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?
A. Howe truss
B. King post truss
C. Fink truss
D. Warren truss
Answer: Option C
Solution (By Examveda Team)
* 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.
This Question Belongs to Civil Engineering >> Applied Mechanics And Graphic Statics
Join The Discussion
Comments (1)
In case of S.H.M. the period of oscillation (T), is given by
A. $${\text{T}} = \frac{{2\omega }}{{{\pi ^2}}}$$
B. $${\text{T}} = \frac{{2\pi }}{\omega }$$
C. $${\text{T}} = \frac{2}{\omega }$$
D. $${\text{T}} = \frac{\pi }{{2\omega }}$$
The angular speed of a car taking a circular turn of radius 100 m at 36 km/hr will be
A. 0.1 rad/sec
B. 1 rad/sec
C. 10 rad/sec
D. 100 rad/sec
A body is said to move with Simple Harmonic Motion if its acceleration, is
A. Always directed away from the centre, the point of reference
B. Proportional to the square of the distance from the point of reference
C. Proportional to the distance from the point of reference and directed towards it
D. Inversely proportion to the distance from the point of reference
The resultant of two forces P and Q acting at an angle $$\theta $$, is
A. $${{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{P}}\sin \theta $$
B. $${{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{PQ}}\cos \theta $$
C. $${{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{PQ}}\tan \theta $$
D. $$\sqrt {{{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{PQ}}\cos \theta } $$
E. $$\sqrt {{{\text{P}}^2} + {{\text{Q}}^2} + 2{\text{PQ}}\sin \theta } $$
The **method of substitution** is required in trusses where the **graphical methods (like Cremona’s diagram or Maxwell’s diagram)** cannot directly solve all the member forces due to **geometric complexity or lack of simple triangulation**.
Among 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.