Transcript of Locate the centroid of the shaded area - Texas A&M...
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Locate the centroid of the shaded area
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straightforward calculus
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Compute the area moment of inertia about its centroidal x0 axis
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See Table D/3. For rectangular pieces: Ix = (b h^3)/3 Ix_bar = (b h^3)/12
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(1) parallel axis thm
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(2) and (3) use I about end (Ix)
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Compute the area moments of inertia about the centroidal x0 and y0 axes
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See Table D/3. For rectangular pieces: Ix = (b h^3)/3 Ix_bar = (b h^3)/12
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(1) parallel axis thm
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There are two number 1 pieces
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Compute the reactions at A and B
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Essentially using N2L and E2L
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E2L
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N2L
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N2L
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Compute the reactions at support A as a function of w0 and b
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This is cute
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Integrate to compute total load
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In moments, each force has a "lever arm"
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Use FBDs to construct the shear and moment diagrams. Determine the internal moment at a section 0.5 m to the right of B
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Compute external reactions
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I don't like this. Should use FBDs to compute V & M. Let's not jump to diagrams
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Use FBDs to construct the shear and moment diagrams. Determine the internal shear & moment at the middle of the beam
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6 < x < 9
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3 < x < 6
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0 < x < 3
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Compute the external reactions
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Use FBDs to find V and M
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Middle: x = 4.5
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Use FBDs to construct the shear and moment diagrams. Determine the internal moment at section C
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Compute the external reactions
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I don't like this. Should use FBDs to compute V & M. Let's not jump to diagrams
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A sign convention: Down = +ive Up = -ive
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Use FBDs to construct the shear and moment diagrams. Determine the distance b from the left end to where the internal moment is zero between the supports
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Compute the external reactions
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Again!
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Here's a nice FBD treatment
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Use FBDs to construct the shear and moment diagrams. Determine the maximum magnitude of the internal moment