6.9
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 membe…
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.
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. 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.
Q1: How do you apply the method of sections to find member forces in a truss?
The method of sections involves making a cut along a plane that intersects the members you want to analyze. Draw a free-body diagram of one section, then apply equilibrium equations. Use moment equilibrium about a strategic point to isolate one unknown force, then solve force equilibrium equations simultaneously to find remaining member forces.
Q2: What does a positive force sign indicate in truss member analysis?
A positive force sign indicates tension in the member, meaning the member is being pulled. Conversely, a negative force sign indicates compression, meaning the member is being pushed. These signs are determined when solving the equilibrium equations and reveal whether each member experiences tensile or compressive stress.
Q3: Why is moment equilibrium about a specific point useful in the method of sections?
Moment equilibrium about a strategic point eliminates unknown forces that pass through that point, allowing you to solve directly for a single unknown member force. By choosing point G in this problem, the moment equation yields the force along member CB without interference from other unknowns, simplifying the solution process.
Q4: How are slope triangles used to express member forces in the method of sections?
Slope triangles relate member forces to the geometry of the truss. For member GB, the force is expressed using the slope triangle in BCG, while force GH uses the slope triangle in CEG. These geometric relationships allow you to decompose forces into vertical and horizontal components for equilibrium equations.
Q5: What information must be known before applying the method of sections to a truss?
The loads applied to the truss and the lengths of horizontal and vertical members must be known parameters. These values are essential for setting up the free-body diagram, writing equilibrium equations, and solving for unknown member forces using moment and force balance conditions.
Q6: How do you solve for multiple unknown member forces using force equilibrium equations?
After using moment equilibrium to find one member force, substitute that value into the vertical and horizontal force equilibrium equations. Solve the resulting system of equations simultaneously to obtain the remaining unknown member forces, as demonstrated when finding forces GH and GB after determining force CB.
Q7: What is the relationship between the method of sections and free-body diagrams?
The method of sections requires drawing a free-body diagram of the section created by the cutting plane. This diagram isolates the forces acting on that section, including member forces and applied loads, enabling you to apply equilibrium equations systematically to solve for unknown internal member forces.