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Analysis of Trusses (Joint Method)

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Problem:

For the given truss, determine the forces in all members.

Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 1: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 1: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 1: – Diagram

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Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 1: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 1: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 1: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 1: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 1: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 1: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 1: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 1: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 1: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 1: – Diagram

Problem:

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Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 2: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 2: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 2: – Diagram

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Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 2: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 2: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 2: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 2: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 2: – Diagram

Problem:

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Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 3: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 3: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 3: – Diagram

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Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 3: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 3: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 3: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 3: – Diagram

Problem:

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Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 4: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 4: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 4: – Diagram

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Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 4: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 4: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 4: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 4: – Diagram

Problem:

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Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 5: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 5: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 5: – Diagram

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Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 5: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 5: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 5: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 5: – Diagram

Problem:

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Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 6: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 6: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 6: – Diagram

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Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 6: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 6: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 6: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 6: – Diagram

Problem:

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Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 7: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 7: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 7: – Diagram

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Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 7: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 7: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 7: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 7: – Diagram

Problem:

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Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 8: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 8: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 8: – Diagram

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Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 8: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 8: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 8: – Diagram Analysis of Trusses: Method of Joints | Statics of Rigid Bodies – Problem 8: – Diagram
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Problem (Symmetric truss by joint method):

A triangular truss has supports at A and C, 6m apart, and joint B located 3m horizontally from A and 4m above AC. A 20kN downward load acts at B. Determine the forces in AB and BC.

The geometry of each inclined member is a 3-4-5 triangle. By symmetry, the vertical reactions are 10kN each.

\[ \begin{aligned} \text{Joint B:}\quad 2F\left({4\over5}\right) &= 20 \\ F &= 12.5\ \text{kN} \end{aligned} \] $\boxed{F_{AB}=12.5\ \text{kN compression}},\qquad \boxed{F_{BC}=12.5\ \text{kN compression}}$

Problem (Bottom chord from joint equilibrium):

Using the same triangular truss, determine the force in member AC after finding that AB and BC are each 12.5kN in compression.

Use joint A. Member AB pushes joint A down-left because it is in compression.

\[ \begin{aligned} \text{Joint A:}\quad \sum F_x=0:\quad F_{AC}-12.5\left({3\over5}\right)&=0 \\ F_{AC}&=7.50\ \text{kN} \end{aligned} \] $\boxed{F_{AC}=7.50\ \text{kN tension}}$

Problem (Joint with vertical and horizontal loads):

At a truss joint, member AB is horizontal to the left and member AC is inclined 30° above the horizontal to the right. A 6kN downward load and a 4kN horizontal load to the right act at the joint. Determine the member forces, assuming tension pulls away from the joint.

Analyze the loaded joint directly.

\[ \begin{aligned} \text{Joint:}\quad \sum F_y=0:\quad F_{AC}\sin30^\circ-6&=0 \\ F_{AC}&=12\ \text{kN} \\ \sum F_x=0:\quad -F_{AB}+F_{AC}\cos30^\circ+4&=0 \\ F_{AB}&=14.39\ \text{kN} \end{aligned} \] $\boxed{F_{AC}=12\ \text{kN tension}},\qquad \boxed{F_{AB}=14.39\ \text{kN tension}}$
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Exam Generator Problems

Additional board-style practice items for this topic.

Question Bank: q27

PSAD - Statics / Analysis of Trusses / Engr. Janclyde Espinosa (Clidez)

For the truss shown below, the allowable forces for each member are the ff.
BC=70kN (T)
EC=60kN (C)
DE=25kN (C).

Compute the maximum safe value of P (in kN) if the strength of member EC governs.

  1. 52
  2. 61
  3. 43
  4. 48

Compute the maximum safe value of P (in kN) if the strength of member BC governs.

  1. 61
  2. 43
  3. 52
  4. 48

Compute the maximum safe value of P (in kN) if the strength of member DE governs.

  1. 43
  2. 52
  3. 61
  4. 48

Solution pending in psadquestions/q27.json.

Question Bank: q53

PSAD - Statics / Analysis of Trusses / Engr. Janclyde Espinosa (Clidez)

For the truss shown,

q53

If P=3000N and Q=1000N, determine the force in member CD.

  1. 5250 (C)
  2. 2250 (C)
  3. 5250 (T)
  4. 2250 (T)

If P=3000N and Q=1000N, determine the force in member JK.

  1. 2250 (T)
  2. 5250 (C)
  3. 2250 (C)
  4. 5250 (T)

If FCD = 6000N and FGD= 1000N (both under compression), determine the value of P.

  1. 5167.95
  2. 5237.89
  3. 5436.75
  4. 5284.86

Solution pending in psadquestions/q53.json.

Question Bank: q324

PSAD - Statics / Analysis of Trusses / Engr. Janclyde Espinosa (Clidez)

For the truss shown, determine the forces in all members by using the method of joints/sections.

q324

Force in AB

  1. 41.408 (T)
  2. 41.408 (C)
  3. 36.592 (T)
  4. 36.592 (C)

Force in AE

  1. 18.262 (C)
  2. 18.262 (T)
  3. 11.408 (C)
  4. 11.408 (T)

Force in BE

  1. 5.74 (C)
  2. 5.74 (T)
  3. 7.493 (T)
  4. 7.493 (C)

Force in EF

  1. 11.408 (C)
  2. 11.408 (T)
  3. 18.262 (C)
  4. 18.262 (T)

Force in BF

  1. 7.493 (T)
  2. 7.493 (C)
  3. 5.74 (C)
  4. 5.74 (T)

Force in BC

  1. 36.592 (T)
  2. 36.592 (C)
  3. 40 (T)
  4. 40 (C)

Force in CD

  1. 36.592 (T)
  2. 36.592 (C)
  3. 40 (T)
  4. 40 (C)

Force in DF

  1. 58.576 (C)
  2. 58.576 (T)
  3. 41.408 (T)
  4. 41.408 (C)

Force in CF

  1. 40 (T)
  2. 40 (C)
  3. 41.408 (T)
  4. 41.408 (C)

Solution pending in psadquestions/q324.json.

Question Bank: q423

PSAD - Statics / Analysis of Trusses / Engr. Janclyde Espinosa (Clidez)

For the truss shown, if P=20kN

q423

Determine the force of member AB in kN

  1. 38
  2. 46
  3. 28
  4. 21

Determine the force of member AC in kN

  1. 6.84
  2. 5.13
  3. 12.42
  4. 9.44

Solution pending in psadquestions/q423.json.

Question Bank: q615

PSAD - Statics / Analysis of Trusses / Engr. Janclyde Espinosa (Clidez)

The truss shown is subjected to a lateral load of F=12kN.
a=1.5m
b=4m
c=3.5m

q615

Determine the reaction at A in kN.

  1. 6
  2. 7
  3. 8
  4. 9

Determine the force in member AE, in kN.

  1. 4.19 (T)
  2. 1.91 (T)
  3. 14.40 (C)
  4. 8.98 (C)

Determine the reaction at D, in kN.

  1. 13.4
  2. 6.0
  3. 12.0
  4. 9.1

Solution pending in psadquestions/q615.json.

Question Bank: q616

PSAD - Statics / Analysis of Trusses / Mastermatician

A transmission tower is loaded as shown.
P1=10kN
P2=13kN
P3=16kN

q616

Determine the total reaction at H in kN.

  1. 46.55
  2. 25.41
  3. 39.00
  4. 52.11

Determine the force in member CJ, in kN.

  1. 10.7
  2. 9.7
  3. 6.1
  4. 16.1

Solution pending in psadquestions/q616.json.

Question Bank: q624

PSAD - Statics / Analysis of Trusses / Mastermatician

Refer to the figure shown. Diagonals BH, CG, HD, and CI are flexible cables and are, therefore, only capable of carrying tensile forces.
P1=2.5kN
P2=1.2kN
P3=1.2kN

L1=3m
L2=2.25m
L3=3m

q624

Determine the force in member HD.

  1. 0.000
  2. 0.800
  3. 0.784
  4. 0.792

Determine the force in member CI.

  1. 0.800
  2. 0.000
  3. 0.792
  4. 0.784

What is the force in member BH?

  1. 0.000
  2. 0.800
  3. 0.792
  4. 0.784

What is the force in member CG?

  1. 0.792
  2. 0.000
  3. 0.800
  4. 0.784

Solution pending in psadquestions/q624.json.

Question Bank: q625

PSAD - Statics / Analysis of Trusses / Mastermatician

Refer to the figure shown. Diagonals BH, CG, HD, and CI are flexible cables and are, therefore, only capable of carrying tensile forces.
P1=2.5kN
P2=0.0kN
P3=1.2kN

L1=3m
L2=2.25m
L3=3m

q625

Determine the force in member CG, in kN.

  1. 2.093
  2. 1.850
  3. 0.445
  4. 1.697

Determine the force in member DH, in kN.

  1. 1.850
  2. 0.445
  3. 1.697
  4. 2.093

Determine the force in member DI, in kN.

  1. 1.48
  2. 1.64
  3. 1.66
  4. 0.784

Solution pending in psadquestions/q625.json.