Problem $3$

A beam segment with parametric loadings shown below $(w1>w2>0$;$M>0$; and $P>0).$ The key

locations of $A,B,C,$ and D $($from the left to the right$)$ are set at $x=0,x=10m,x=20m,$ and $x=25m,$

respectively.

Given its internal shear diagram and the internal shear values at $A,B,C,$ and $D$ as shown in the

following shear diagram with $V_1=100K,V_2=-50K,V_3^{-}=-100K,$ and $V_3^{+}=V_4=-200K,$

determine the external loadings of $w1,w2,$ and P $.$

If the internal moment at the left end is zero ; also as shown in the following moment

diagram$).$ Complete the moment diagram, calculate the key moment values at $B,C,$ and D $,$ and

denote the slope values at all key locations. Determine that at what condition the right$-$end moment

$($M$4)$ will be zero as well $($hint $-$ this is equivalent to determine the value of the external moment

value M $).$