2D Free-Body Diagrams (FBDs)
Conceptual Questions: Drawing FBD’s
The image below depicts a beam with external forces F[sub]1[/sub] and F[sub]2[/sub]. The beam is made of members AB and BC with a fixed support at A, an internal hinge at B, and a roller support at C. [br][br]Use the image to answer the questions below.
Draw the FBD of member ABC.[br][br]On the FBD of member ABC, how many reaction forces (excluding moments) will there be at supports A and C?
On the FBD of member ABC, how many couple moments will there be at supports A and C?
[br]Draw the FBD’s of members AB and BC.[br][br]When member AB is “freed” from its supports, how many total forces (including F[sub]1[/sub]) will there be on the FBD?
[br]What external forces will there be at supports A and B?
How many moments will there be on the FBD of AB?
[br]When member BC is “freed” from its supports, how many total forces (including F[sub]2[/sub]) will there be on the FBD? [br]
[br]On the FBD of BC, what external forces will there be at the roller support at C?[br]
How many moments will there be on the FBD of BC?
Use the Figure to Analyze the FBD of each Member
In the interactive Figure below, click and drag the red dot in the center of each member to free it from its constraints and see its FBD. [br]
Click and drag the red dot at A to reveal its support reactions on member AB.[br][br]Why are there two force reactions, in the x and y axes, at the fixed support at A?[br]
Why is there a couple moment at the fixed support at A?
Click and drag the red dot at C to reveal its support reactions on the beam.[br][br]Why is there only one vertical force, C[sub]y[/sub] at the roller support at C?[br]
Isolate member BC to see its FBD.[br][br]As the angle of F[sub]2[/sub]increases from 0[sup]o[/sup] to 90[sup]o[/sup], what happens to the magnitude of B[sub]x[/sub]?[br][br]
If its magnitude stays the same, for what angle of F[sub]2[/sub] does the magnitudes of B[sub]y[/sub] and C[sub]y[b] [/b][/sub]reach a maximum?
If F[sub]2[/sub] = 400 N at an angle of 90[sup]o[/sup], then in terms of F[sub]2[/sub], B[sub]y[/sub] is equal to?
Isolate member AB to see its FBD. [br][br]For member AB, moment M[sub]a[/sub] reaches a maximum when force F[sub]1 [/sub]is at which angle?[br]
Using FBD’s to write Equations of Equilibrium
Writing equilibrium equations requires defining coordinate axes. We will use the following coordinate system:[br][br] x is positive to the right [math]\text{+→}[/math][br][br] y is positive toward the top of the page [math]\text{+↑}[/math][br][br] positive moments result in a counterclockwise rotation [math]+\text{↺}[/math][br][br]
[br]Using the above coordinates and with F[sub]1 [/sub]and F[sub]2[/sub] at 60[sup]o[/sup], which is the correct equilibrium equation in the y direction [math]\text{∑}[/math]F[sub]y[/sub] for member BC?
Using the above coordinates and with F[sub]1 [/sub]and F[sub]2[/sub] at 60[sup]o[/sup], which is the correct equilibrium equation in the x direction [math]\text{∑}[/math]F[sub]x[/sub] for member BC?
Using the above coordinates and with F[sub]1 [/sub]and F[sub]2[/sub] at 75[sup]o[/sup], which is the correct equilibrium equation in the y direction [math]\text{∑}[/math]F[sub]y [/sub]for member AB?
Using the above coordinates and with F[sub]1 [/sub]and F[sub]2[/sub] at 75[sup]o[/sup], which is the correct equilibrium equation in the x direction [math]\text{∑}[/math]F[sub]x [/sub]for member AB?
For the FBD of AB and with F[sub]1 [/sub]at 75[sup]o[/sup], which expression for the sum of moments about A, [math]\text{∑}[/math]M[sub]a[/sub] is correct?