Symmetric loading vs antisymmetric loading

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Homework Statement


For the circled beam , we can see that for both cases , the load are loaded in the same way ... Why the M / EI diagram for the first case is different from the second case ? Why for the first case , it's symmetric loading ? For the second case , it's antisymmetric loading ?

Homework Equations

The Attempt at a Solution


I think the second case is wrong . Only the first case make sense . From the figure , we can see that the load P is applied at the midspan of AB and CD . So . it's symmetric loading , am i right ?
 
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  • Two-panel textbook figure: (a) a symmetric simply supported beam with loads P at supports A and D and a span BC, labeled real beam; (b) the conjugate beam for span BC with M/EI loading and the end slope theta, labeled conjugate beam.
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  • Textbook figure 12-12: (a) a real beam with a central point load P and a sketch of the beam's deflected shape; (b) the conjugate beam with M/EI loading diagrams, with the end reactions and moment-area terms circled in red.
    575.PNG
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  • Conjugate beam diagram (b): a horizontal beam with supports V_B' upward at left end B' and V_C' upward at right end C', spans marked L/2 and L/2, a downward load M/EI L at midspan, and an M/EI load label at the right end.
    576.PNG
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  • Conjugate beam diagram (b) with a horizontal beam supported at B' and C', showing M/EI loads as triangular distributions with labels 1/2 (M/EI)(L/2), 5/6 L, and 1/6 L, plus reactions V_B' and V_C'.
    577.PNG
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