Question

If a truss consists of 6 joints and 3 reaction components, then the number of members required for determinate truss is

• A. 8
• B. 9
• C. 12
• D. 15

Hint:

Memorize the determinacy formula for trusses:
- 2D Truss: $m + r = 2j$
- 3D Truss: $m + r = 3j$
If $m+r \gt 2j$, the truss is indeterminate (redundant).
If $m+r \lt 2j$, the truss is unstable (a mechanism).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the number of members ($m$) required for a planar truss to be statically determinate, given the number of joints ($j$) and reaction components ($r$).

Step 2: Key Formula or Approach:
For a planar (2D) truss, the condition for static determinacy is given by the formula:
\[ m + r = 2j \] where:
$m$ = number of members
$r$ = number of external reaction components
$j$ = number of joints
This equation comes from the fact that at each of the $j$ joints, there are two equilibrium equations ($\Sigma F_x = 0$ and $\Sigma F_y = 0$), giving a total of $2j$ available equations. The unknowns are the forces in the $m$ members and the $r$ reactions. For determinacy, the number of unknowns must equal the number of equations.

Step 3: Detailed Explanation:
We are given:
- Number of joints ($j$) = 6
- Number of reaction components ($r$) = 3 (This corresponds to a typical simply supported truss with one pin and one roller support).
We need to find the required number of members ($m$).
Substitute the given values into the formula:
\[ m + 3 = 2 \times 6 \] \[ m + 3 = 12 \] \[ m = 12 - 3 \] \[ m = 9 \]

Step 4: Final Answer:
The number of members required for the truss to be determinate is 9.