Given the section FBD below, what is the correct y-force equilibrium equation?

Question

BlackTom AI · Accepted Answer

Let's restate the problem and the options to ensure we’re evaluating the right statements.
Question: Given the section FBD below, what is the correct y-force equilibrium equation?
Answer options:
1) FGCsin(45°) = - 1000
2) FGCsin(45°) - 1000 =0
3) FGCsin(45°) +FBC - FGF - 1000 =0
4) FGC - 1000 =0

Now, analyze each option one by one.
Option 1: FGCsin(45°) = -1000. This form incorrectly places all vertical forces on one side with a negative 1000, implying FGCsin(45°) equals a negative load. In a standard sum of forces in the y-direction, we don’t typically equate a positive upward component to a negative downward load without including the sign convention explicitly. Here the vertical components involved are FGC’s y-component (upward) and the 1000 N downward load. Simply stating equality in magnitude without accounting for the sign convention leads to an incorrect representation.
Option 2: FGCsin(45°) - 1000 = 0. This expresses that the upward vertical component of FGC (which is FGC sin(45°)) minus the downward 1000 N equals zero, which matches the typical y-direction equilibrium sum Fy = 0 with upward positive. It correctly accounts for direction and magnitude of the two vertical forces involved.
Option 3: FGCsin(45°) + FBC - FGF - 1000 = 0. This introduces additional forces FBC and FGF into the y-equilibrium. From the diagram, FBC is horizontal, so its vertical component is zero; FGF appears to be horizontal as well, contributing no vertical component. Including them as vertical terms is incorrect, making this equation inconsistent with the actual force directions.
Option 4: FGC - 1000 = 0. This treats FGC as a scalar magnitude without taking its vertical component into account. Since FGC acts along a 45° member, its vertical component is FGC sin(45°), not FGC itself. Therefore this form neglects the necessary projection onto the y-axis.

In summary, the only expression that correctly represents the vertical force balance by incorporating the proper vertical component of FGC and the downward 1000 N load, with consistent sign convention, is the second option: FGCsin(45°) - 1000 = 0.

Given the section FBD below, what is the correct y-force equilibrium equation? 单项选择题

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