1.0
OBJECTIVE
1.1 1.1
Part Part 1: To plot plot Shea Shearr for force ce inf influ luen ence ce lin line. e.
1.2
Part Part 2: To veri verify fy the the use use of a shear shear force force infl influen uence ce on on a sim simply ply
supported Beam
2.0 2.0
LEAR EARNING OU OUTCOMES
2.1
The
application
the
engineer eering
knowledge
in
practical
application 2.2 2.2
To enha enhanc nce e techni technica call compe compete tenc ncy y in struc structu tura rall engin enginee eeri ring ng
through laboratory application. application. 2.3 2.4
To communicate effectively in group To identi entiffy prob roblem lem, sol solving ving and and fin findin ding out appr appro opri priate ate solution through laboratory application.
3.0
INTRODUCTION
Moving loads on beams are common features of design. Many road bridges are constructed from beam, and as such have to be designed to carry a knife edge load, or a string of wheel loads, or a uniformly distributed load, or perhaps the worst combination of all three. The method of solving the problem is to use influence lines.
An influence line for a given function, such as a reaction, axial force, shear force, or bending moment, is a graph that shows the variation of that function at any given point on a structure due to the application of a unit load at any point on the structure. An influence line for a function differs from a shear, axial or bending moment
diagram.
Influence
lines
can
be
generated
by
independently applying a unit load at several points on a structure and determining the value of the function due to this load, i.e. shear, axial, and moment at the desired location. The calculated values for each function are then plotted where the load was applied and then connected together to generate the influence line for the function. For a statically determinate structure the influence line will consist of only straight line segments between critical ordinate values. The influence line for a shear force at a given location will contain a translational discontinuity at this location. The summation of the positive and negative shear forces at this location is equal to unity.
4.0
THEORY
Definition: Shear 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:
This Experiment examines how shear force varies at a cut section as a unit load moves from one end to another ( see Figure 1). From the diagram, shear force influence line equation can be writen. For 0 ≤ x ≤ a a shear line is given by : Sy = − x L…………… (1) For a ≤ x ≤ b shear line is given by: Sy = 1− x L . ……………(2)
Part 2: If the beam are loaded as shown in Figure 2, the shear force at the ‘cut’ can be calculated using the influence line. (See diagram 2). Shear force at ‘cut’ section 1 1 2 2 3 3 = F y + F y + F y … (3) (y1 , y2 and y3 are ordinates derived from the influence line in terms of x1, x2, x3 ,a , b and L)
5.0
APPARATUS
a) Shear force machine b) Weights c) Weight hangers d) Electronic load cell
Beam
Digital Force Display
Weight 6.0
PROCEDURES
Part 1 1.
Digital Force Display meter reads zero with no load is
checking. 2.
Hanger with any mass range between 100g to 300g was placed at the first grooved hanger support at the left support and the Digital Force reading recorded in Table 1.
3.
The procedure to the next grooved hanger until to the last grooved hanger at the right hand support was repeated.
4.
Part 2
The calculation in Table 1 was completed.
1.
Three
load
hangers
with
100g.
200g
and
300g
mass
respectively placed at any position between the supports. The positions and the Digital Force Display reading recorded in Table 2. 2. 3.
7.0
The produce with three other locations was repeated. The calculation in Table 2 was completed
RESULT
Part 1
Location of load from left hand support (m) 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.34 0.36 0.38 0.40
Digital Force Display Reading (N)
Shear Force at cut section (N)
Experimen tal Influence line value
Theoretical Influence line value
0.1 0.1 0.1 0.2 0.4 0.5 0.8 0.6 1.0 1.1 1.2 1.0 -0.6 -0.6 -0.5 -0.5
0.1 0.1 0.1 0.2 0.4 0.5 0.8 0.6 1.0 1.1 1.2 1.0 0.6 0.6 0.5 0.5
0.05 0.05 0.05 0.10 0.20 0.25 0.41 0.31 0.51 0.56 0.61 0.51 0.31 0.31 0.25 0.25
-0.09 -0.14 -0.18 -0.23 -0.27 -0.32 -0.36 -0.41 -0.45 -0.50 -0.55 -0.59 0.23 0.18 0.14 0.09
Part 2 Locatio n
8.0
Position of hanger from left hand support (m) 100g
200g
300g
1
0.08
0.24
0.32
Shear force Digital Reading (N) 1.1
2
0.06
0.18
0.28
1.9
3.09
3
0.04
0.28
0.36
0.8
2.13
4
0.10
0.16
0.34
1.1
2.68
DATA ANALYSIS
Theoretica l Shear (Nm)
2.48
Part 1 1.
Shear force at cut section is the same value given by Digital Force reading. Add negative (-) sign to the value for positions 320mm to 380mm. 2. 3.
Experimental Influence line values = Shear force (N) Load (N) Calculate the theoretical value using the equation 1 for load position 40 to 260 mm and equation 2 for load position 320mm to 380mm.
For 0.14m of load from left hand support Load =
200g
=
(200/1000) x 9.81
=
1.962 N
Digital Force Display Reading (N) = 0.5 L = 0.44m
a) Shear Force at cut section (N) = Digital Force Display Reading = 0.5 N b) Experimental Influence line value = Shear force(N) / Load (N) = 0.5 / 1.962 = 0.25 N c) Theoretical Influence line value Equation 1 Sy = -x / L = -0.14 / 0.44 = - 0.32
For 0.36m of load from left hand support Load =
200g
=
(200/1000) x 9.81
=
1.962 N
Digital Force Display Reading (N) = - 0.6 L = 0.44m
a) Shear Force at cut section (N) = Digital Force Display Reading = - 0.6 N b) Experimental Influence line value = Shear force(N) / Load (N) = - 0.6 / 1.962 = - 0.31 N c) Theoretical Influence line value Equation 2 Sy = 1 - x / L = 1 – (0.36 / 0.44) = 0.18
Part 2 Theoretical Shear Force is calculated using equation 3. Shear force at ‘cut’ section = F1y1 + F2y2 + F3y3 ....
a/L = 300/440 = 0.68 b/L = 140/440 = 0.32 F1 = 2.943 N F2 = 1.962 N F3 = 0.981 N
Location 1 Y1/120 = 0.68 / 300 Y1 = 0.27 Y2/200 = 0.68 / 300 Y2 = 0.45 Y3/360 = 0.32 / 140 Y2 = 0.82
F1y1 + F2y2 + F3y3 = 2.943(0.27) + 1.962( 0.45) + 0.981(0.82) = 2.48 Nm
8.0
DISCUSSION
Part 1 1. Derive equation 1 and 2 Equation 1 ∑ Mcut = 0 ∑ Fy = 0 (L-x) / L-1-Sy = 0 Sy = -x / L Equation 2 ∑ Mcut = 0 ∑ Fy = 0 (L-x) / L – Sy = 0 Sy = (L-x) /L Sy = 1 – x / L
2. On the same graph paper, plot the theoretical and experimental values against distance from left hand support.
Theoretical an experimental value against distance
0.8 0.6 0.4 0.2 theory
0 -0.2
experime 1 . 0 2 . 0 4 . 0 . 0 0 . 8 0 4 . 0 6 1 0 0 . 1 . 1 2 . 8 1 4 0 . 0 6 2 0 0 . 2 . 2 2 . 3 4 0 . 3 0 6 . 8 3 0 4 . 6 0 0
-0.4 -0.6 -
3. Comment on the shape of the graph. What does it tell you about how shear force varies at the cut section as a load moved on the beam?
Based on the graph, there are differential between theoretical and experimental value. Theoretical value that we had obtained was proportional with the distance and gets the linear graph. But have a drastic increasing at the end of the distance. While the influence lines for experimental value was increasing due to the distance and decreasing at 0.34m distance.
4. Comment on the experimental result compared to the theoretical result
Based on the result that we got, shows a totally different result between the theoretical and experimental values. For the experimental influence line value, there are a big different between those experimental and theoretical. Overall, based on the procedure, we followed the right instruction. It might be the error of the machine itself and not in the good condition. Part 2 1.
Comment the experimental result and the theoretical result in Table 2.
In this part, we used the load 100g, 200g and 300g. From this experiment, the value for the location 1 to 4, the value for the experimental is bigger than the theoretical value. The value is depend on the location but value for both result is not so much differences.
10.0 CONCLUSION
What can you prove from the experiment?
Part 1 :
From the experiment, we know that the value for the experimental and theoretical values is totally difference. From the graph it shows totally difference result between theoretical and experimental result. Based on the result, the values of shear force
at cut section (N) increases when a load moves towards the cut section.
Part 2 :
From the experiment, its shows that the location is one of the causes for the differences between the value. We should know that, influence lines can be used to calculate the shear force at the cut section.
11.0 REFERENCE
http://www.scribd.com/doc/3607962/The-Structure-EngineeringHandbooks-2-Structural-Analysis
Russell C. Hibbeler, Fifth Edition “Structural Analysis”
