Discussion
Two structural members are connected by a hinge and they are externally loaded as shown in the figure below. A and B are roller supports, and C is a pin support. Neglecting the mass of the members, the magnitude of the vertical reaction force at C in kN is
Answer: A
The vertical reaction at C is 5 kN.
The hinge transmits no moment, so treat the left member A-hinge first. It is 1 m long with the 10 kN load at its middle, so A and the hinge each carry 5 kN. The hinge therefore pushes 5 kN down on the right member.
The right member runs from the hinge to C (1.0 m), with roller B 0.2 m from the hinge and the 25 kN load 0.4 m from the hinge. Take moments about B:
\[ \begin{aligned} R_{C}(0.8) &= 25(0.2) - 5(0.2) = 4 \\ R_{C} &= 5\ \text{kN} \end{aligned} \]
Then \(R_{B} = 30 - 5 = 25\) kN. Answers of 10, 15 or 20 come from treating the beam as one continuous member, ignoring the hinge's zero-moment condition.
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