The strut test is a method used to determine the critical Euler’s buckling load of a strut. Struts are long, slender columns that are prone to fail by buckling before reaching the yield stress in compression. The Euler’s buckling load is a crucial value that indicates the point at which the strut suddenly bends to one side and buckles. At this point, the compressive stress at the point of failure may be lower than the ultimate compressive strength due to the buckling of the strut.
The buckling of the strut occurs due to various factors such as imperfections in the straightness of the strut, non-aligned applied loads, and lack of uniformity in material properties. To determine the Euler’s buckling load of a strut, a strut testing apparatus is utilized. The apparatus is designed to carry out tests on struts of different lengths with either hinged or fixed ends. Through this testing process, the critical Euler’s buckling load of the strut can be accurately determined.
Theory and Principle
When columns are very long, they are prone to failure due to bending. To calculate the crippling load for long columns, Euler’s relations are used. These relations provide the maximum load that a column can withstand without buckling or collapsing under various end conditions.
The Euler’s relations take into account the modulus of elasticity of the material, which is a measure of its stiffness. For most materials, the modulus of elasticity is around 2.1 x 10^5 N/mm2.
The relations also factor in the moment of inertia of the cross section of the strut. The moment of inertia is a measure of how resistant the cross section is to bending. The greater the moment of inertia, the greater the resistance to bending.
Finally, the effective length of the strut is considered. The effective length is determined by the end conditions of the strut. For example, if both ends are hinged, the effective length is equal to the total length of the strut (L). If the ends are fixed, the effective length is 0.5L. If one end is fixed and the other end is hinged, the effective length is L/(2)^0.5. And if one end is fixed and the other end is free, the effective length is 2L.
Equipment
Strut Testing Apparatus is a device used to test the load-bearing capacity of struts. It helps to determine the maximum force that a strut can withstand before buckling or collapsing. This equipment is commonly used in construction and engineering projects to ensure the safety and reliability of structures.
On the other hand, Venire Caliper Scale is a measuring tool used to measure the distance between two opposite sides of an object. It is commonly used in metalworking, machining, and woodworking applications, as well as in scientific research and education. This tool is designed to provide precise and accurate measurements, making it useful in a wide range of fields.
Strut Test Procedure
To begin the process, the strut needs to be cleaned with sandpaper. Once this is done, the rope slide should be adjusted to fit the length of the strut, and the strut should be placed between the top and bottom adapters. If the tests involve a hinged end, two balls should be used and tightened to ensure that the end is fixed properly.
The next step involves moving the side sliding block so that the micrometer strut is approximately in the middle of the strut’s length, and then firmly clamping it in place. The micrometer sliding holder should then be adjusted so that the micrometer is positioned precisely at the midpoint of the strut.
To load the strut, the weight hanger should be placed over the top socket to ensure that the loading is purely axial. The switch should then be turned on, so that the indicator lamp will glow whenever the micrometer touches the strut.
To determine the direction of curvature of the strut and the amount of initial curvature, the strut needs to be carefully rotated with fingers through one revolution, noting the maximum and minimum readings of the micrometer. The strut should be placed such that the initial curvature is away from the micrometer side. The initial reading of the micrometer should be determined with the initial curvature away from the micrometer.
Weights should then be added in steps of one kilogram to both sides of the hanger, so that the strut bends in the direction away from the micrometer. It is important not to rotate the strut while adding loads, as the curvature must remain pointing in the same direction throughout the process. The difference between the two readings gives the actual deflection due to the weights that have been added.
Graphs
Plot a graph of load (P) versus the total deflection of the strut when a particular load is applied (Delta).
Calculation
Euler’s formula can be used to calculate the buckling load of a strut. This formula relates the critical buckling load of a slender strut to its material properties, geometry, and boundary conditions. The equation can be expressed as:
$F_{cr} = frac{pi^2 EI}{(KL)^2}$
Where $F_{cr}$ is the critical buckling load, $E$ is the modulus of elasticity of the material, $I$ is the second moment of area of the cross-section of the strut, $K$ is the effective length factor, and $L$ is the actual length of the strut.
This formula is important for engineers and designers because it helps them determine the maximum compressive load that a strut can withstand before buckling under the applied load. Buckling is a failure mode that occurs when a slender member undergoes a sudden, unstable deformation due to compressive stress. By using Euler’s formula, engineers can ensure that their designs are safe and can withstand the expected loads.
Results
- Euler’s formula states that for any polyhedron (a 3D shape with flat faces), the number of vertices (points where the faces meet), minus the number of edges (the lines where the faces meet), plus the number of faces, is always equal to 2. In mathematical terms, this is written as V – E + F = 2, where V is the number of vertices, E is the number of edges, and F is the number of faces. This formula has been proven to hold true for all convex polyhedra, and is an important result in geometry.
- In scientific experiments, researchers often collect data and measure various quantities in order to test their hypotheses or answer research questions. These measured values are known as experimental values. Depending on the experiment, different types of data may be collected, such as numerical measurements, counts, or observations of certain phenomena. The accuracy and precision of experimental values are important factors in determining the validity of the results and the conclusions that can be drawn from them.
Rewritten:
- Euler’s formula provides a mathematical relationship between the number of vertices, edges, and faces in any polyhedron. It states that the sum of vertices minus the sum of edges plus the sum of faces equals 2. This formula has been proven to be true for all convex polyhedra and is an important discovery in geometry.
- In scientific experiments, researchers gather data to test their hypotheses or answer research questions. These measured values are called experimental values, and they can take the form of numerical measurements, counts, or observations of phenomena. The accuracy and precision of these values are crucial in determining the reliability of the experiment’s results and the validity of any conclusions drawn from them.