2D Free-Body Diagrams (FBDs)

Konu:2D (İki-Boyutlu) Vektörler, Vektörler

Conceptual Questions: Drawing FBD’s

The image below depicts a beam with external forces F₁ and F₂. 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. Use the image to answer the questions below.

Draw the FBD of member ABC. On the FBD of member ABC, how many reaction forces (excluding moments) will there be at supports A and C?

Tüm uygun cevapları seçin

A
1 at A, 1 at C
B
1 at A, 2 at C
C
2 at A, 1 at C
D
2 at A, 2 at C

Cevabımı kontrol et (3)

On the FBD of member ABC, how many couple moments will there be at supports A and C?

Tüm uygun cevapları seçin

A
None at either
B
1 at A, 0 at C
C
0 at A, 1 at C
D
1 at A, 1 at C

Cevabımı kontrol et (3)

Draw the FBD’s of members AB and BC. When member AB is “freed” from its supports, how many total forces (including F₁) will there be on the FBD?

What external forces will there be at supports A and B?

Tüm uygun cevapları seçin

A
A_yat A, B_yat B
B
A_x and A_y at A, B_y at B
C
A_x and A_y at A, B_xand B_y at B
D
A_y at A, B_xand B_y at B

Cevabımı kontrol et (3)

How many moments will there be on the FBD of AB?

Tüm uygun cevapları seçin

A
none
B
1 at A
C
1 at B
D
1 at A, 1 at B

Cevabımı kontrol et (3)

When member BC is “freed” from its supports, how many total forces (including F₂) will there be on the FBD?

On the FBD of BC, what external forces will there be at the roller support at C?

Tüm uygun cevapları seçin

A
none
B
Only C_x
C
Only C_y
D
C_xand C_y

Cevabımı kontrol et (3)

How many moments will there be on the FBD of BC?

Tüm uygun cevapları seçin

A
none
B
1 at B
C
1 at C
D
1 at B, 1 at C

Cevabımı kontrol et (3)

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.

Click and drag the red dot at A to reveal its support reactions on member AB. Why are there two force reactions, in the x and y axes, at the fixed support at A?

Tüm uygun cevapları seçin

A
It resists translation of the beam along the x and y axes
B
It resists translation of the beam in the x direction, the y-component is due to other external forces
C
It resists translation of the beam in the y direction, the x-component is due to other external forces
D
It allows for translation of the beam along both axes
E
Some other reason not listed here

Cevabımı kontrol et (3)

Why is there a couple moment at the fixed support at A?

Tüm uygun cevapları seçin

A
The fixed support allows for rotation of the beam
B
The fixed support does not allow for rotation of the beam (it prevents rotation)
C
The moment is there to balance moments due to forces at B and C
D
Some other reason not listed here

Cevabımı kontrol et (3)

Click and drag the red dot at C to reveal its support reactions on the beam. Why is there only one vertical force, C_y at the roller support at C?

Tüm uygun cevapları seçin

A
The roller resists translation of the beam along the x axis
B
The roller resists translation of the beam along the y axis
C
The roller allows translation of the beam along the y axis
D
Some other reason not listed here

Cevabımı kontrol et (3)

Isolate member BC to see its FBD. As the angle of F₂increases from 0^o to 90^o, what happens to the magnitude of B_x?

Tüm uygun cevapları seçin

A
It increases
B
It decreases
C
It stays the same

Cevabımı kontrol et (3)

If its magnitude stays the same, for what angle of F₂ does the magnitudes of B_y and C_yreach a maximum?

Tüm uygun cevapları seçin

A
0^o
B
45^o
C
90^o
D
180^o

Cevabımı kontrol et (3)

If F₂ = 400 N at an angle of 90^o, then in terms of F₂, B_y is equal to?

Tüm uygun cevapları seçin

A
F₂
B
F₂
C
2F₂
D
F₂

Cevabımı kontrol et (3)

Isolate member AB to see its FBD. For member AB, moment M_a reaches a maximum when force F₁is at which angle?

Tüm uygun cevapları seçin

A
0^o
B
45^o
C
90^o
D
180^o

Cevabımı kontrol et (3)

Using FBD’s to write Equations of Equilibrium

Writing equilibrium equations requires defining coordinate axes. We will use the following coordinate system: x is positive to the right

y is positive toward the top of the page

positive moments result in a counterclockwise rotation

Using the above coordinates and with F₁and F₂ at 60^o, which is the correct equilibrium equation in the y direction F_y for member BC?

Tüm uygun cevapları seçin

A
B_y + C_y - F₂sin(60) = 0
B
B_y + C_y + F₂sin(60) = 0
C
B_y - C_y - F₂sin(60) = 0
D
B_y + C_y - F₂cos(60) = 0

Cevabımı kontrol et (3)

Using the above coordinates and with F₁and F₂ at 60^o, which is the correct equilibrium equation in the x direction F_x for member BC?

Tüm uygun cevapları seçin

A
B_x + F₂cos(60) = 0
B
B_x - F₂sin(60) = 0
C
B_x + F₂sin(60) = 0
D
B_x - F₂cos(60) = 0

Cevabımı kontrol et (3)

Using the above coordinates and with F₁and F₂ at 75^o, which is the correct equilibrium equation in the y direction F_yfor member AB?

Tüm uygun cevapları seçin

A
A_y + B_y + F₂sin(75) = 0
B
A_y - B_y - F₂sin(75) = 0
C
A_y + B_y - F₂sin(75) = 0
D
A_y + B_y + F₂cos(75) = 0

Cevabımı kontrol et (3)

Using the above coordinates and with F₁and F₂ at 75^o, which is the correct equilibrium equation in the x direction F_xfor member AB?

Tüm uygun cevapları seçin

Cevabımı kontrol et (3)

For the FBD of AB and with F₁at 75^o, which expression for the sum of moments about A, M_a is correct?

Tüm uygun cevapları seçin

A
-M_a - 2F₁sin(75) - 4B_y= 0
B
-M_a - 2F₁cos(75) - 4B_y= 0
C
M_a + 2F₁sin(75) - 4B_y= 0
D
M_a - 2F₁sin(75) - 4B_y= 0

Cevabımı kontrol et (3)

2D Free-Body Diagrams (FBDs)

Conceptual Questions: Drawing FBD’s

Use the Figure to Analyze the FBD of each Member

Using FBD’s to write Equations of Equilibrium

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