# Please show all steps and applicable diagrams a = 2.0m b = 4.0m c = 2.0m...

###### Question:

Please show all steps and applicable diagrams

a = 2.0m

b = 4.0m

c = 2.0m

d = 6.0m

e = 3.0m

M = 48kN*m

w1 = 8kN/m

w2 = 6kN/m

W1 W2 M BE 5 •d
ye Beam DBE has the cross-section shown in the figure to the right Calculate: c) the vertical position y, of the centroid of the girder cross-section, and d) the moment of inertia Ix' about the horizontal axis x'x' passing through the centroid of the girder cross-section. The indicated dimensions on the figure have the following values: a = 25 mm b = 150 mm c=25 mm d = 75 mm e = 100 mm The bending stress o at any point in the beam is given by the formula My where M is the bending moment at that point in the beam, 1x) is the moment of inertia about the horizontal axis x'x' passing through the centroid of the beam cross-section, and y is the distance measured vertically from the centroid of the beam. Since at the centroid of the beam y = 0 and therefore o = 0, the centroid of the beam also corresponds to what is called the neutral axis of the beam, that is the point within the beam that the bending stresses are equal to zero. Distance y can be positive or negative depending on whether one is moving vertically up or down from the centroid, as can the bending moment M in response to the loads being applied to the beam. This means that the bending stress o can also be positive (acting in tension) or negative (acting in compression), as one moves above or below the neutral axis. The selection of a suitable cross-section for the beam will be determined in part by the need to keep the maximum bending stress, positive or negative, in the beam below the yield stress of the material the beam is to be made from. e) Calculate the maximum value, positive or negative, of the bending stress occurring at any point along the beam DBE.

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