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In which of the following trusses, the method of substitution is required for determining the forces in all the members of the truss by graphic statics?
Answer & Solution
Correct Answer:
Option
C
* Truss: A structure made of connected straight members forming triangles.
* Graphic Statics: A visual way to analyze forces in trusses using diagrams.
* Method of Substitution: A technique where you temporarily remove a member and replace it with an equivalent force to solve for unknowns, then put the member back in and adjust calculations.
Now, let's look at the options:
* A: Howe Truss: These are generally straightforward to solve with basic graphic statics, without needing substitution.
* B: King Post Truss: Also usually simple and solvable without substitution.
* C: Fink Truss: This type of truss often has complex geometry, making it statically indeterminate. This means you *cannot* solve for all the forces using just simple equilibrium equations at each joint with graphic statics alone initially. The method of substitution is often required to determine the forces in all the members.
* D: Warren Truss: Warren trusses are often solvable using standard graphic statics methods.
Therefore, the answer is C: Fink truss. Fink trusses commonly require the method of substitution due to their geometry.
* Graphic Statics: A visual way to analyze forces in trusses using diagrams.
* Method of Substitution: A technique where you temporarily remove a member and replace it with an equivalent force to solve for unknowns, then put the member back in and adjust calculations.
Now, let's look at the options:
* A: Howe Truss: These are generally straightforward to solve with basic graphic statics, without needing substitution.
* B: King Post Truss: Also usually simple and solvable without substitution.
* C: Fink Truss: This type of truss often has complex geometry, making it statically indeterminate. This means you *cannot* solve for all the forces using just simple equilibrium equations at each joint with graphic statics alone initially. The method of substitution is often required to determine the forces in all the members.
* D: Warren Truss: Warren trusses are often solvable using standard graphic statics methods.
Therefore, the answer is C: Fink truss. Fink trusses commonly require the method of substitution due to their geometry.
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LoginAmong the given options:
- **Howe truss (A)** and **Warren truss (D)** are **simple trusses** that can be analyzed entirely using graphical statics without substitution.
- **King post truss (B)** is a very basic truss that is easily solvable graphically.
- **Fink truss (C)** is a **compound truss** with **internal secondary members** that introduce complexity, often requiring the **method of substitution** to resolve forces in certain members.
### **Correct Answer: C. Fink truss**
The Fink truss typically requires substitution because its internal members create interdependent force distributions that cannot be resolved by simple graphical methods alone.