Name: truss member force calculation by sections
Uploaded: 2025-05-22T09:06:03.000Z
Duration: 1 min 27 s
Channel: JoVE

Consider a symmetrical roof truss structure comprising the vertical, diagonal and horizontal members.
A free-body diagram is drawn to analyze the forces on DC and HC members using the method of section.
Here, the loads and the lengths of the horizontal and vertical members are the known parameters.
First, summing the moments about point A, the reaction force at E is calculated.
Further, using the force equilibrium condition for the truss, the reaction force at A is determined.
The symmetry of the truss ensures that both the reaction forces are equal.
Now, a cut is made along a plane intersecting DC, HC and HG members, and a free-body diagram of the smaller section is drawn.
Taking the summation of the moments about H gives the force along DC. The positive sign indicates the tensile force.
The force along HC is resolved into its sine and cosine components, and trigonometry is used to estimate the angle theta.
The moment equilibrium condition at E yields the force on HC, with the negative sign indicating the compressive force.

method of sections: problem solving i

Consider a symmetrical roof truss structure, composed of vertical, diagonal, and horizontal members. The length of each horizontal member is 4 m. The lengths of the vertical members FB and HD are 4 m, while the length of member GC is 6 m. The loads acting at joints F, G, and H are 2 kN, while those at joints A and E are 1 kN.
<img alt="Truss equilibrium diagram; forces labeled F1-F5; nodes A-E; reaction forces RA, RE; static analysis." src="/files/ftp_upload/14286/14286_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium diagram; forces on a truss beam with labeled force vectors F1-F5 and reactions RA, RE.">
The method of sections is employed to calculate the forces acting on members DC and HC. The moment equilibrium condition is applied to point A, and the known values of forces and distances are substituted into the moment equation.
<img alt="Static equilibrium equation ΣMd=0; diagram of forces and distances in mechanical system analysis." src="/files/ftp_upload/14286/14286_PT_Equation_1v2.svg" style="text-align: center; height: 13px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium equation diagram with torque balance formula ΣF(d)=0, illustrating forces.">
This results in an estimated reaction force of 4 kN at point E. Subsequently, the vertical force equilibrium condition at point A reveals that the reaction force at A is also 4 kN.
<img alt="Static equilibrium equation ΣF=0, diagram for force balance analysis, educational use." src="/files/ftp_upload/14286/14286_PT_Equation_2v2.svg" style="text-align: center; height: 13px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium equation ΣF=0; diagram for force analysis in mechanical systems.">
Due to the symmetry of the truss, the reaction forces at points A and E are equal.
The forces acting on members DC and HC can be obtained upon determining the reaction forces. A sectional cut is made along a plane intersecting members DC, HC, and HG, and a free-body diagram of the smaller section is considered.
<img alt="Static equilibrium diagram: truss forces, labeled vectors, ΣFx=0, ΣFy=0, structural analysis." src="/files/ftp_upload/14286/14286_PT_Fig_2v2.svg" style="text-align: center; height: 350px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium diagram with force vectors; truss analysis; ΣFx=0, ΣFy=0, moments at joints.">
By summing the moments about point H, the force along DC is calculated to be a positive 3 kN, indicating a tensile force.
<img alt="Static equilibrium formula: \( R_E \cdot d_{DE} - F_5 \cdot d_{DE} - F_{DC} \cdot d_{HD} = 0 \)." src="/files/ftp_upload/14286/14286_PT_Equation_3v2.svg" style="text-align: center; height: 13px;" data-altupdatedat="1754904545000" data-alt="Equilibrium equation, ΣF=0, static equilibrium, formula for force distribution analysis.">
The force along CH is resolved into its sine and cosine components. Trigonometry is used to find the angle between member CH and the horizontal axis to be 45°. Finally, applying the moment equilibrium condition at point E yields a force of -1.41 kN for FCH.
<img alt="Static equilibrium equation diagram: Σ(F x d) + (F cos θ x d) + (F sin θ x d) = 0." src="/files/ftp_upload/14286/14286_PT_Equation_4v2.svg" style="text-align: center; height: 13px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium equation; torque balance formula; ΣFx=0 analysis.">
In this case, the negative result signifies a compressive force acting on member CH.

Method of Sections: Problem Solving I

Consider a symmetrical roof truss structure, composed of vertical, diagonal, and horizontal members. The length of each horizontal member is 4 m. The ...

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truss member force calculation by sections

Truss member forces can be found with the method of sections in a symmetrical roof truss. The structure here includes vertical, diagonal, and horizontal members. Each horizontal member is 4 m long. The vertical members FB and HD are 4 m long, and member GC is 6 m long.

The roof truss carries loads at several joints. Joints F, G, and H each have a 2 kN load. Joints A and E each have a 1 kN load. To start the analysis, moment equilibrium is used at point A. The force and distance values are placed into the moment equation, which gives a reaction force of 4 kN at point E.

Next, vertical force equilibrium at point A gives the reaction force at A as 4 kN. Because the truss is symmetrical, the reactions at A and E are equal. Once the reactions are known, the forces in members DC and HC can be found. A section is cut through members DC, HC, and HG, and a free-body diagram is drawn for the smaller part.

Moments about point H are then summed to solve for the force in DC. The result is 3 kN, which is positive and shows tension. The force in CH is handled with trigonometry. The angle between member CH and the horizontal axis is found to be 45°. Using moment equilibrium at point E gives FCH = -1.41 kN. The negative sign means member CH is in compression.

Truss Member Force Calculation by Sections

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key terms and concepts

Learn how the method of sections is used on a symmetrical roof truss to find support reactions and member forces, including tension and compression.

Truss Member Force Calculation by Sections | JoVE K12

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Truss Member Force Calculation by Sections

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