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Shear and moment diagram for beam

Shear and moment diagram is a graphical representation of shear and moment for a structural member. Shear and moment diagram are essential for designers. The designer will use shear and moment diagram to determine the shear and moment at different locations. Also, it will be used to determine the maximum moment and shear for a structural member. Acquiring the shear and moment equations for a structural member with several point load and distributed load will be a lengthy and complicated process. Many equations will be derived for a single member. This will consume a great time. Drawing shear and moment diagram is easy and not wasting a long time.







Procedure for Analysis



  • Let consider the beam in figure 1. the first step is to determine the reactions on a beam using equilibrium equations. Reactions determined, as shown in figure 2.




Figure 1
Figure 2




  • Draw x-axis from the end of the beam and y-axis for the shear values. In Figure 2 at x=0, the shear value equals the reaction V=+37.23 kn. The slope of the line from the support to point load dv/dx=w. From the support to point load there is no load so the slope of shear=0 or horizontal as shown in figure 2. at the point load(-25 kn), the shear value reduced  by 25 kn so at this point shear value is 12.23 kn, then again from the point load to the edge of distributed load the slope is zero, so the line is horizontal. The slope of the line at the distributed load .dv/dx=w=5kn/m and the value of shear for distributed load=5*-5=-25 kn, so our shear diagram will go down by 25 kn with a slope of 5 kn/m and so on. For moment diagram. At the support or point of x=0. If there is no moment at this point, we start the diagram from zero. The moment is the area of the shear diagram. We begin calculating areas and representing it on moment diagram. From the support to point load=25 kn. The area is 186.15 kn-m. The moment is the integration of the shear diagram. So we divide the shear diagram into different portions. Each portion with the same slope. If the slop is zero, the moment diagram will be linear. dM/dx=V, the moment diagram slope at a given point is equal to the intensity of shear at this point. if the shear diagram is linear, the moment diagram will have a parabolic shape.



Figure 3








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