Experiment 3

Four Point Bending
Student’s name
Institutional affiliation

Abstract
Bending of beams refers to a situation which involves loading. A slim member which is subjected to loads which are traverse is known as a structural member which is undergoing bending. The loads which are traverse produce bending moment and shear at any given cross-sectional area in order to keep the beam in equilibrium. First yield criterion is one of the common principle which is normally used to establish the loading capacity of the beam. In essence, the principle stipulates that the beam attains the maximum load when the stress approaches the yield stress. However, for beams that sustain the static load, the first yield criterion rule does not apply. In this case, the use of the rule is disregarded unlike in other beams which do not have a static load.
The main aim of the experiment is to relate strain quantities found from electrical and mechanical strain gage with the quantities in the theoretical strains. The experiment also tries to establish the neutral axis location of the cross section of the beam then compare it with the theoretical measurement which was predicted previously. Moreover, examining the validity in the assumption which was taken during the experiment that the cross sections would remain plane all through the experiment period is one of the factors to be determined. Along a similar line, comparing the deflections values obtained experimentally with the predicted deflections is one of the areas where the scope of the experiment will discuss.

Introduction
Beam Flexure is one of the common loading classes found in mechanical systems. The experiment in consideration revolves around four points bending (FPB).The beam deflection is an important element that develops the (FPB) from free body diagrams. One can easily analyze, verify and validate the concept of beam flexure in the laboratory. In this case experimentally; one can obtain the correct connection that exists between the values obtain experimentally, and the values obtained theoretically. The four point bending enables one to determine various properties of the material such as the defections at various points, young are modulus and tensile strengths of the material. The use of the electrical and mechanical gauges improves the accuracy of the data to be generated in the experiment.
Discussion
The calculated values prove to be lower than the measured values in the experiment. In particular, the theoretical analysis methods limit the accuracy of the experiment in that it understates the actual deflection of the beam. The errors in and reading and recording the values from the experiment limit the use of theoretical equations and formulas hence, the calculated values are found to be slightly different from the theoretically predicted values. The electrical gaging machine was found to be the best in examining the beam deflection as compared to mechanical gaging. The factors to consider before choosing the type of gauge to be used include the length, resistance, material adaptability and the protection method of the gauge. The other factor that is considered when selecting a type gage is the geometry of the gage.
Neutral axis describes the axis located in a cross section side of a beam resisting bending. Neutral axis refers also to the shaft in which longitudinal stresses nor strains passes through it. In case the section of the beam is symmetric and isotropic the neutral axis is located at the geometric centroid. All the fibers located on one of the neutral axes are under compression while the fibers on the other side are under tension. In structural beams such as steel, aluminum, and plastic which are shaped like I and an H-beam, or a pipe, the neutral axis will be located along the centerline. The determination and calculation of the centroids and moment of inertia of a beam has a great impact in the determination of the neutral axis.
The values of the theoretical deflections are found to be higher than the calculated values. The theoretical formulas and equations which are applied in determining the deflections understate the values of the deflections hence the method is not conservative.
The data generated from the graphs indicates that the beam obeys Hooke’s law. Hence, the beam linearly elastic hence it does not undergo plastic deformation. Before the start of the experiment, the material is straight, and it has a cross section which is constant over its entire distance. The structural member has the axis of symmetry which acts along the plane of bending. Since the beam is homogenous, isotropic, obeys Hooke’s law and its cross-sectional area is constant over its length then it shows that the plane sections will remain plane after bending.
Conclusion
The objective of the experiment was achieved in that the comparison of strain prediction and strain measurements was made. A table which compares the values obtained was drawn, and the values were analyzed against each other. Secondly, the values of the neutral axis were determined, and its value was compared with the predicted value. Thirdly, the validity of the assumption that cross section would remain plane throughout the experiment was examined. Additionally, the experimental and predicted values of deflections were compared in detail. As a result of the analysis done in the experiment, the experiment was successful.