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ch07 - Chapter7 InternalForces :Statics ChapterObjectives...

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Engineering Mechanics: Statics Chapter 7:  Internal Forces  
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Chapter 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 the internal shear and moment  throughout a member. To analyze the forces and study the  geometry of cables supporting a load.
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Chapter Outline Internal Forces Developed in  Structural Members Shear and Moment Equations and  Diagrams Relations between Distributed  Load, Shear and Moment Cables
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7.1 Internal Forces Developed in  Structural Members The design of any structural or  mechanical member requires the  material to be used to be able to resist  the loading acting on the member These internal loadings can be  determined by the method of sections
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7.1 Internal Forces Developed in  Structural Members Consider the “simply supported” beam To determine the internal loadings acting on the cross  section at C, an imaginary section is passed through  the beam, cutting it into two By doing so, the internal loadings become external on  the FBD
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7.1 Internal Forces Developed in  Structural Members Since both segments (AC and CB) were in  equilibrium before the sectioning, equilibrium of  the segment is maintained by rectangular force  components and a resultant couple moment Magnitude of the loadings is determined by the  equilibrium equations
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7.1 Internal Forces Developed in  Structural Members Force component  N , acting normal to the  beam at the cut session and  V , acting t angent to the session are known as normal  or axial force  and the shear force Couple moment  M  is  referred as the bending  moment
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7.1 Internal Forces Developed in  Structural Members For 3D, a general internal force and couple  moment resultant will act at the section N y  is the normal force, and V x  and V z  are  the shear components M y  is the torisonal or  twisting moment, and  M x  and M z  are the  bending moment  components
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7.1 Internal Forces Developed in  Structural Members For most applications, these resultant  loadings will act at the geometric center  or centroid (C) of the section’s cross  sectional area Although the magnitude of each loading  differs at different points along the axis  of the member, the method of section  can be used to determine the values
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7.1 Internal Forces Developed in  Structural Members Free Body Diagrams Since frames and machines are composed of  multi-force members, each of these members will 
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