Slender Column Test for Different End Condition || Strength of Materials Lab || Power Lab

"Determination of Slender Column Test" OBJECTIVES: a. To find the critical load of slender columns for different end conditions. b. Compare the .experimental critical load with that given by the Euler's equation. THEORY Column is a compression member that is very slender compared to its length. Under compressive load column fails by buckling. Buckling loads are considerably less than those required to cause failure •by crushing. A compression member is generally considered to be a column when its unsupported length is more than 10 times its least lateral dimension. Columns may be subdivided into three groups — long, intermediate and short compression block. Long columns fail by buckling or excessive lateral bending; intermediate columns by a combination of buckling and crushing; short compression blacks by crushing. Theoretically, a slender column is a perfectly straight, homogeneous slender member having its ends held against movement in certain directions. Actual columns will always have small imperfections of material and fabrication as well as unavoidable accidental eccentricities of load. The initial crookedness of the column together with the placement of the load causes an indeterminate eccentricity of e with respect to the centroid of a typical section m-n. The resultant stress is due to a combination of a direct compressive and a flexural stress. For this reason, slender columns under axial load will have a tendency to buckle or bend. The load which is just sufficient to hold the column in a bent condition is called the critical load or buckling load for the column. It is also the greatest load the column will support. In the above expression P = Axial load A = Cross-sectional area of the column Le = Effective length of the column, depends on the loading condition K = Least radius of gyration E = Modulus of elasticity of column material The ration (L0/k) is called the slenderness ratio of the column. For circular cross-section, k = d divided by 4 where d is the diameter of the column. For mild steel that has a proportional limit of about 200 MPa and E = 200 GPa, it has limiting slenderness ratio. Apparatus: 1. Dead weight column testing apparatus. 2. grips for different end conditions. 3. Slide calipers . 4. Steel tape etc. DIFFERENT LOADING CONDITIONS: a. Both ends hinged. b. Both ends fixed. c. One end fixed, other end free. d. One end fixed, other end hinged. DISCUSSIONS: Discuss on the following points a. Shape/pattern of the graphs. b. Reasons if there is difference between the experimental and theoretical critical/buckling loads c. Effect of the test speed of the testing machine d. Effect of imperfection in the column e. Reasons of the imperfection of the column f. The placement of the column in the testing machine. g. The effect of slenderness ratio. h. The effect of end condition on the critical loads of the columns. i. How to improve the testing procedure j. How to improve the critical load or buckling load. k. Limitations of Euler& formula