Name: truss member force analysis by sections
Uploaded: 2025-05-22T09:06:03.000Z
Duration: 1 min 30 s
Channel: JoVE

Consider an arbitrary truss structure comprising of diagonal, vertical, and horizontal members fixed to the wall.
The method of sections can be used to calculate the force acting on members CB, GB and GH.
Here, the loads and the lengths of the horizontal and vertical members are the known parameters.
A cut is made along a plane intersecting CB, GB and GH members and a free-body diagram of the right side section is drawn.
The moment equilibrium equation about point G gives the force along CB. The positive sign indicates tension in the member.&#160;
Now, FGB can be expressed using a slope triangle in BCG, while FGH can be expressed using a slope triangle in CEG.
Considering the summation of vertical and horizontal forces, the force equilibrium equations can be written.
The value of FCB is substituted.&#160; The force equilibrium equations are solved simultaneously to obtain the force along GH and GB members.
The negative sign of FGH indicates that the force is compressive, while the positive sign for FGB indicates the tensile force.

method of sections: problem solving ii

Consider an arbitrary truss structure composed of diagonal, vertical, and horizontal members fixed to the wall. To calculate the force acting on members CB, GB, and GH, method of sections can be used. The loads and lengths of the horizontal and vertical members are known parameters, as shown in the figure.
<img alt="Truss static equilibrium diagram with force vectors and dimensions for load analysis." src="/files/ftp_upload/14287/14287_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" data-altupdatedat="1754904545000" data-alt="Truss equilibrium diagram; force analysis with labeled distances, load distribution, static analysis.">
To begin, a cut is made along a plane intersecting CB, GB, and GH members, and a free-body diagram of the right side section is drawn.
<img alt="Static equilibrium in truss diagram with force analysis; ΣFx=0, ΣFy=0, method illustration." src="/files/ftp_upload/14287/14287_PT_Fig_2v2.svg" style="text-align: center; height: 350px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium diagram, ΣFx=0, ΣFy=0, truss forces F1=4kN, F2=2kN, method of joints analysis.">
The moment equilibrium equation about point G is applied.
<img alt="Static equilibrium equation, \( F_{CB}(2m) - 2kN(4m) = 0 \), torque balance diagram." src="/files/ftp_upload/14287/14287_PT_Equation_1v2.svg" style="text-align: center; height: 13px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium equation showing F_CB and 2 kN at distances, diagram for force balance study.">
The result gives the force along member CB as 4 kN, with a positive sign indicating tension in the member.
Now, FCB can be expressed using a slope triangle in BCG, while FGH can be expressed using a slope triangle in CEG. Considering the summation of vertical and horizontal forces, the force equilibrium equations can be written as the following:
<img alt="Static equilibrium equation ΣF=0; Newton's laws; vector forces diagram; physics analysis." src="/files/ftp_upload/14287/14287_PT_Equation_2v2.svg" style="text-align: center; height: 15px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium equation, ΣFy=0, formula in physics, includes forces F1, F2, FGB, FGH.">
<img alt="Static equilibrium equation, ΣFx=0, diagram showing force components in mechanics analysis." src="/files/ftp_upload/14287/14287_PT_Equation_3v2.svg" style="text-align: center; height: 13px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium equation; diagram of forces in balance, -FCB - FGHx - FGBx = 0.">
The value of FCB is substituted, and the force equilibrium equations are solved simultaneously. The result yields the force FGH as -7.454 kN and FGB as 3.772 kN. The negative sign of FGH indicates that the force is compressive, while the positive sign for FGB indicates the tensile force.

Method of Sections: Problem Solving II

Consider an arbitrary truss structure composed of diagonal, vertical, and horizontal members fixed to the wall. To calculate the force acting on members ...

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truss member force analysis by sections

Truss member force analysis by sections finds the forces in selected members of a wall-mounted truss. The structure here includes diagonal, vertical, and horizontal members. The known loads and member lengths are used to solve for the forces in CB, GB, and GH.

A cut is made through members CB, GB, and GH. The right side of the truss is then isolated as a free-body diagram. Next, the moment equilibrium equation is taken about point G. This step gives the force in member CB as 4 kN, and the positive sign shows that CB is in tension.

The force in CB is then written with a slope triangle in triangle BCG. The force in GH is written with a slope triangle in triangle CEG. After that, the sums of vertical and horizontal forces are set equal to zero. The equation for CB is substituted, and the remaining equations are solved at the same time.

The final values are FGH = -7.454 kN and FGB = 3.772 kN. The negative sign for GH means the member is in compression. The positive sign for GB means the member is in tension.

Truss Member Force Analysis by Sections

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Learn how the method of sections isolates a truss cut, uses moment and force balance, and identifies tension or compression in members CB, GB, and GH.

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JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

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Truss Member Force Analysis by Sections

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