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Problem: Draw the internal force (N,V,M) diagrams and include all significant figures

Here is all of my work:

**Resulting F from W**

_{1}:_{1}

∴ F

_{2}=∫

_{0}

^{2b}W

_{1}dx

__eq (1)__⇒ F

_{2}= W

_{1}⋅2b

_{1}= (F

_{1})

^{-1}∫

_{0}

^{2b}W

_{1}dx = 1/(W

_{1}⋅2b)⋅(W

_{1}/2 ⋅ x

^{2}) |

_{0}

^{2b}

__eq (2)__⇒ x

_{1}= b;

SUPPORT REACTIONS DIAGRAM &FBD:

FBD:

****

SUPPORT REACTIONS VARIABLE SOLUTION:SUPPORT REACTIONS VARIABLE SOLUTION:

_{x}= 0 : 0 = R

_{AX}

__eq (3)__⇒ R

_{AX}= 0 ;

_{y}= 0 : 0 = (R

_{AY}+ R

_{BY}+ R

_{DY}) - (F

_{1}+ F

_{2})

__eq (4)__⇒ R

_{AY}+ R

_{BY}+ R

_{DY}= F

_{1}+ W

_{1}⋅2b;

_{A}= 0 : 0 = (F

_{2}⋅b + F

_{1}(2b + a)) - (R

_{BY}⋅b + R

_{DY}(2b+2a))

→R

_{BY}⋅b + R

_{DY}(2b+2a) = W

_{1}⋅2b⋅b + F

_{1}(2b + a)

__eq (5)__⇒ R

_{BY}⋅b + R

_{DY}(2b+2a) = 2⋅W

_{1}⋅b

^{2}+ F

_{1}(2b + a) ;

_{B}= 0 : 0 = (R

_{AY}⋅b + F

_{1}(b+a)) - R

_{DY}(b+2a)

__eq (6)__⇒ R

_{DY}(b+2a) = R

_{AY}⋅b + F

_{1}(b+a) ;

_{B}= 0 : 0 = (F

_{1}⋅a + F

_{2}(2a+b)) - (R

_{BY}(2a+b)+R

_{AY}(2b+2a))

__eq (7)__⇒ R

_{BY}(2a+b)+R

_{AY}(2b+2a) = F

_{1}⋅a + F

_{2}(2a+b) ;

SEPARATE FBDs:

I:
II:

Separating the system at the hinge (C) will allow us to solve for the support reactions: In Figure 1, we can solve for the support reactions in the separate part, and therefore solve for the support reactions in the whole beam.

[+CW]∑M

_{B}= 0 : 0 = R

_{AY}⋅b

__eq (8)__⇒ R

_{AY}= 0 ;

_{y}= 0 : 0 = R

_{AY}+ R

_{BY}- F

_{2}

__eq (9)__⇒ R

_{BY}= F

_{2}

So now, using eq's (8) & (9) in eq (4) we can determine R

_{DY}

eq (4) : R

_{AY}+ R

_{BY}+ R

_{DY}= F

_{1}+ W

_{1}⋅2b

→F

_{2}+ R

_{DY}= F

_{1}+ W

_{1}⋅2b

→ R

_{DY}= F

_{1}+ W

_{1}⋅2b - W

_{1}⋅2b

__eq (10)__⇒ R

_{DY}= F

_{1}

(9) > (5) : F

_{2}⋅b + R

_{DY}(2b+2a) = 2⋅W

_{1}⋅b

^{2}+ F

_{1}(2b + a)

→ R

_{DY}(2b+2a) = 2⋅W

_{1}⋅b

^{2}+ F

_{1}(2b + a) - (W

_{1}⋅2b)⋅b

→ R

_{DY}= 1/(2b+2a)[F

_{1}(2b + a) + 2⋅W

_{1}⋅b

^{2}- (W

_{1}⋅2b)⋅b]

→ R

_{DY}= F

_{1}(2b + a)/(2b+2a)

I'm just super lost, I guess, on where to go and if I'm even starting in the right direction... could someone please help me?