Question

The truss which follows the law $n =$ _________ is known as simple truss

• A. $n = 2j + 3$
• B. $n = 2j - 3$
• C. $n = 3j + 2$
• D. $n = 3j - 2$

Hint:

Remember that the minimum stable plane truss is a triangle with $3$ members and $3$ joints.
Plugging $j = 3$ into the equation $n = 2j - 3$ gives $n = 2(3) - 3 = 3$, verifying the formula immediately.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question is from structural mechanics, specifically regarding the classification of plane trusses.
It requires the mathematical relation that defines a simple, statically determinate plane truss.

Step 2: Key Formula or Approach:
For a plane truss (two-dimensional truss), the relationship between the number of members ($n$) and the number of joints ($j$) for determinacy is:
\[ n = 2j - 3 \]

Step 3: Detailed Explanation:

• A simple truss is constructed starting with a basic triangular frame of three members ($n=3$) connected at three joints ($j=3$).

• To expand this truss, for every new joint added, two new members are required to maintain stability and determinacy.

• This progression can be written as: $n - 3 = 2(j - 3)$, which simplifies to $n = 2j - 3$.

• If $n < 2j - 3$, the truss is unstable (under-determinate).

• If $n > 2j - 3$, the truss is statically indeterminate (redundant).

Step 4: Final Answer:
The standard equation for a simple plane truss is $n = 2j - 3$.