o" the graph. %hat does it tell you

a&out ho' moment varies at the ut se tion as a load moved on the &eam.

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6ased on the graph of the e$periment and theoretical values, it is show of curves.

Dhen the moment applied on the beam increase, the influence line value become

decrease and the moment applied on the beam also decrease. After the distance for

'.0'm the curve become down. his is because more load were applied cause the

decreasing of the influence line value.

#. $omment on the e!perimental results and ompare it to the theoreti al results.

%rom the graph influences line value against distance, it shows the value of influences

line for theoretical and e$perimental are not far different. he average different of

value influences line for theoretical and e$perimental is 1.00= F 1.01= * '.'! and

percentage of errors between theoretical and e$perimental values is '.! T. #o thise$periment can be e$cept. he different of value between the theoretical and

e$perimental or also known errors happen cause the careless and mistaken during in

this e$periment. his errors come because of :

i he digital force very alert to any changes or resistance like wind resistance

and make the true value did not e$act.

ii he observer take the value during the load is not stable

iii he value of the digital force did not take again.

iv Lave a movement while taking the value.

he method to solve this problem :

i 9ake sure the area around the e$periment doing is free from any movement

and better to the this e$periment in closed room.

ii 9ake sure the load is static or not more during the value taken.

iii ake the value against and against. hen take the average value.

Part 2

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1. $al ulate the per entage di""eren e &et'een e!perimental and theoreti al results in

*a&le 2. $omment on 'hy results di""er.

>$perimental9oment ?m

heoretical 9oment?m

Percentage "ifferenceT

'.!.0 CONCLUSIONS

%hat an &e proved "rom the e!periment (

%rom this e$periment, we can prove that the moment is e$ist in the load. >ach

distance of load loading have different moment. After this e$periment had done, we canknow that the reaction e$erted on 5 A and 5 6 . De also know that the value of reaction at

each section of moment and the result it cause the e$isting of critical point which the

point that the ma$imum force needed to support the load.

o find the moment, the distance become the main factor that effected the

reaction of the moment to the beam which is the moment value is proportional to the

force that e$erted.

he application from this e$periment is to show that this e$periment is important

to find the value of the force or the moment that e$erted to the beam. 6eside that, to find

whether the beam has an afford to support the load.

shear force and moment

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