A bending moment is simply defined as “the algebraic sum of the moments of all the forces which induces bending of an element” (1).
The aim of this assignment is to work out the bending moment in a simply supported beam when different concentrated loads are applied to it. A simply supported beam is a structure, usually with a straight profile supported at the ends, often pinned on one side and simply supported or on a roller on the other. There will be three series of loads applied to this beam & the findings will be recorded. The results will then be compared with the theoretical bending moment & the reasons for any variation explained.
The main reason for the experiment to be conducted is to examine, not only the accuracy of the testing equipment, but also the accuracy of bending moment calculations and diagrams compared to a real-world assessment. It will hopefully prove that “the bending moment at a cut section is equal to the algebraic sum of the moments acting to the left or right of the section”. (2) After this introduction, there will be a little background information about this experiment and its apparatus, followed by a breakdown of the experimental procedure.
Then, there will be the displayed results before a comparison with the theoretical results that have been calculated. Finally, while the conclusions are made, I will attempt to explain the reasons for any discrepancy and state how I would improve the process. (1)The Science Dictionary (2012) http://thesciencedictionary. org/bending-moment/#ixzz2uKaWzF9e (Accessed: 26/02/14) (2)Momade, H (2011) Shear Force, Bending Moment, Deflection in beams & Strut Apparatus Test http://www. academia. edu/3671106/shear_forc e_bending_moment_deflection_beams_strut_apparatus_test (Accessed: 27/02/14) Background/Theory
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A beam with a constant height and width is said to be prismatic. When a beam’s width or height (more common) varies, the member is said to be non-prismatic. Horizontal applications of beams are typically at resists the rotation. TYPES OF LOADS AND BEAMS Beams can be catalogued into types based on how they are loaded and how they are supported. Loads that are applied to a small section of the beam ...
When a force is applied perpendicularly to a point at a given distance away from that point, the rotational force that occur is called a moment. “It is calculated as the perpendicular force multiplied by the distance from the point. A Bending Moment is simply the bend that occurs in a beam due to a moment. ” (4) This moment is measured in Newton-meters (Nm) and anti-clockwise bending is positive. The bending moment of a beam is the resultant turning moment due to all the forces acting on one side of the point. The beam is in equilibrium with the application of these forces and its reactions as it is not moving.
(3) “A beam is a member or bar subjected to forces that act perpendicular to its longitudinal axis”. (1) In engineering, one of the most important mechanical and structural elements is the beam. Some of the factors that need to be considered during the beam design process include the load to be supported, the type of structure, the strength and stresses involved in the beam, the type of structure, as well as others. When a load is applied to a beam, it develops a shear force & bending moment that will vary along it. This experiment is solely to work out bending moments; therefore I will focus my research thusly.
Finding this moment is an essential step in the design of any beam. There are several types of beam including simply supported, cantilever and overhanging, however this experiment will deal wholly with a simply supported beam. A beam that has pin support at either ends, or a pin at one end and a roller support at the other is called a simply supported beam. The pin support is capable of developing a force reaction in its horizontal and vertical components, but it cannot develop a moment reaction. The roller support cannot resist horizontal force, only vertical.
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This beam is used specifically for testing loads and has a split down it which is connected to a spring load gauge, which takes the slack and is used for measuring the force applied. (3) The type of load we will be applying to the beam will be concentrated. This means the load will be applied at a specific point rather than the weight distributed across the beam. Finally, when an experiment such as this is undertaken, or when calculating a theoretical bending moment, a few assumptions have to be made: 1. “The beam is initially straight, that is, no initial curvature in the beam.
2. The material of the beam is homogeneous, that is, it possesses same physical properties throughout the volume. 3. The material of the beam is isotropic, that is, its elastic constants do not vary throughout its volume. 4. Young’s modulus of the material in tension Et is the same as Young’s modulus in compression EC. 5. The elastic limit of the material ? e is not exceeded, that is, stresses in the material at any section at any layer do not exceed ? e, in other words when bending moment is removed from the beam, it comes back to its original shape and original dimensions. ” (2)
