Chapter 2 - Properties of Steel Areas.pptx | Beam (Structure) | Mechanical Engineering

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CE134- STRUCTURAL STEEL DESIGN CHAPTER 2 PROPERTIES OF STEEL AREAS AND SECTIONS PROPERTIES OF AREAS  CENTROID OF AN AREA  The centroid of a area is analogous to the center of gravity of a homogenous body. The centroid s often described as the point at which a thin homogenous plate would balance.  The centroid of complex area can be found by dividing the area into basic shapes (rectangles, triangles, circles, etc.) AT Xc = a1
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  PROPERTIES OF STEEL AREAS AND SECTIONS CE134-STRUCTURAL STEEL DESIGN CHAPTER 2  PROPERTIES OF AREAS   CENTROID OF AN AREA   The centroid of a area is analogous to the center of gravity of a homogenous body.  The centroid s often described as the point at which a thin homogenous plate would balance.   The centroid of complex area can be found by dividing the area into basic shapes (rectangles, triangles, circles, etc.)A  T X c  = a  x   ! a x  ! a # x #  ! $A  T  % c  = a  y   ! a y  ! a # y #  ! $  COMMON CENTRODS OF BASIC AREAS  9 - 4 oment o nert! o !n Are! ã Consider distributed forceswhose magnitudes are proportional to the elemental areason which they act and also vary linearly with the distance of from a given axis. ã Example: Consider a beam subjected to pure bending. Internal forces vary linearly with distance from the neutral axis which passes through the section centroid. ã Example: Consider the net hydrostatic force on a submerged circular gate.  F  ∆  A ∆  A ∆ momentsecondmomentfirst 0 22 ====== ∆=∆ ∫ ∫ ∫ ∫  dA ydA yk  M  QdA ydA yk  R  Aky F   x ∫ ∫  ==∆=∆=∆ dA y M dA y R A y A p F   x 2 γ γ γ 
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