2528.sagews

In the input boxes, you may enter numbers or expressions involving any of the following variables.

var( 'L w M0 M1 m0 m1 m M' )

(L, w, M0, M1, m0, m1, m, M)

Use beam sign convention: loads are +ive downwards, and moments are +ive causing compression on the top (clockwise at the left end of a segment and counter-clockwise at the right end).

@interact
def integrate_mM( L=("Length of segment: L", L),
                  w=("Real distributed load: w", w),
                  M0=("Real moment at left: M0", M0), 
                  M1=("Real moment at right: M1", M1),
                  m0=("Virtual moment at left: m0", m0), 
                  m1=("Virtual moment at right: m1", m1),
                  auto_update=False ):
    V0 = w*L/2 + (M1-M0)/L
    x = var('x', domain=RR)
    Mx = M0 + V0*x - w*x*x/2
    v0 = (m1 - m0)/L
    mx = m0 + v0*x
    if Mx.variables() == (x,):  # plot M if x is the only variable
        p = plot( Mx, (0,L), axes_labels=('x','Real Moment') )
        p.show()
    return integrate( mx*Mx, x, 0, L )