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Objectives To show how to use the method of sections for determining the internal loadings in a member To generalize this procedure by formulating equations that can be plotted so that they describe e internal shear and moment throughout a the internal shear and moment throughout a member Chapter Chapter 7 7 – Internal Loadings Internal Loadings 7-2
Introduction The design of any structural member requires finding the forces acting within the member to make sure the material can resist those loads. For example, we want to determine the internal rces acting on the cross section at C. forces acting on the cross section at C. First, we first need to determine the support actions Then we need to cut the beam at C reactions. Then, we need to cut the beam at C and draw a Free Body Diagram (FBD) of one of the halves of the beam. This FBD will include the internal forces acting at C. Finally, gy , we need to solve for these unknowns using the Equations of Equilibrium. Chapter 7 Chapter 7 – Internal Loadings Internal Loadings 7-3

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Internal Forces In two-dimensional cases, typical internal forces are normal or axial forces ( N, ting perpendicular to the section) shear acting perpendicular to the section), shear forces ( V , acting along the surface), and the bending moment ( M ) . In three-dimensional cases, typical internal forces are normal force N y , shear forces V x and V z , torsional or twisting oment d the bending moments moment M y and the bending moments M x and M z . Chapter 7 Chapter 7 – Internal Loadings Internal Loadings 7-4
Free-Body Diagram (FBD) ± The loads on the left and right sides of the section at C are equal in magnitude but opposite in direction. This is ecause when the two sides are reconnected the net loads because when the two sides are reconnected, the net loads are zero at the section. Chapter 7 Chapter 7 – Internal Loadings Internal Loadings 7-5

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Steps for Determining Internal Forces 1. Take an imaginary cut at the place where we need to determine the internal forces. Then, decide which resulting section or piece will be easier to analyze. necessary determine any support reactions or joint forces we 2. If necessary , determine any support reactions or joint forces we need by drawing a FBD of the entire structure and solving for the unknown reactions. FBD fth i fth t t h d id dt 3. Draw a FBD of the piece of the structure we have decided to analyze. Remember to show the N, V, and M loads at the “cut” surface. 4. Apply the Equations of Equilibrium to the FBD (drawn in step 3) and solve for the unknown internal loads. Chapter 7 Chapter 7 – Internal Loadings Internal Loadings 7-6
Example 7.1 Determine the resultant internal loadings acting on the cross section at C f the beam. of the beam.

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