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Analysis of Trusses (Method of Sections)

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Problem:

Determine the force in members CD, CH, GH, and CG and state if these members are in tension or compression.

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

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

Problem:

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

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

Problem:

In the truss shown below:
a. Determine the force in AD
b. Determine the force in BD
c. Determine the force in BC.

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

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

Problem: Maximum Value of the Applied P based on Given Capacities of Members

Given the truss shown in the figure,

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

a. If the strength of the truss is governed by the compressive load of member BD which is 100 kN, compute the maximum value of P in kilonewtons.
a. 25
b. 30
c. 20
d. Not in the list

b. If its strength is governed by the tensile force of member CD of 50 kN, compute the maximum value of P in kilonewtons.
a. 20
b. 50
c. 30
d. 40

c. If its strength is governed by the tensile force of member CF of 75 kN, compute the maximum value of P in kilonewtons.
a. 25
b. 30
c. 20
d. 15

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

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Analysis of Trusses: Method of Sections | Statics of Rigid Bodies – Problem 4: – Diagram Analysis of Trusses: Method of Sections | Statics of Rigid Bodies – Problem 4: – Diagram Analysis of Trusses: Method of Sections | Statics of Rigid Bodies – Problem 4: – Diagram Analysis of Trusses: Method of Sections | Statics of Rigid Bodies – Problem 4: – Diagram
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Problem (Section member from moment):

A truss section cuts member DE. Taking moments about a joint where the other two cut members intersect gives a perpendicular distance of 3m from DE. If the external moment about that joint is 45kN-m clockwise, determine the force in DE.

Use moment equilibrium of the cut free body.

\[ \begin{aligned} \sum M=0:\quad F_{DE}(3)-45&=0 \\ F_{DE}&=15\ \text{kN} \end{aligned} \] $\boxed{F_{DE}=15\ \text{kN}}$

Problem (Section with inclined member components):

A cut exposes an inclined member with a 3-4-5 slope. The vertical equilibrium of the free body requires an upward component of 24kN from this member. Determine the member force.

The vertical component is four-fifths of the member force.

\[ \begin{aligned} F\left({4\over5}\right)&=24 \\ F&=30\ \text{kN} \end{aligned} \] $\boxed{F=30\ \text{kN}}$

Problem (Solving two cut members by sections):

After cutting a truss, horizontal equilibrium gives F1 + 0.6F2 = 18, and vertical equilibrium gives 0.8F2 = 16. Determine F1 and F2.

Solve the vertical equation first, then substitute into the horizontal equation.

\[ \begin{aligned} 0.8F_2&=16 \\ F_2&=20\ \text{kN} \\ F_1+0.6(20)&=18 \\ F_1&=6\ \text{kN} \end{aligned} \] $\boxed{F_1=6\ \text{kN}},\qquad \boxed{F_2=20\ \text{kN}}$
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Exam Generator Problems

Additional board-style practice items for this topic.

Truss with Given Allowable Load and Applied Load is Unknown

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

For the truss shown,
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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
Use the method of joints, starting at the supported lower joints. At every joint, apply $\sum F_x=0$ and $\sum F_y=0$; a negative result relative to an assumed tensile force means compression.
Part 1. With $P=3000\text{ N}$ and $Q=1000\text{ N}$, propagating the joint forces upward gives $F_{CD}=\boxed{5250\text{ N (compression)}}$.
Part 2. The same joint solution gives $F_{JK}=\boxed{2250\text{ N (tension)}}$.
Part 3. Use the specified compression forces at CD and GD in the equilibrium equations of joints C and D. Solving for the applied vertical load gives $\boxed{P=5167.95\text{ N}}$.