Table of Contents LIST OF FIGURES and CHARTS 1 EXPERIMENT 1: INFLUENCE LINE FOR DEFLECTION 2 1.1. INTORDUCTION 2 1.2. OBJECTIVES 2 1.3. EQUIPMENT NEEDED 2 1.4. PROCEDURE 3 1.5. RESULTS 4 1.6. ANALYSIS OF THE RESULTS 4 1.7. DISCUSSION 6 1.8. CONCLUSION 7 1.9. REFERENCES 7

LIST OF FIGURES and CHARTS

Figure 1: Force diagram for influence line of deflection
Figure 2: Set-up for influence line of deflection
Chart 1: Deflection curves (0 N, 5 N, 10 N)
Chart 2: Deflection curves (15 N, 20 N, 25 N)

EXPERIMENT 1: INFLUENCE LINE FOR DEFLECTION

1.1. INTORDUCTION
Structural members subjected to a system of stationary loads are easily to analysis and determine completely the maximum design loads, deflection and rotation at supports of the member. However, in some members, such as bridge girders and crane gantry, which are subjected to moving loads, it is not easy to analyse since the maximum design loads and deflections depends on the position of the applied load(s) with time. An analytical procedure which deals specifically with the determination of the location of the moving load that will produce the design loads of the highest magnitude in the members was reached by using influence lines.
Influence line can be defined as a graphical representation of the variation of internal member force or deflection in a fixed member section due to a unit load moving along or traversing a member of a given structural. It may also be defined as a response function of support reaction, axial force, shear force, bending moment or deflection. A deflection influence line is an influence line which only shows the relationship between the deflection of a point on the member, usually a beam, and the position of the unit load on the member. The actual deflection is found by superposition principle after multiplying the ordinate of the influence line by the magnitude of the load.
For statically determinate structures, the influence lines are always piecewise linear while the influence line for statically indeterminate structure are always curvilinear, depending on the nature of the applied load.
In this experiment, the influence line of statically determinate structure, that is, a simply supported beam was investigated. 1.2. OBJECTIVES * To show how to plot influence lines * To show how to use influence lines to predict deflection for any given load(s) 1.3. EQUIPMENT NEEDED * Two load cells * Digital indicator * A weight hanger * A set of weights * One beam 1.4. PROCEDURE
Table 1 for recording the results was first created before anything else was done.
The overall length (L) of the beam was measured and a pencil used to mark it at the mid-span and equal distances (l/2) from the mid-point. The thickness and width of the beam were also measured. A suitable reading near the middle of the upper scale of the apparatus was chosen to match to the mid-span of the beam. Beam and two load cells were set up so that the load cells were at the pencil mark, with the mid-span of the beam being directly under the chosen scale reading and making sure that the load cells locking pins were fitted. The arrangement was such that the beam had an overhang on both ends.
After setting up the beam, deflection indicator was used above each support to ensure that the beam was horizontal. Adjustments were made where necessary to level the beam. Deflection indicator was then moved to a known distance, a = 200 mm, then a weight hanged to the beam at a known distance, b = 450 mm. Before any reading was taken, it was checked that the stem of the digital indicator was vertical and there was enough travel in the downward direction. The deflection indicator was then zeroed.
5 N increment of load was added. Each time the load was added, the apparatus was tapped very gently and deflection readings taken. The procedure was repeated by reducing the distance b by 50 mm until the deflection indicator was passed by 100 mm. The results were recorded in table 1.

Figure 1: Force diagram for influence line of deflection

Figure 2: Set-up for influence line of deflection 1.5. RESULTS b (mm) | 450 | 400 | 350 | 300 | 250 | 200 | 150 | 100 | 50 | 0 | -50 | -100 | W (N) | z | z | z | z | z | z | z | z | z | z | z | z | 0 | -0.11 | -0.16 | -0.21 | -0.25 | -0.28 | -0.31 | -0.31 | -0.33 | -0.30 | -0.31 | -1.38 | -1.35 | 5 | -0.24 | -0.61 | -0.76 | -0.88 | -1.03 | -1.10 | -1.15 | -1.10 | -1.02 | -0.98 | -1.85 | -1.60 | 10 | -0.69 | -1.04 | -1.31 | -1.55 | -1.77 | -1.90 | -1.95 | -1.89 | -1.74 | -1.64 | -2.30 | -1.88 | 15 | -1.00 | -1.47 | -1.86 | -2.20 | -2.50 | -2.67 | -2.74 | -2.66 | -2.46 | -2.27 | -2.76 | -2.12 | 20 | -1.31 | -1.90 | -2.40 | -2.86 | -3.23 | -3.45 | -3.55 | -3.43 | -3.15 | -2.94 | -3.21 | -2.38 | 25 | -1.60 | -2.34 | -2.96 | -3.50 | -3.94 | -4.23 | -4.34 | -4.20 | -3.88 | -3.62 | -3.66 | -2.63 | k | -0.30 | -0.44 | -0.55 | -0.65 | -0.73 | -0.75 | -0.81 | -0.77 | -0.72 | -0.66 | -0.46 | -0.26 |
Table 1 1.6. ANALYSIS OF THE RESULTS
The mean deflection for a unit load of 1 N at that position, k, was calculated for each column of the result. This was done by:
Finding the difference in z for each of 5 N additional load. The differences in z were then summed and divided by 5 to find the average.
A plot of deflection values as curves for each load was made in a chart of z (vertical axis) against b (horizontal axis). The chart below:

The k values obtained in table 1 and chart 1 can be used to predict the total deflection for any given load(s) of 5 N divisions. This could be done by choosing a suitable curve on chart 1 then scaling the k value at each point by that given. Illustration Using curve W = 5 N to predict the total deflection for a theoretical load of 10 N at positions 250 mm and 450 mm. At position 250 mm: scaling factor=105=2 at this position, k=0.55 scaling it, z=2×0.55=1.10 mm At position 450 mm: scaling factor=105=2 at this position, k=0.24 scaling it, z=2×0.24=0.48 mm total deflection=1.10+0.48=1.58 mm 1.7. DISCUSSION

it can be seen throughout this investigation that the influence line of a simply supported beam can be easily simulated in the laboratory. This is particularly important especially to the design of costly bridges which requires high accuracy and precision in design and construction. The structures of such kinds are always modelled in the laboratory where their structural properties and behaviours are predicted before the real structure is put in place. To successfully do this, not only the influence line based on deflection should be investigated, but also other moving-load related parameters such as bending moment, shear forces and axial force should also be put in to consideration.
The variation of the deflection of a beam with load was established. Both the theoretical and experimental deflection of the beam were determined and the theoretical values were found to follow the relationship established through the experiment. Once the mean deflection for a unit load of 1 N was obtained, to deflection of any other would be quite easy since it would just involve simple arithmetic of multiplication, as long as the load was divisible by the experimental load increment. Important to mention is the theoretical concept that the deflection of a beam is greatest at the position of the moving load, and changes with point of the moving load was also proved in this experiment.

1.8. CONCLUSION

The experiment was successfully done. Of the experimental objectives, that is: learning how to plot influence lines, and using the plotted influence lines to predict deflection for any given load(s) was successfully achieved. It is thus, very important for engineers to equip themselves with all influence lines techniques since they are very important when it comes to the design of structures that will carry moving loads, for example bridges and cranes.

1.9. REFERENCES

* Structural Analysis 1 (BE 1311),Laboratory Handbook, 2015 - 2016 * Hibbeler, R. C. (2002). Structural Analysis, Pearson Education (Singapore) Pte. Ltd., Delhi, ISBN 81-7808-750-2 * Leet, K. M. and Uang, C-M. (2003). Fundamentals of Structural Analysis, Tata McGraw-Hill Publishing Company Limited, New Delhi, ISBN 0-07-058208-4