1.0 OBJECTIVE
1.1 Part 1: To plot Shear force influence line.
1.2 Part 2: To verify the use of a shear force influence on a simply supported beam
2.0 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.
3.0 THEORY
Defination: 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 written.
For 0 ≤ x ≤ a a shear line is given by:
Sy = − x/ L……… (1)
For a ≤ x ≤ b shear line is given by:
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 = F1 y1 + F2 y2 + F3 y3 … (3)
(y1, y2 and y3 are ordinates derived from the influence line in terms of x1, x2, x3, a, b and L)
4.0 APPARATUS
4.1 Shear Force machine 4.2 Weight (Loadings)
Beam
Load
5.0 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. The calculation in Table 1 was completed.
Part 2
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. The produce with three other locations was repeated. 3. The calculation in Table 2 was completed.
6.0 RESULT Part 1:
Location of load from left hand
support (m) Digital Force Display Reading ( N ) Shear Force at cut section ( N ) Experimental Influence line value Theoretical Influence lines value 0.04 0.2 0.2 0.102 -0.091 0.06 0.3 0.3 0.153 -0.136 0.08 0.4 0.4 0.204 -0.182 0.10 0.5 0.5 0.255 -0.227 0.12 0.6 0.6 0.306 -0.273 0.14 0.7 0.7 0.357 -0.318 0.16 0.8 0.8 0.408 -0.364 0.18 0.9 0.9 0.459 -0.409 0.20 1.0 1.0 0.510 -0.455 0.22 1.0 1.0 0.510 -0.500 0.24 1.1 1.1 0.561 -0.545 0.26 1.2 1.2 0.612 -0.591 0.34 -0.5 -0.5 -0.255 0.227 0.36 -0.4 -0.4 -0.204 0.182 0.38 -0.3 -0.3 -0.153 0.136 0.40 -0.2 -0.2 -0.051 0.091 Part 2:
Position of hanger from left hand Shear force Digital Reading (N) Theoretical Shear ( Nm ) Location support ( m ) 100g 200g 300g 1 0.22 0.24 0.06 2.0 1.962 2 0.16 0.08 0.24 2.4 1.581 3 0.26 0.04 0.14 1.8 1.156 4 0.10 0.24 0.38 0.9 1.000 6.1 CALCULATION
Part 1:
1) Experimental Influence line values = Shear Force (N) Load (N)
Eg. Experimental Influence line values = 0.2 N = 0.102 200 x 9.81/1000
2) Theoretical Influence lines value; 0.04 ≤ x ≤ 0.26m
Theoretical value, Sy = -x/L
Eg. Theoretical value, Sy = -0.04/ 0.44 = - 0.091
3) Theoretical Influence lines value; 0.32 ≤ x ≤ 0.38m
Theoretical value, Sy =1 -x/L
Eg. Theoretical value, Sy = 1 -0.34/ 0.44 = 0.227
Part 2: Location 1
Y3 Y1 Y2 300g 100g 200g 60mm 220mm 140mm 240mm 300mm a/L b/L 1. a/L = 300/440 = 0.682 2. b/L = 140/440 = 0.318 3. y1 / 220 = 0.682 / 300 y1 = 0.500 4. y2 / 240 = 0.682 / 300 y2 = 0.546 5. y3 / 60 = 0.682 / 300
y3 = 0.136 Theoretical Shear = F1y1 + F2y2 + F3y3…. = [(0.1 x 0.5) + (0.2 x 0.546) + (0.3 x 0.136)] x 9.81 = 1.962 Nm Location 2 Y2 Y1 Y3 200g 100g 300g 80mm 160mm 140mm 240mm 300mm a/L b/L 1. y1 / 160 = 0.682 / 300 y1 = 0.248 2. y2 / 80 = 0.682 / 300 y2 = 0.124 3. y3 / 240 = 0.682 / 300 y3 = 0.372
Theoretical Shear = F1y1 + F2y2 + F3y3…. = [(0.1 x 0.248) + (0.2 x 0.124) + (0.3 x 0.372)] x 9.81 = 1.581 Nm Location 3 Y2 Y3 Y1 200g 300g 100g 40mm 140mm 140mm 260mm 300mm a/L b/L 1. y1 / 200 = 0.682 / 300 y1 = 0.403 2. y2 / 40 = 0.682 / 300
y2 = 0.062 3. y3 / 140 = 0.682 / 300 y3 = 0.217 Theoretical Shear = F1y1 + F2y2 + F3y3…. = [(0.1 x 0.403) + (0.2 x 0.062) + (0.3 x 0.217)] x 9.81 = 1.156 Nm Location 4 Y1 Y2 Y3 100g 200g 300g 100mm 140mm 240mm 60mm 300mm a/L b/L 4. y1 / 100 = 0.682 / 300
y1 = 0.155 5. y2 / 240 = 0.682 / 300 y2 = 0.372 6. y3 / 60 = 0.682 / 300 y3 = 0.043 Theoretical Shear = F1y1 + F2y2 + F3y3…. = [(0.1 x 0.155) + (0.2 x 0.372) + (0.3 x 0.043)] x 9.81 = 1.008 Nm 7.0 DISCUSSIONS 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.
3. Comment on the shape of graph. What does it tell you about how shear force varies at the cut section as a load moved on the beam?
The experimental result increases with the increasing of the distance of load from the left hand support at the left side of the cut. Based on the result, the values of shear force at cut section (N) increases when a load moves nearer towards the cut.
4. Comment on the experimental result compared to the theoretical result.
Based on the results 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 the value for both results is not so much differences.
8.0 CONCLUSION
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 nearer towards the cut.
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.
