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The centroid parallel set of

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Unformatted text preview: ross secTons (or composite areas) x0 x Problem 4 : Problem 5 : C top D E y0 y side bo=om WIDE FLANGE SECTION CHANNEL- SECTION 1.  Make a simple table in order to keep track of the areas and centroids of each consTtuent secTon. 2.  Label each secTon and calculate area of each individual secTon 3.  Determine centroid locaTon within each secTon (in case of channel- secTon tabulate Xc for each secTon). b b b1 top bottom side 4.  For example, in case of channel secTon : Xc = Xc = Xc = 2 2 5.  Determine Xc of the enTre secTon ((Yc) is obvious by symmetry) Xc = 2/22/13 P3 x i Ai c A i=1 (with respect to x0, y0 axes) M. Mello/Georgia Tech Aerospace 6 MOMENT OF INERTIA OF A CHANNEL SECTION Problem 5 : Assignment 5 ~ M x0 6.  Calculate moment of inerTa of each consTtuent rectangular secTon. Use: Iy = bh3t/12 ectangle moment of inerTa 7.  The dimension “b” in he r calculaTon is always the side aligned the direcTon of moment vector (in this case the y axis)… top 8.  Next, set up (x,y) coordinate system with origin at the centroid. C D 9.  Establish y values of all points of interest (C,D,E) in the problem w.r.t centroid (you have to think about the direcTon in which y0 E the beam will bend). y side 10.  Next, obtain distances (di) from the centroid of each individual secTon to the centroid of the composite secTon (again think bo=om about how the beam will bend and the moment of inerTa that is CHANNEL- SECTION relevant to the problem). 11.  Apply the parallel- axis theorem to compute the moment of inerTa of the composite secTon. 2/22/13 x 12.  Use the the individual moments of inerTa, areas, and distances di which you just finished determining. M. Mello/Georgia Tech Aerospace 7 Maximum Stresses at a Cross SecTon ²་  Maximum tensile and compressive bending stresses acTng at any given cross secTon occur along the top and bo=om edges of the beam along points furthest from the neutral axis (c1,c2 in the figure below) M c1 M M c2 M ²་  Maximum normal stress from flexure formula: 1 = = = = (5- 14) 2 I c1 ²་  where: S1 = and S2 = I S1 I S2 I are called secFon moduli. Units of secFon moduli: [Length]3 c2 ²་  Convenient quanFty used in beam design lumps beams cross secFonal properFes into a single term ²...
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