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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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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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

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Locate the centroid of the shaded area - Texas A&M...

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