Buckling Case

Summary

This experiment divided into 4 experiments; 1.Deflection of a Cantilever, 2.Deflection of a Simply Supported Beam, 3.The Shape of a Deflected Beam, 4.Circular Bending. This first experiment was done to understand and to investigate the principles; the deflection of a cantilever subjected to an increasing point load by applying different length materials: Aluminium, steel for the relationship between the deflection and the length of the beam. The experiment 2 was done not only to examine the deflection of a simply supported beam subjected to an increasing point load but also to observe the relationship between the deflection and the length of the beam. The experiment 3 was done to examine how the deflection of a load beam can be varied with span. The experiment was done by applying loads to a simply supported beam at its end to induce a moment and thus produce circular bending as well establish an important relationship and measure Young's modulus.

All of the theoretical values are closer to the actual values. In the 2 experiment

Objectives

The aim of this experiment is to investigate the principles; the effect of the strut length via various load struts, the correlated relationship between the buckling load and the different length of the struts. This experiment is also to compare the experiment values to those calculated by Euler formula and to demonstrate the prediction of the bucking loads by Euler formula

Theory

Unlike a tension member which will generally only fail if the ultimate tensile stress is exceeded, a compressive member can fail in two ways. The first is via rupture due to the direct stress, and the second is by an elastic mode of failure called Buckling. Generally, short wide compressive members that tend to fail by the material crushing are called columns. Long thin compressive members that tend to fail by buckling are called struts. When buckling occurs the strut will no longer carry any more loads it will simply continue to displace i.e. its stiffness then becomes zero and it is useless as a structural member.

In order to predict the buckling load, Euler buckling formulae is applied. Critical to the application of the Euler formulae is the slenderness ratio, which is the ratio of the length of the strut to its radius gyration (l/k). The Euler formulae become inaccurate for struts with a l/k ratio of less than 125 and this should be taken into account in any design work. The struts provided have an l/k ratio of between 520 and 870 to show clearly the buckling load and the deflected shape of the struts. In practice struts with an l/k ratio of more than 200 are of little use in real structures

This Euler buckling formula is used for a pinned strut.

Pe= Euler buckling load (N);

E = Young's modulus (Nm-1); the aluminum of which = 69GPA

I = Second moment of area (m4);

L = Length of strut (m).

Apparatus

The experimental structures frame

 5 different chucks

 Vernier

 Tools

 Lead to connect to Digital force display (STR1a)

Procedure

1. Fix the bottom chuck to the machine and remove the top chuck (figure 1.3) to give 2 pinned ends.

2. Select the a strut, number 1, and measure the cross section using venire provided and calculated the second moment of area, I, for the strut.

3. Adjust the position of the sliding crosshead to accept the strut using the thumbnuts to lock off the slider.

4. Make sure that there is the maximum amount of travel available on the hand-wheel thread to compress the struts.

5. Tighten the locking screws.

6. Carefully back off the hand-wheel so that the strut is resting in the notch but not transmitting any load.

7. Make the force-meter zero by using the front panel control.

8. Carefully start to load the strut.

9. Turn the hand-wheel until there is no further increase in load.

10. Record the final load from the force-meter.

11. Turn the hand-wheel to loosen the crosshead take of the strut.

12. Take the same strut, and repeat the procedures from 3-11 for 2 times and record three different values for each experiment and calculate the mean of the strut.

13. Write the average value down in the table 5.1 under 'buckling load'.

14. Take another strut, and repeat the procedures from 2-13, and get 5 sorts of data.

15. Using the Euler formula calculates the theoretical values of buckling load.

16. Draw a graph with the theoretical buckling lead and the reciprocal of the length of the struts.

17. Compare the experimental value to those calculated from the Euler formula by entering a theoretical line onto the graph.

Results and Calculations

Strut number Length (mm) Buckling Load (N)

1 320 -85

2 370 -64

3 420 -51

4 470 -41

5 520 -29

Second moment of the area, I, can be obtained by measuring the length and wide of the struts, and use the formula:

Strut number Length (b) (mm) Wide (h)

(mm) I (mm4)

(2 decimal places)

1 19.8 2 13.2

2 19.9 2 13.26