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Equilibrium of Non-concurrent Force Systems

  1. Translational Equilibrium: The sum of all external forces in every direction must be zero
$$\sum F_x = 0,\quad \sum F_y = 0,\quad \sum F_z = 0 \quad \text{(for 3D systems)}$$
  1. Rotational Equilibrium: The sum of all moments about any point must also be zero
$$\sum M = 0$$

In engineering mechanics, a non-concurrent force system refers to a group of forces whose lines of action do not intersect at a single point. These forces may act on different parts of a rigid body and can include forces and moments (torques). To achieve equilibrium in such systems, a body must satisfy both conditions above.


    General Resultant of Non-concurrent Force Systems:
$$R = \sqrt{(\sum F_x)^2 + (\sum F_y)^2 + (\sum F_z)^2}$$


    For Forces Lying on a 2D Plane Only
$$\tan(\theta) = \frac{\sum F_y}{\sum F_x}$$
    Directional Cosines:
\(\cos(\theta_x) = \frac{F_x}{F}\)

\(\cos(\theta_y) = \frac{F_y}{F}\)

\(\cos(\theta_z) = \frac{F_z}{F}\)
    The location of the resultant force is determined by Varignon's Theorem.
$$ R(d_x) = F_1(x_1) + F_2(x_2) + \cdots + F_n(x_n) $$ $$ R(d_y) = F_1(y_1) + F_2(y_2) + \cdots + F_n(y_n) $$
Concept Concept Concept Concept Concept Concept Concept Concept Concept

Problem:

a. Calculate the location of the resultant from point D.
b. Prove that the resultant force intersects point E (as indicated below)
c. Determine the distance dx and dy from point D to the resultant force and indicate the location relative to D.
d. Determine the distance from point B to the resultant force.
e. Resolve the system into a resultant-couple system.

Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 1: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 1: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 1: – Diagram

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Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 1: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 1: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 1: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 1: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 1: – Diagram
    Below is a scaled drawing of the figure (modeled using AutoCad).
Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 1: – Diagram
    We can obtain the moment caused by the resultant force about point D so that we can transfer the resultant so that it intersects point D. The moment (couple) will be applied at point D for clarity.
Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 1: – Diagram
    Finally, we have this resultant-couple system that replaces the system above.
Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 1: – Diagram

Problem:

For the beam shown, beam ABC is supporting beam CD.
Which of the following most nearly gives the reaction at C in kN.
A. 250
B. 150
C. 100
D. 200

Which of the following most nearly gives the reaction at D in kN.
A. 250
B. 150
C. 100
D. 200

Which of the following most nearly gives the value of "x" if the reaction at B is 380 N.
A. 1
B. 1.5
C. 2
D. 3

Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 2: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 2: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 2: – Diagram

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Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 2: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 2: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 2: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 2: – Diagram

Problem:

The uniform 30kg bar with end rollers is supported by the horizontal and vertical surfaces and the wire AC.

a. Determine the tension in the wire.
b. Determine the reaction at A.
c. Determine the moment at B.

Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 3: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 3: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 3: – Diagram

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Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 3: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 3: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 3: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 3: – Diagram

Problem:

The uniform rod weighs 420N and has its center of gravity at G as shown.

a. What is the reaction at B?
b. What is the tension in the cable?
c. What is the reaction at A?

Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 4: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 4: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 4: – Diagram

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Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 4: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 4: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 4: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 4: – Diagram

Problem:

A three-legged stool is subjected to the load P as shown. If P=200N, compute the following:

a. Reaction under leg A
b. Reaction under leg B
c. Reaction under leg C

Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 5: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 5: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 5: – Diagram

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Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 5: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 5: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 5: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 5: – Diagram

Problem:

For the figure shown, compute the reaction at the hinged support at A if the weight of the cylinder is 1000N.

Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 6: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 6: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 6: – Diagram

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Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 6: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 6: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 6: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 6: – Diagram

Problem:

For the figure shown, calculate the angle of tilt, θ, so that the contact force at B will be one-half that of A for the smooth cylinder.

Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 7: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 7: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 7: – Diagram

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Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 7: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 7: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 7: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 7: – Diagram

Problem: Walkway from a Pier to a Float

To accomodate the rise and fall of tide, a walkway from a pier to a float is supported by two rollers as shown. The center of mass of the 300-kg walkway is at G.
a. Calculate the force under the roller at A in Newtons.
b. Calculate the tension T in the horizontal cable which is attached to the cleat in Newtons.
c. Calculate the force in the roller at B in Newtons.

Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 8: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 8: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 8: – Diagram

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Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 8: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 8: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 8: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 8: – Diagram

Problem: Cylinder Placed between a Rigid Member

The cylinder below has a mass of 200kg. Determine the following:
a. The normal reaction at D in Newtons.
b. The normal reaction at the wall at C in Newtons.
c. The tension in the cable at D in Newtons.

Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 9: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 9: – Diagram Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 9: – Diagram

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Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 9: – Diagram

FBD of cylinder

Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 9: – Diagram
$$ W = 200(9.81) = 1962\ \text{N}, \qquad r = 1\ \text{m}, \qquad h = 3\ \text{m} $$ $$ \theta = 30^\circ, \qquad a = 90^\circ - 30^\circ = 60^\circ $$

Vertical equilibrium of the cylinder:

$$ \sum F_y = 0 $$ $$ -1962 + N_D\sin 60^\circ = 0 $$ $$ N_D = \frac{1962}{\sin 60^\circ} = 1308\sqrt{3} = 2265.52246\ \text{N} $$

Horizontal equilibrium of the cylinder:

$$ \sum F_x = 0 $$ $$ -2265.52246\cos 60^\circ + N_C = 0 $$ $$ N_C = 1132.76123\ \text{N} $$

Geometry of the contact point and cable line:

$$ x = 1\cos 60^\circ = 0.5\ \text{m}, \qquad y = 1\sin 60^\circ = 0.86603\ \text{m} $$ $$ \cos 30^\circ = \frac{1 + 0.5}{d_{AD}} $$ $$ d_{AD} = 1.732050807568877\ \text{m} $$ $$ z = 1.732050807568877\sin 30^\circ = 0.86603\ \text{m} $$

All moment equations are taken about point A, the hinge support, so the unknown hinge reactions at A are eliminated. The normal reaction used depends on the chosen FBD: the FBD considering the contact at D uses $N_D$ and does not include $N_C$, while the external FBD uses the normal reaction at C and does not include $N_D$. Since $N_D$ is the resultant effect of the cylinder's weight $W$ and the wall reaction $N_C$, $N_C$ is not written separately when $N_D$ is already being considered.

FBD considering the normal reaction at D:

Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 9: – Diagram
$$ \sum M_A = 0 $$ $$ 2265.52246(1.732050807568877) - T_B(3) = 0 $$ $$ T_B = 1308\ \text{N} $$

Using the external FBD, the moment equation uses the normal reaction at C instead of the normal reaction at D:

Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 9: – Diagram
$$ \sum M_A = 0 $$ $$ -T_B(3) + 1132.76123(0.86603 + 0.86603) + 1962(1) = 0 $$ $$ T_B = 1308\ \text{N} $$
Equilibrium of Non-Concurrent Force Systems | Statics of Rigid Bodies – Problem 9: – Diagram

Additional equilibrium equations from the external FBD (checking):

$$ \sum M_B = 0 $$ $$ -A_x(3) - 1132.76123(3 - 0.86603 - 0.86603) + 1962(1) = 0 $$ $$ A_x = 175.23877\ \text{N} $$ $$ \sum F_x = 0 $$ $$ -T_B + 1132.76123 + 175.23877 = 0 $$ $$ T_B = 1308\ \text{N} $$ $$ \sum F_y = 0 $$ $$ A_y = 1962\ \text{N} $$
$$ \boxed{N_D = 2265.52\ \text{N}}, \qquad \boxed{N_C = 1132.76\ \text{N}}, \qquad \boxed{T_B = 1308\ \text{N}} $$

Problem (Simple beam reactions):

A simply supported 6m beam carries a 12kN point load 2m from the left support A. Determine the reactions at A and B.

Use moment equilibrium to find one reaction, then vertical equilibrium for the other.

\[ \begin{aligned} \sum M_A=0:\quad B_y(6)-12(2) &= 0 \\ B_y &= 4\ \text{kN} \\ \sum F_y=0:\quad A_y+B_y-12 &= 0 \\ A_y &= 8\ \text{kN} \end{aligned} \] $\boxed{A_y=8\ \text{kN upward}},\qquad \boxed{B_y=4\ \text{kN upward}}$

Problem (Beam with an inclined force):

A 5m simply supported beam has a 10kN force applied at midspan, inclined 30° from the vertical toward the right. Determine the support reactions if A is a pin and B is a roller.

Resolve the inclined force first. The roller at B has only a vertical reaction.

\[ \begin{aligned} F_x &= 10\sin30^\circ=5\ \text{kN} \\ F_y &= 10\cos30^\circ=8.66\ \text{kN} \\ \sum M_A=0:\quad B_y(5)-8.66(2.5) &= 0 \\ B_y &= 4.33\ \text{kN},\quad A_y=4.33\ \text{kN},\quad A_x=5\ \text{kN left} \end{aligned} \] $\boxed{A_x=5\ \text{kN left}},\quad \boxed{A_y=4.33\ \text{kN}},\quad \boxed{B_y=4.33\ \text{kN}}$

Problem (Beam with a couple moment):

A 4m simply supported beam carries a 20kN downward load 1m from A and a clockwise couple moment of 12kN-m. Determine the vertical reactions.

Take counterclockwise moment as positive.

\[ \begin{aligned} \sum M_A=0:\quad B_y(4)-20(1)-12 &= 0 \\ B_y &= 8\ \text{kN} \\ A_y+B_y-20 &= 0 \\ A_y &= 12\ \text{kN} \end{aligned} \] $\boxed{A_y=12\ \text{kN upward}},\qquad \boxed{B_y=8\ \text{kN upward}}$
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Exam Generator Problems

Additional board-style practice items for this topic.

Question Bank: q1

PSAD - Statics / Equilibrium of Nonconcurrent Force Systems / Engr. Janclyde Espinosa (Clidez)

CE Board Nov. 2012
A concrete block of weight W is held by a ring anchor bolt fastened to two guy wires.

q1

Calculate the resultant force acting on the bolt in kN.

  1. 10.9
  2. 9.8
  3. 7.8
  4. 11.3

Determine the angle (in degrees) the resultant pull makes with the horizontal.

  1. 54.5
  2. 55.67
  3. 53.13
  4. 56.37

To prevent uplift, what is the minimum weight (in kN) of the concrete block if the required factor of safety is 1.3?

  1. 11.53
  2. 8.87
  3. 6.34
  4. 12.92

Part 1.

Resolve each wire tension into horizontal and vertical components and sum:
$ \Sigma F_x = (14 - 7)\cos 25^\circ = 6.33 \text{ kN} $
$ \Sigma F_y = (14 + 7)\sin 25^\circ = 8.87 \text{ kN} $
$ R = \sqrt{(\Sigma F_x)^2 + (\Sigma F_y)^2} = \sqrt{6.33^2 + 8.87^2} $
$ \boxed{R = 10.9 \text{ kN}} $

Part 2.

$ \tan\theta = \dfrac{\Sigma F_y}{\Sigma F_x} = \dfrac{8.87}{6.33} $
$ \boxed{\theta = 54.5^\circ} $

Part 3.

The weight must resist the vertical (uplift) component of the resultant with the required factor of safety:
$ W_{min} = FS \times \Sigma F_y = 1.3 \times 8.87 $
$ \boxed{W_{min} = 11.53 \text{ kN}} $

Question Bank: q2

PSAD - Statics / Equilibrium of Nonconcurrent Force Systems / Engr. Janclyde Espinosa (Clidez)

A boom supports a 100N load. If the tension in the cable is 200N,

q2

Determine the angle α (in degrees)

  1. 21.47
  2. 20.92
  3. 23.45
  4. 19.87

Determine the angle θ (in degrees)

  1. 42.94
  2. 41.84
  3. 46.9
  4. 39.74

Determine the force in the boom in Newtons.

  1. 254.26 (C)
  2. 254.26 (T)
  3. 264.52 (C)
  4. 264.52 (T)

Solution pending in psadquestions/q2.json.

Question Bank: q3

PSAD - Statics / Equilibrium of Nonconcurrent Force Systems / Engr. Janclyde Espinosa (Clidez)

CE Board Nov. 2024
For the truss shown, members AD and BC are flexible cables.

q3

Calculate the vertical reaction (kN) at A.

  1. 30.286
  2. 31.218
  3. 20.616
  4. 42.333

Calculate the force in member AC (kN).

  1. 31.218 (C)
  2. 31.218 (T)
  3. 42.333 (C)
  4. 42.333 (T)

Calculate the force in member BD (kN).

  1. 20.616 (C)
  2. 30.386 (C)
  3. 30.386 (T)
  4. 20.616 (T)

Solution pending in psadquestions/q3.json.

Question Bank: q6

PSAD - Statics / Equlibrium of Rigid Bodies / Engr. Janclyde Espinosa (Clidez)

A load W = 20kN is to be lifted using the crane which is hinged at B as shown. Neglect the weight of the crane.

q6

Determine the force in cable AC (in kN)

  1. 22.627
  2. 19.618
  3. 24.879
  4. 29.6

Determine the resultant reaction at B (in kN)

  1. 39.4
  2. 46.78
  3. 23.43
  4. 27.9

Determine the largest load W the can be lifted if the maximum force of cable AC is 50kN.

  1. 44.194
  2. 56.78
  3. 30.16
  4. 23.27

Solution pending in psadquestions/q6.json.

Question Bank: q18

PSAD - Statics / Equilibrium of Rigid Bodies / Engr. Janclyde Espinosa (Clidez)

CE Board November 2024
Two cylinders are loaded as shown and are connected by a rigid curved rod parallel to the smooth cylindrical surface. Neglect the diameter of the cylinders.
W1=750N, W2=420N
ϴ=90º, R=6m

q18

If the surfaces are frictionless, what is α to maintain equilibrium?

  1. 60.75
  2. 50.17
  3. 45.14
  4. 76.12

If the coefficient of friction is μs=0.2 in the contacting surfaces, what is α to prevent rotation counterclockwise?

  1. 38.66
  2. 56.88
  3. 49.44
  4. 50.17

If the coefficient of friction is μs=0.015 in the contacting surfaces, which of the following gives α to impend motion?

  1. 59.15
  2. 47.15
  3. 34.34
  4. 62.34

Solution pending in psadquestions/q18.json.

Question Bank: q24

PSAD - Statics / Equilibrium of Rigid Bodies / Engr. Janclyde Espinosa (Clidez)

For the assembly shown, beam AB weighs 100lbs. It is loaded with a force P=200lbs. A frictionless pulley with radius "r" weighs 80lbs and is attached at the end of the beam at point B, supported by two ropes inclined at angles x and y at points C and D. If a=2ft, b=3ft, angles x & y are 30º and 40º, respectively, and r=6 in.,

What is the reaction at B?

  1. 327
  2. 130
  3. 300
  4. 343

What is the tension in the rope?

  1. 183.8
  2. 118.8
  3. 131.9
  4. 123.7

What is the reaction at A?

  1. 345
  2. 355
  3. 370
  4. 327

Solution pending in psadquestions/q24.json.

Question Bank: q32

PSAD - Statics / Equilibrium of Rigid Bodies / Engr. Janclyde Espinosa (Clidez)

CE Board Nov 2011 and April 2025
A load W=30kN is lifted by a boom BCD making an angle, α=60º from the vertical axis as shown. Neglect the weight of the boom.

q32

Determine the angle β between the cables AC and AD, in degrees. Note: Point C is midway points B and D.

  1. 30
  2. 35
  3. 25
  4. 20

Compute the tension in cable AC, in kN.

  1. 25.36
  2. 43.92
  3. 25.98
  4. 34.92

Determine the reaction at B in kN.

  1. 54.77
  2. 51.96
  3. 58.09
  4. 53.49

Solution pending in psadquestions/q32.json.

Question Bank: q41

PSAD - Statics / Equilibrium of Rigid Bodies / Engr. Janclyde Espinosa (Clidez)

A cylindrical rum 2m in radius is held by a rigid bar AB hinged at A and a flexible wire cable BC as shown. The drum weighs 1500N and strut AB has a length of 10m. Neglect friction in all contact surfaces.

q41

Which of the following gives the normal reaction at D in Newtons.

  1. 3000
  2. 2000
  3. 3500
  4. 2500

Which of the following gives the vertical reaction at A in Newtons.

  1. 146.8
  2. 185.3
  3. 125.9
  4. 564.2

Which of the following gives the tension in cable BC in Newtons.

  1. 2255.4
  2. 2768.3
  3. 2143.9
  4. 2854.1

Solution pending in psadquestions/q41.json.

Question Bank: q127

PSAD - Statics / Equilibrium of Rigid Bodies / Engr. Janclyde Espinosa (Clidez)

For a system of pulleys shown,

q127

Determine the value of P in kN if W=450kN

  1. 50
  2. 40
  3. 90
  4. 75

If each pulley weighs 36kN and W=720kN, compute the value of P in kN to make the system in equilibrium.

  1. 96
  2. 72
  3. 80
  4. 108

If each pulley weighs 24kN and P=60kN, compute the ratio of W to P to make the system in equilibrium.

  1. 28
  2. 32
  3. 25
  4. 36

Solution pending in psadquestions/q127.json.

Question Bank: q136

PSAD - Statics / Equilibrium of Rigid Bodies / Engr. Janclyde Espinosa (Clidez)

For the beam shown, if w=22kN/m and F=135kN,

q136

Which of the following most nearly gives the moment at A in kN-m?

  1. 2130.50
  2. 1982.50
  3. 2170.30
  4. 2120.60

Which of the following most nearly gives the vertical reaction at A in kN?

  1. 123.20
  2. 125.20
  3. 122.20
  4. 120.20

Solution pending in psadquestions/q136.json.

Question Bank: q143

PSAD - Statics / Equilibrium of Rigid Bodies / Engr. Janclyde Espinosa (Clidez)

A load W = 50kN is lifted by a boom BCD as shown. Neglecting the weight of the boom,

q143

Compute the horizontal reaction at B in kN.

  1. 86.60
  2. 54.56
  3. 72.33
  4. 68.66

Compute the tension in cable AC in kN.

  1. 42.24
  2. 44.77
  3. 37.83
  4. 47.64

Caclulate the vertical reaction at B in kN.

  1. 28.88
  2. 30.87
  3. 41.33
  4. 34.64

Solution pending in psadquestions/q143.json.

Question Bank: q154

PSAD - Statics / Equilibrium of Rigid Bodies / Engr. Janclyde Espinosa (Clidez)

A quarter-circular cantilever beam is subjected to a uniform pressure as shown. If the pressure p = 15kN/m and r = 6m, compute the moment at A.

Answer:

  1. 599.79
  2. 732.35
  3. 662.42
  4. 492.82

Solution pending in psadquestions/q154.json.

Question Bank: q155

PSAD - Statics / Equilibrium of Rigid Bodies / Engr. Janclyde Espinosa (Clidez)

In the figure below,

Find the force P required to turn the wheel over the block.

  1. 666.67N
  2. 433.33N
  3. 777.78N
  4. 866.67N

If P will be inclined at an angle ⌀, find ⌀ so that P is minimum.

  1. 53.13º
  2. 36.87º
  3. 45º
  4. 50º

Solution pending in psadquestions/q155.json.

Question Bank: q283

PSAD - Statics / Equilibrium of Rigid Bodies / Engr. Janclyde Espinosa (Clidez)

A 40-kg cylinder is held on position on an inclined plane by means of a wire AB as shown in the figure.

q283

Determine the reaction at the surface of the inclined plane.

  1. 436.02N @45º
  2. 436.02N @74.75º
  3. 463.02N @45º
  4. 463.02N @74.75º

Determine the tension in the wire.

  1. 319.5N
  2. 392.4N
  3. 350N
  4. 326.75N

Solution pending in psadquestions/q283.json.

Question Bank: q285

PSAD - Statics / Moment of Forces / Engr. Janclyde Espinosa (Clidez)

Three forces are applied to a beam. Determine the moments produced by each of the forces about point A and find their resultant moment.

q285

Moment about A caused by F1.

  1. 1272.79lb-ft (counter-clockwise)
  2. 1272.79lb-ft (clockwise)
  3. 6388.27lb-ft (counter-clockwise)
  4. 6388.27lb-ft (clockwise)

Moment about A caused by F2.

  1. 7794.23lb-ft (counter-clockwise)
  2. 7794.23lb-ft (clockwise)
  3. 3897.11lb-ft (counter-clockwise)
  4. 3897.11lb-ft (clockwise)

Moment about A caused by F3.

  1. 1711.73lb-ft (clockwise)
  2. 1711.73lb-ft (counter-clockwise)
  3. 2545.56lb-ft (counter-clockwise)
  4. 2545.56lb-ft (clockwise)

Total moment about A.

  1. 7355.29lb-ft (counter-clockwise)
  2. 7355.29lb-ft (clockwise)
  3. 8233.17lb-ft (counter-clockwise)
  4. 8233.17lb-ft (clockwise)

Solution pending in psadquestions/q285.json.

Question Bank: q316

PSAD - Statics / Equilibrium of Rigid Bodies / Engr. Janclyde Espinosa (Clidez)

Compute the horizontal and vertical components of the support reactions of the beam shown.

q316

What is the internal horizontal reaction at C?

  1. 0
  2. 10
  3. 20
  4. 15

What is the internal vertical reaction at C?

  1. 10
  2. 20
  3. 15
  4. 40

What is the horizontal reaction at A?

  1. 0
  2. 10
  3. 74
  4. 20

What is the vertical reaction at A?

  1. 18
  2. 16
  3. 14
  4. 12

What is the vertical reaction at B?

  1. 56
  2. 42
  3. 64
  4. 68

Solution pending in psadquestions/q316.json.

Question Bank: q317

PSAD - Statics / Equilibrium of Rigid Bodies / Engr. Janclyde Espinosa (Clidez)

Compute the horizontal and vertical components of the support reactions of the compound beam shown. Each support is labeled as A, B, C, and D, respectively.

q317

What is the horizontal reaction at A?

  1. 0
  2. 10
  3. 20
  4. 15

What is the vertical reaction at A?

  1. 20
  2. 10
  3. 15
  4. 40

What is the vertical reaction of the internal roller at B?

  1. 20
  2. 10
  3. 15
  4. 30

What is the vertical reaction at C?

  1. 30.67
  2. 26.67
  3. 27.85
  4. 28.75

What is the horizontal reaction at D?

  1. 0
  2. 10
  3. 15
  4. 40

What is the vertical reaction at D?

  1. 1.33
  2. 2.67
  3. 5.33
  4. 4.67

Solution pending in psadquestions/q317.json.

Question Bank: q323

PSAD - Statics / Equilibrium of Rigid Bodies / Engr. Janclyde Espinosa (Clidez)

If the coefficient of static friction at contact points A and B in the figure below is μs=0.25, the weight of the spool is 70kg, and R1=0.6m; R2=0.9m, determine the following:

q323

Maximum force P that can be applied without causing the spool to move.

  1. 210.214
  2. 448.457
  3. 112.114
  4. 103.48

Normal Reaction at B.

  1. 448.457
  2. 210.214
  3. 112.114
  4. 103.48

Normal Reaction at A.

  1. 112.114
  2. 448.457
  3. 210.214
  4. 103.48

Solution pending in psadquestions/q323.json.

Question Bank: q527

PSAD - Statics / Resultant/Equilibrium of Nonconcurrent Force Systems / Engr. Janclyde Espinosa (Clidez)

For the system shown:

q527

Calculate the location of the resultant from point D.

  1. 0.832m left of D
  2. 0.832m right of D
  3. 1.5m left of D
  4. 1.5m right of D

Determine the horizontal distance from the resultant to point D and indicate the direction.

  1. 1.5m left of D
  2. 1.5m right of D
  3. 0.832m left of D
  4. 0.832m right of D

Determine the vertical distance from the resultant to point D and indicate the direction.

  1. 1m above D
  2. 1m below D
  3. 1.5m above D
  4. 1.5m below D

Determine the distance from point B to the resultant force.

  1. 0.55m
  2. 0.66m
  3. 0.44m
  4. 0.33m

Solution pending in psadquestions/q527.json.

Question Bank: q528

PSAD - Statics / Resultant/Equilibrium of Nonconcurrent Force Systems / Engr. Deguma

The uniform 30kg bar with end rollers is supported by the horizontal and vertical surfaces and the wire AC.

q528

Determine the tension in the wire in Newtons.

  1. 295.34
  2. 235.44
  3. 196.20
  4. 73.55

Determine the reaction at A in Newtons.

  1. 73.55
  2. 76.48
  3. 83.42
  4. 90.54

Determine the moment at B in Newton-meter.

  1. 235.44
  2. 295.34
  3. 196.20
  4. 194.72

Solution pending in psadquestions/q528.json.

Question Bank: q530

PSAD - Statics / Resultant/Equilibrium of Nonconcurrent Force Systems / Engr. Deguma

A three-legged stool is subjected to the load P as shown. If P=200N, compute the following:

q530

Reaction under leg A in Newtons

  1. 106.67
  2. 46.67
  3. 143.33
  4. 56.67

Reaction under leg B in Newtons

  1. 46.67
  2. 106.67
  3. 143.33
  4. 56.67

Reaction under leg C in Newtons

  1. 46.67
  2. 106.67
  3. 143.33
  4. 56.67

Solution pending in psadquestions/q530.json.

Question Bank: q531

PSAD - Statics / Resultant/Equilibrium of Nonconcurrent Force Systems / Engr. Deguma

The weight of the cylinder in the figure shown is 1000N.

q531

Compute the normal force between the cylinder and bar AB.

  1. 1666.67
  2. 833.33
  3. 1000.00
  4. 1118.03

Compute the tension in cable BC.

  1. 833.33
  2. 1118.03
  3. 1000.00
  4. 1666.67

Compute the reaction at the hinged support at A.

  1. 1118.03
  2. 1666.67
  3. 1000.00
  4. 833.33

Solution pending in psadquestions/q531.json.

Question Bank: q532

PSAD - Statics / Resultant/Equilibrium of Nonconcurrent Force Systems / Engr. Deguma

For the figure shown, calculate the angle of tilt, θ, so that the contact force at B will be one-half that of A for the smooth cylinder.

q532

Answer:

  1. 18.43º
  2. 20.54º
  3. 17.56º
  4. 23.20º

Solution pending in psadquestions/q532.json.

Question Bank: q548

PSAD - Statics / Equilibrium of Rigid Bodies / Engr. Deguma

In the figure shown, if w=800N/m, compute the following:

q548

The reaction at A in kN.

  1. 3.33
  2. 2.40
  3. 4.20
  4. 3.67

The horizontal reaction at B in kN.

  1. 2.40
  2. 3.33
  3. 4.20
  4. 3.67

The vertical reaction at B in Newtons.

  1. 133
  2. 233
  3. 166
  4. 240

Solution pending in psadquestions/q548.json.

Question Bank: q550

PSAD - Structural Theory / Equilibrium of Rigid Bodies / Engr. Deguma

The rigid bar CDE is welded at point C to the uniform steel beam shown in. A steel beam has dimensions b=25 mm and d = 85 mm. Use E = 200 GPa.

q550

Determine the reaction at the roller support in Newtons.

  1. 2580
  2. 2340
  3. 2150
  4. 1870

Determine the rotation (in degrees) at the roller support.

  1. 1.22
  2. 1.02
  3. 0.67
  4. 2.43

Determine the deflection (in mm) at the midspan.

  1. 33.12
  2. 16.80
  3. 22.10
  4. 27.60

Solution pending in psadquestions/q550.json.

Question Bank: q554

PSAD - Statics / Resultant/Equilibrium of Nonconcurrent Force Systems / Engr. Deguma

For the truss shown,

q554

Which of the following most nearly gives the horizontal component of the resultant of forces acting in the truss?

  1. 4000N
  2. 3000N
  3. 5000N
  4. 6000N

Which of the following most nearly gives the vertical component of the resultant of forces acting in the truss.

  1. 10000N
  2. 11000N
  3. 9000N
  4. 12000N

Which of the following most nearly gives the horizontal distance from the left support where the resultant of the forces acts.

  1. 4.80m
  2. 3.60m
  3. 5.40m
  4. 6.80m

Solution pending in psadquestions/q554.json.

Question Bank: q587

PSAD - Statics / Resultant/Equilibrium of Nonconcurrent Force Systems / Mastermatician

Consider the figure shown below. Neglect the self-weight of members AB and BC.

q587

Determine the horizontal reaction at A.

  1. 4.59
  2. 2.34
  3. 2.16
  4. 5.40

Determine the vertical reaction at C.

  1. 2.34
  2. 4.59
  3. 2.16
  4. 5.40

Solution pending in psadquestions/q587.json.

Question Bank: t30

PSAD - Statics / Equilibrium of Rigid Bodies / Civil Engineering Refresher

Forces P1 = 1.8 kN (30°), P2 = 0.9 kN (vertical), and P3 = 0.45 kN (45°) act on a beam.

Determine the magnitude of the resultant.

  1. 2.45 kN
  2. 3.15 kN
  3. 2.12 kN
  4. 1.24 kN

From the beam system in Question 34, calculate the vertical reaction at support B, assuming the beam is 2 m long and forces act at the midpoint.

  1. 1.07 kN
  2. 2.12 kN
  3. 0.90 kN
  4. 1.24 kN

From the beam system in Question 34, determine the horizontal reaction at support B, assuming B is a roller support.

  1. 0 kN
  2. 1.24 kN
  3. 1.56 kN
  4. 0.45 kN

Part 1.

Resolve the inclined forces into components. Taking the horizontal components of $P_1$ and $P_3$ in opposite directions:
$R_x = 1.8\cos 30^\circ - 0.45\cos 45^\circ = 1.241$ kN
$R_y = 0.9 + 1.8\sin 30^\circ + 0.45\sin 45^\circ = 2.118$ kN
$R = \sqrt{R_x^2 + R_y^2} = \sqrt{1.241^2 + 2.118^2}$
$\boxed{R = 2.45\text{ kN}}$

Part 2.

The total downward vertical component is:
$R_y = 0.9 + 1.8\sin 30^\circ + 0.45\sin 45^\circ = 2.118$ kN
Since the forces act at the midpoint of a simply supported 2 m beam, the vertical reactions are equal:
$B_y = \frac{R_y}{2} = \frac{2.118}{2}$
$\boxed{B_y = 1.07\text{ kN}}$

Part 3.

A roller support cannot resist horizontal force. Therefore the horizontal reaction at support B is zero regardless of the applied horizontal components.
$\boxed{B_x = 0\text{ kN}}$

Question Bank: t32

PSAD - Statics / Equilibrium of Rigid Bodies / Civil Engineering Refresher

Three cylinders (A, B, C) with radii 4 m, 6 m, and 5 m are piled in a ditch.

Find the reaction between cylinder A and B.

  1. 100 kN
  2. 93.36 kN
  3. 75.04 kN
  4. 40.00 kN

From the cylinder configuration in Question 40, find the reaction between the vertical wall and cylinder B.

  1. 93.36 kN
  2. 100.00 kN
  3. 75.04 kN
  4. 15.00 kN

From the cylinder configuration in Question 40, find the reaction between the floor and cylinder A.

  1. 75.04 kN
  2. 93.36 kN
  3. 100.00 kN
  4. 80.00 kN

Solution pending in psadquestions/t32.json.

Question Bank: t33

PSAD - Statics / Equilibrium of Rigid Bodies / Civil Engineering Refresher

A storage tank (W = 2000 N, r = 1.0 m) is pushed over a 0.25 m step.

Find the horizontal force F required to just break contact at point A.

  1. 1732 N
  2. 2000 N
  3. 2646 N
  4. 1500 N

From Question 43, find the magnitude of the reaction at point B at the instant contact at A is broken.

  1. 2646 N
  2. 2000 N
  3. 1732 N
  4. 3732 N

Part 1.

At impending motion over the step, contact at A is just broken and the tank tends to rotate about point B. Taking moments about B eliminates the reaction at B.
$F(1.00) = 2000(0.866)$
$F = 1732$ N
$\boxed{F = 1732\text{ N}}$

Part 2.

At the instant contact at A is broken, equilibrium requires the reaction at B to balance the horizontal push and the weight components:
$R_B = \sqrt{F^2 + W^2}$
$R_B = \sqrt{1732^2 + 2000^2}$
$\boxed{R_B = 2646\text{ N}}$

Question Bank: t34

PSAD - Statics / Equilibrium of Rigid Bodies / Civil Engineering Refresher

A rod is connected to a pin at A and a chord at B. It holds a 176 N cylindrical drum.

Find the force between the drum and the rod.

  1. 352 N
  2. 176 N
  3. 88 N
  4. 304 N

From the rod/drum system in Question 45, find the force in the chord BC if the chord is at a 36.87° angle.

  1. 132.32 N
  2. 352.00 N
  3. 96.61 N
  4. 221.19 N

From the rod/drum system in Question 45, calculate the magnitude of the total reaction at pin A.

  1. 221.19 N
  2. 132.32 N
  3. 198.94 N
  4. 96.61 N

Solution pending in psadquestions/t34.json.