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[Virtual Presenter] We are pleased to present on the analysis and design of beams for bending. We are excited to introduce this topic to you. In this presentation we will discuss various aspects of beam bending including shear and bending moment diagrams sample problems and design of prismatic beams. Our objective is to determine the location and magnitude of the largest bending moment for a given beam and loading. We will also cover the maximum normal stress as the critical design criteria. By the end of this presentation you will have a better understanding of how to determine the shear and bending moments for a given beam and loading. So let's get started!.

[Audio] We will now analyze some sample problems related to shear and bending moment diagrams. We will analyze Sample Problem 1 Sample Problem 2 Sample Problem 3 Sample Problem 5 Sample Problem 8 and Sample Problem 8 to determine the maximum shear force and bending moment in the beam. By analyzing these sample problems we can gain a better understanding of the relationships between load shear and bending moment in beams. This knowledge can be applied to the design of beams for various applications..

[Audio] Beams are a fundamental structural element in engineering that supports loads at various points along the member. The objective of analyzing and designing beams is to ensure that they can carry the loads placed upon them without collapsing or deforming. When it comes to transverse loading of beams there are two main types of loads: concentrated loads and distributed loads. Beams must withstand the loads placed upon them and the shear force and bending couple resulting from applied loads must be carefully analyzed and designed to ensure that the beam can carry the loads placed upon it. In summary beams are an important structural element in engineering and analyzing and designing them is crucial for ensuring that they can carry the loads placed upon them without collapsing or deforming..

[Audio] We will now discuss the classification of beam supports. A beam support is a device or structure that carries the weight of the beam and distributes the load to the ground. There are several types of beam supports including simple supports cantilever supports continuous supports fixed supports and free supports. Each of these supports has its own unique characteristics and can be used in different situations. We will discuss the properties and applications of each of these supports in more detail in the following sections..

[Audio] To determine the maximum normal and shearing stresses in a beam it is essential to identify the maximum internal shear force and bending couple. This can be achieved by passing a section through the beam and performing an equilibrium analysis on the beam portions on either side of the section..

[Audio] We need to draw shear and bend-moment diagrams and calculate the internal shear forces and bending couples to determine the maximum normal stress due to bending. This can be done by treating the entire beam as a rigid body and applying equilibrium analyses on the resulting free-bodies. It is crucial to section the beam at points near supports and load application points to ensure an accurate analysis. By following these steps we can ensure a safe and effective design for the timber beam and loading shown..

[Audio] To solve the problem at hand we recommend treating the entire beam as a rigid body. This will enable us to determine the reaction forces that are acting on the beam. We will then section the beam and apply equilibrium analyses on the resulting free-bodies. This will allow us to determine the forces that are acting on each section of the beam and how they are distributed throughout the length of the beam. By using this method we can ensure that the beam is properly designed to withstand the forces that are being applied to it. This will help to prevent any deformation or failure of the beam..

[Audio] We will discuss the analysis and design of beams for bending. We will focus specifically on identifying the maximum shear and bending-moment from plots of their distributions and applying the elastic flexure formulas to determine the corresponding maximum normal stress. It is crucial to understand these concepts to ensure that the beam can withstand the forces it will be subjected to. We will take you through this process step by step so please pay attention and take notes. If you have any questions feel free to ask..

[Audio] To determine the normal stress in sections just to the right and left of point D we will replace the 10 kip load with an equivalent force-coupler system at D Then we will consider the beam as a rigid body and find the reactions at B We will section the beam at points near the support and load application points and apply equilibrium analyses on resulting free-bodies to determine internal shear forces and bending couples. Finally we will apply the elastic flexure formulas to determine the maximum normal stress to the left and right of point D We will now begin the analysis..

[Audio] At D we have identified an equivalent force-coupler system to distribute the 10 kip load more evenly and ensure that the beam can withstand the load. In order to understand the beam's behavior under the load we will section it and apply equilibrium analyses on the resulting free-bodies. This will help us to analyze how the forces are distributed throughout the beam and ensure that it is able to withstand the load..

[Audio] We are discussing elastic flexure formulas for determining maximum normal stress to the left and right of point D We are using formulas from Appendix C for a W10x112 rolled steel shape with S = 126 in3 about the X-X axis. By applying these formulas we can ensure our beams withstand stresses during bending..

[Audio] When designing a beam it is important to consider the relationships between load and shear and between shear and bending moment. These factors are closely related and can affect each other in different ways. Understanding these relationships is essential for ensuring the safety and stability of the beam. By taking load and shear as well as bending moment into account you can design a strong and durable beam..

[Audio] To gain a better understanding of how beams behave under different types of loads and how they can be designed to withstand these loads we need to draw shear and bending moment diagrams for the beam and loading shown. We will take the entire beam as a free body and determine the reactions at A and D We can use the relationship between shear and load to develop the shear diagram. Finally we can use the relationship between bending moment and shear to develop the bending moment diagram..

[Audio] Discuss the determination of reactions at points A and D of a beam under load and the development of shear diagrams. Use free body diagrams and the relationship between shear and load to develop the shear diagram for the beam. Recognize the zero slope between concentrated loads and the linear variation over the uniform load segment. This will help to understand the distribution of shear forces in the beam..

[Audio] Understanding the relationship between bending moment and shear is essential in developing the bending moment diagram which is a critical component in the analysis and design of beams. We must understand the bending moment at points A and E which are zero meaning that these points do not experience any bending. We also need to understand the net change in bending moment between points A and E which is equal to the areas under the shear distribution segments. The variation in bending moment between points D and E is quadratic while the variation in bending moment between points A B C and D is linear. Comprehending these relationships is crucial in creating an accurate bending moment diagram which is then utilized to analyze and design beams for bending..

[Audio] We will discuss the analysis and design of beams for bending. We will look at how to draw the shear and bending moment diagrams for a given beam and loading. The first step in this process is to take the entire beam as a free body and determine the reactions at the point C This will help us understand the forces acting on the beam and how they are distributed. We can apply the relationship between shear and load to develop the shear diagram. By understanding how the shear forces are distributed along the length of the beam we can determine the shear stress at various points. Finally we can apply the relationship between bending moment and shear to develop the bending moment diagram. This will help us understand how the beam is deforming under the applied loads and how the stresses are distributed along the length of the beam. In summary by following these steps we can effectively analyze and design beams for bending..

[Audio] We need to determine the reactions at C apply the relationship between shear and load to develop the shear diagram check for no change in shear between B and C and ensure that our solution is compatible with free body analysis..

[Audio] The bending moment diagram is an important tool used in the design of beams. It can be developed using the relationship between bending moment and shear. The results at point C indicate that the forces acting on the beam are balanced at that point..

[Audio] This slide will discuss the significance of determining the minimum acceptable section modulus for a safe design. The maximum bending moment and corresponding normal stress will be identified. A safe design requires that the maximum normal stress be less than the allowable stress for the material used. This criterion leads to the determination of the minimum acceptable section modulus. By ensuring that the section modulus is adequate the safety and durability of our designs can be ensured..

[Audio] To design a simply supported steel beam we need to consider the allowable normal stress for the steel grade and the load to be carried. We will use a wide-flange shape for the beam design. Next we will analyze the entire beam as a free-body and determine the reactions at points A and D This will help us to create a shear diagram and distribute the loads. From the diagram we will determine the maximum bending moment and the minimum acceptable beam section modulus. We will choose the best standard section based on these criteria. Finally we will select the best standard section for our beam design..

[Audio] 1. We will focus on the determination of the reactions at points A and D as well as the development of a shear diagram and the calculation of the maximum bending moment. We will treat the entire beam as a free-body considering all the forces acting on the beam. At points A and D we will have the force of the load as well as any other forces such as friction or support forces. Using the shear diagram we will calculate the maximum bending moment which is the force that will cause the beam to bend the most. This information is important for designing beams that can withstand the loads and forces they will be subjected to. In summary our presentation focuses on the determination of the reactions at points A and D as well as the development of a shear diagram and the calculation of the maximum bending moment. This information is crucial for the analysis and design of beams for bending..

[Audio] Discussed various factors affecting beam bending analyzed and designed beams for bending and the importance of determining the minimum acceptable beam section modulus and choosing the best standard section which meets this criteria..