Buckling of Struts Lab report PDF

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Buckling of Struts Lab report Buckling of Struts Lab report...

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Nathan Golsby-Taylor

University of Salford School of Science, Engineering and Environment Aircraft Structures/Structural Mechanics E2

Structural Mechanics Buckling of Struts Group 7

By Nathan Golsby-Taylor @00559936

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Nathan Golsby-Taylor

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Context Summary Introduction Theory and Equations Apparatus Procedures Measurements, Analysis and Calculations Conclusion Discussion References

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Summary In this laboratory we are testing the buckling of struts when a load is applied We use a dial gauge on the beams to measure the deflection when the Load (N) is added. We first calculate the dimensions of the struts that we tested, breath and depth, as we will use the averages in the calculations after the results have been taken. The tests are carried out on two beams we measured the deflection. We use the results to plot a graph and calculate the gradient, this is called the experimental data. The theoretical data is calculated using equation 1 shown below. The results will be shown in theoretical and experimental results. These results when the be used together to calculate if there is an error between them and in the discussion I will talk about why there is an error if there is one.

Introduction The objective of this laboratory is to measure the buckling load of two struts. using pinnedpinned condition, and compare with the theory. Being able to calculate the buckling of struts is important because buckling is a major cause of failure in structures and it mostly occurs in slender columns. Buckling of a strut is caused by the failure whilst its being compressed due to the material strength and stiffness properties. Buckling of a strut is when a sudden change in the shape of a structural component happens when a load is applied. An example of this is when a column bows under compression. The purpose of this experiment is to analyse the performance of these two beams of columns under compressive load. The goal is to assess the correlations between experimental data and the theoretical model, determining accuracy of the measurements and evaluating the effects of variable loading profiles on lateral deflections. Compressive loads are present in several civil engineering applications, an example of this is when a load bearing wall at ground floor level is removed, a steel beam is required to support the ceiling joists, non-load bearing timber stud partitions, first floor joists and brick wall above the proposed opening in the wall.

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Theory and Equations Buckling is caused by the result of imperfections in a strut that prevents the load from being applied perfectly axially. The combined effects of these imperfections on overall buckling behaviour is predictable when long struts are to operate under elastic conditions. There are many ways that a strut could buckle in, this is shown below in figure 1.

Figure 1:

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Different shape struts buckle in different ways, if a strut is long and thin when they are subjected to a compressive load they can become unstable and buckle which is shown in figure 6 above. However if a short and thick strut fails it will most likely fracture and become unstable.

When a strut is loaded and reaches over its maximum load the strut will start to deflect sideways by small amounts. When a certain critical value, Pcr is reached, the strut becomes unstable and buckles in an almost instantly. Euler theory predicts the axial compressive force required to initiate the bucking of a long and thin strut. The combined effects of these imperfections on overall buckling behaviour is predictable when long struts are to operate under elastic conditions. Using Euler’s theory the value of Pcr, depends on the length, Young’s Modulus, second moment of area and pined-pined conditions of the strut. For pinedpined end conditions, the critical Euler buckling load may be written in the forms,

Eq. 1 Where, L = Length (between end conditions) I = Second moment of area = bt3/12 for a rectangular cross section E = Young’s Modulus (200 kN/mm2 in this case) Also, the critical axial buckling stress in the strut may be written in the form: �

Eq. 2 5

Nathan Golsby-Taylor Where, A = Cross sectional area Many engineering structures consist of long slender members, o en called struts or columns, subjected to compressive lo

Apparatus:   

Two rectangular steel struts, Beam A Length 744mm and Beam B Length 694mm Both beams have a Young’s Modulus of 200 kN/mm2 Buckling testing rig this includes hydraulic actuator which applies the load, load cell that measures the applied load, P and a dial gauge to measure deflection, δ

Figure 2: Buckling test rig

Figure 3: Digital Gauge and Strut

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Figure 4: Hydraulic Actuator control knob

Figure 5: Actuator, Load cell and dial

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Figure 6: Vernier scale

Procedures We start the laboratory by measuring the width (b) and thickness (t) on the two struts. We do this using a vernier scale showed above in FIGURE…, this is done three times and different spots on the strut then an average is calculated. The length (L) is measured using a ruler. The length for beam A is 744mm and the length for beam B is 694 

The strut will then be fitted into the testing rig using the pin-pin configuration

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Using the hydraulic actuator, a pre load of 25N will be applied and the dial gauge will be set to zero

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Nathan Golsby-Taylor 

After the pre-load is applied, apply the load P incrementally and measure deflection δ, at midpoint of the strut using the dial gauge, this equipment is shown above in FIGURE....

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Once each load has been applied and deflection/load (δ/P) has been calculated plot the graph of Deflection δ, against deflection/load δ/P, and determine the gradient.

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This gradient should predict the Euler collapse load, which is also called the critical buckling load (Pcr).

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Determine the theoretical critical buckling, Pcr, using equation 1

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Compare the theoretical and experimental results for Pcr.

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Determine the experimental and theoretical critical axial stress, σcr using equation 2

Measurements, Analysis and Calculations Beam A

Beam B

Load, P

Deflection δ

δ/P

Load, P

Deflection δ

(N)

(mm)

(mm/N)

(N)

(mm)

25 50 75 100 125 150 175 180 190

0 0.29 0.7 1.5 2.8 5 9.8 10 15.1

0 0.0058 0.0093 0.015 0.0224 0.033 0.056 0.056 0.079

25 50 75 100 125 150 175 200

(mm)

Breadth

9

0 0.1 0.2 0.7 1.8 2.7 4.6 7.4

(mm)

δ/P 0 0.002 0.0027 0.007 0.014 0.018 0.026 0.037

Nathan Golsby-Taylor Breadth b1 b2 b3 bav Thickness t1 t2 t3 tav

A (mm2) I (mm2)

20.15 20.12 20.18 20.13

b1 b2 b3 bav

(mm)

Thickness t1

3.02 3.2 3.12 3.08

t2 t3 tav

62 49.01

A (mm2) I (mm2)

Experimental Data Calculations

Beam A

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20.09 20.01 20.02 20.04 (mm) 3.12 3.05 3.07 3.08

61.72 48.79

Nathan Golsby-Taylor Beam B

Theoretical Calculated results Beam A

Beam B

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Graphs

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Nathan Golsby-Taylor Calculations to find the error between the experimental data and the theoretical data.

Calculations using Equation 2

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Nathan Golsby-Taylor Summary of Results

Theo.

Pcr (N) Difference ( .) x 100 (%) Experimental Theoretical

Strut A (Length 744mm) 187.76

174.77

7.43%

Strut B (Length 694mm) 228.57

199.96

14.31%

Student Name: Nathan Golsby-Taylor

Group Number: 7

Discussion In this laboratory we tested the deflection of a strut when a load is applied. The lengths of the beams where measured with strut A being 744mm and strut B being 649mm long. From the results gained we drew a graph of Deflection δ, against deflection/load δ/P, this was used to calculate the gradient, which is the experimental data. The experimental data for strut A is 187.76 and for strut B it is 228.57. The theoretical data was calculated using equation 2. The theoretical data for strut A is 174.77 and for strut B it is 199.96. The data that was calculated for strut A and strut B where compared together and where used to calculate the difference between then to see what the error is between using the experimental or the theoretical data. For strut A there was a 7.43% error and for strut B there was a 14.31% error. The error has occurred due to the fact the experimental data was gained from a graph being plotted and from the results then a line of best fit was hand drawn onto the graph. This error will be down to human error and calculating a the gradient from choosing four points. However even though there is an error I am not concerned as the error is not too high and is under 15%, this leads me to believe that the results calculated is infract correct. Conclusion In conclusion the values of the deflection of Beams A and Beam B worked out from this laboratory are presented in the tables bellow and graphs above I will use these to discuss and compare the experimental and theoretical results. Both strut A and strut B faced an error percentage of 7.43% and 14.31% respectively this will have been caused by human error with plotting the graph as the points were very small, for example on strut A the second point was plotted at 0.29 and 0.0058, as the numbers are so small mistakes are easily make. This laboratory experiment shows the that the longer strut will buckle sooner the a shorter strut. This is backed up by the amount of weight (N) the beams could hold before they buckled.

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References

Gangamwar, Y., Deo, V., Chate, S. and Bhandare, M., 2016. [online] Ijrest.net. Available at: [Accessed 2 January 2021]. n.d. [online] Available at: [Accessed 5 January 2021].

Courses.washington.edu. n.d. [online] Available at:

[Accessed 5 January 2021]. Ghuku, S. and Nath Saha, K., 2017. [online] Scipress.com. Available at: [Accessed 6 January 2021]. Eis.hu.edu.jo. n.d. [online] Available at: [Accessed 7 January 2021].

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