Buckling test of a column
ID:
20106272
Name: Liu Shiming
1. Objective This experiment aims to observe the buckling phenomenon, and study the critical load and other factors having influence on structure stability. 2. Method (1) The experimental devices shall be installed like the illustration in Fig 1. The data that will be obtained in the experiment are load, longitudinal displacement and transverse displacement at the middle of the column, namely the deflection.
(2) When experiment preparation is completed, the conditions of system shall be checked by imposing a bit of load, and then the load shall be eliminated. (3) Putting load again, we will observe the relationship between the load and deflaction. At this time, we need to record the load and displacement value in every direction on a work sheet, after increasing the load as much as ?p(? 50 N ) . (4) After observing the critical load approximately, we will continuously observe and record the deflection as the load is surpassing the critical load.
(5) Making use of the aquired data, we will calculate the bucking stress after drawing a Southwell plot. (6) We need to repeatedly carry out the process mentioned above concerning with the columns on which the 1.5mm of eccentric load is imposed.
3. Results
(1) Theoretical value Column dimensions: Length: Diameter: Material proporties: Young’s Modulus: E ? 69GPa Proportional limit: ? pl ? 276MPa Computation of slenderness ratio of the specimen:
l ? 250mm
d ? 5mm
L ? 2E ( )c ? ? 49.673 r ? pl
Critical limit:
Pcr ?
? 2 EI
( Kl ) 2
?
? 2E
4 ? 1.337 KN , A ? ? d ? 1.9634 ?10?5 m2 4 (0.5 ? l ) 2
2
? r4
? cr ?
Pcr ? 68.096MPa A
(2) Experimental value Figure 2 shows the relationship between the load and the deflection. Figure shows the figure of
W ? AW ? B . From which we can find that: P
A?
1 Z ? ?0.9174( KN ?1 ) , B ? ? ?0.0368(mm * KN ?1 ) (Z: eccentricity) Pcr1 Pcr 2
? Pcr ? ?1.09004( KN ), _ Z ? 0.0401(mm) , ? cr ?
Pcr ? 55.518MPa A
4. Discuss
(一) Theoretical value of buckling load: Experimental value of buckling load:
( Pcr )theo ? 1.337 KN
( Pcr )ex ? 1.09004( KN)
??
( Pcr )ex ? ( Pcr )theo ? ?0.1847 ( Pcr )theo
The difference between the theotetical value and the experimental value is a bit big in some aspect. The experimental value is smaller than the theoretical value. (二) innertial deffects and the influence of eccentricity: The theoretical value is expected when the eccentrcity is zero. But the eccentricity exists at any experiment. The bigger the eccentricity is, the easier the column is going to perform a buckling, and the buckling stress is smaller. So the experiment value is smaller than the theoretical value.
References:
(1) http://en.wikipedia.org/wiki/Buckling (2)MAE309 Aerospace Engineering Laboratory Ⅱ (3) Top lateral bracing of steel U-shaped griders