simple beam (L = 9 m) with attached bracket BDE has force P = 5 kN applied downward at E. The bending moment just right of $B$ is approximately:
A) 6 N ∙ m
B) 10 N ∙ m
C) 19 N ∙ m
D) 22 N ∙ m

Question

simple beam (L = 9 m) with attached bracket BDE has force P = 5 kN applied downward at E. The bending moment just right of $B$ is approximately: 
A) 6 N ∙ m 
B) 10 N ∙ m 
C) 19 N ∙ m 
D) 22 N ∙ m

Quizplus · Accepted Answer

To find the bending moment just right of B, we need to first find the reactions at the supports. Since the beam is simply supported, the reactions will be equal and half the total load (P=5kN) which is 2.5kN each. 
Now, taking moments about B gives us:
\begin{align}
2.5 	ext{ kN} 	imes 9 	ext{ m} - P 	imes DE &= 	ext{Bending moment just right of B} \
22.5 	ext{ kN}\cdot m - P 	imes DE &= 	ext{Bending moment just right of B} \
\end{align}
To find DE, we can use similar triangles. Since triangle AED is similar to triangle BDE, we can say:
\begin{align}
\frac{DE}{9} &= \frac{BD}{BE} \
\frac{DE}{9} &= \frac{1}{2} \
DE &= 4.5	ext{ m}
\end{align}
Substituting this into the equation gives us:
\begin{align}
22.5 	ext{ kN}\cdot m - 5 	ext{ kN} 	imes 4.5 	ext{ m} &= 	ext{Bending moment just right of B} \
19 	ext{ kN}\cdot m &= 	ext{Bending moment just right of B}
\end{align}
Therefore, the bending moment just right of B is approximately 19 N·m, which is closest to choice C (19 N·m).

Simple Beam (L = 9 M) with Attached Bracket BDE BBB

Simple Beam (L = 9 M) with Attached Bracket BDE $B$