The formula to calculate Buckling load is given by, Where, E – Young Modulus, – Area Moment of Inertia, Lee – Effective length of the column, which depends on the boundary conditions. For Pinned-Pinned condition, Lee = L For Fixed- Pinned condition, Lee 0. AL For Fixed-Fixed condition, Lee = 0. 51 Where, L- Length of the column In this experiment an attempt is made to calculate Critical Buckling Load of a column experimentally and theoretically with different boundary conditions. These values will then be compared. Equipment and Procedure Equipment 1.
Column Buckling Machine 2. Test Specimen: Three Metal Beams. In this experiment, steel beams of known length were used. The modulus of elasticity for the material tested was predefined. The thickness and width of the beams were found to be mm and mm respectively 3. Calipers and Load Cells: Calipers are used to measure the width and thickness of the specimen. And Load cells measures the force. Experiment Setup The specimen should be secured on the column buckling machine with each end of the specimen being supported per case requirements.
Procedure Load is gradually applied by twisting the knob present in the machine, till the column starts to buckle. The load cells display the load which is noted down when buckling starts. This procedure is repeated for different lengths. Then the noonday conditions are changed and the experiment is set up as required and this procedure is repeated. Effective lengths are calculated and from that the theoretical values are derived. The error is calculated and tabulated. Calculations The experimental values were recorded in the Tabular Column. The theoretical values are calculated using (1).
This is because critical buckling load is inversely proportional to the square of the length of the column. Conclusion Although there were errors in the outcome of the experiment, the values were fairly acceptable. The accuracy depends on the clamping of the machine and the level of calibration of the machine. The values also depend on condition of the test samples. The test samples were used a lot of times and were slightly deformed even before the conduction of the experiment. References Advanced Mechanics of Materials – Arthur P Borers and Richard J Schmidt, Sixth edition 2003, John Wiley and sons.
Experiment – 2 : Deflection in Curved Beams Introduction: Curved beams are those beams in which the radius of curvature is large compared to the dimensions of the cross section. When a load is applied to the beam, one component of the force gets cancelled while the other gets added. This creates a difference from the straight beams and the analysis is tougher. The objective of this experiment is to calculate the deflection in the beams in 2 conditions. 1. Semi-Circle beam 2. Quarter Circle beam Equipment and Procedure Apparatus 1. Test Frame 2.
A pair of dial indicators – These are used to measure the deflections in the Horizontal and Vertical directions 3. Two test structures – A semi circular beam and a quarter circular beam of radii mm and mm respectively were used as test specimens 4. Weight set – These weights (ION, NON, NON) acted as applied dads on the beams 5. Fernier caliper 1 . The width and thickness of the test specimen are measured using the fernier caliper and the second moment of inertia is calculated from this. 2. The specimen is mounted and clamped onto the test frame. . The dials are mounted onto the test frame, vertically and horizontally. They are then adjusted according to the specimen such that they are just in contact with them 4. The beam is loaded by adding weights to the hanger. The frame is tapped so as to reduce the spring lag. 5 The readings are recorded in both directions. . Loads are added to the beam and readings are tabulated (Loading condition). 7. Readings are also taken when the loads are removed one after the other. (Unloading condition) 8. This procedure is conducted on both beams.