https://file.aiquickdraw.com/mathbot/file/1726140373534qyet3mjn.jpg

To solve this problem, we need to determine the force in rod A when a load of \( P = 35 \, \text{kN} \) is applied.

### Step-by-Step Solution

#### 1. Understanding the Setup

- A rigid beam is pinned at point \( O \).
- The beam is supported by two rods: 
  - Rod \( A \) is located at a distance of \( L_1 = 2.5 \, \text{m} \) from point \( O \).
  - Rod \( B \) is located at a distance of \( L_2 = 3.0 \, \text{m} \) from point \( O \).
- A downward force \( P = 35 \, \text{kN} \) is applied at a point 3 meters to the left of \( O \).

#### 2. Identify Reaction Forces

The beam is in static equilibrium, meaning the sum of all forces and moments around point \( O \) must be zero.

Let:
- \( F_A \) be the force in rod \( A \).
- \( F_B \) be the force in rod \( B \).

#### 3. Sum of Vertical Forces

\[
F_A + F_B = P = 35 \, \text{kN}
\]

#### 4. Sum of Moments about Point \( O \)

Taking moments around point \( O \) (counterclockwise moments are positive):

\[
- F_A \cdot 2.5 + F_B \cdot 3 = P \cdot 3 
\]

Substitute \( P = 35 \, \text{kN} \):

\[
- F_A \cdot 2.5 + F_B \cdot 3 = 35 \cdot 3 
\]

\[
- F_A \cdot 2.5 + F_B \cdot 3 = 105 
\]

#### 5. Solve the System of Equations

We have two equations:

1. \( F_A + F_B = 35 \)
2. \( -2.5F_A + 3F_B = 105 \)

Substitute \( F_B = 35 - F_A \) into the second equation:

\[
-2.5F_A + 3(35 - F_A) = 105 
\]

Expand and simplify:

\[
-2.5F_A + 105 - 3F_A = 105 
\]

\[
-5.5F_A = 0 
\]

\[
F_A = 0 
\]

#### 6. Substitute Back to Find \( F_B \)

\[
F_B = 35 - F_A = 35 - 0 = 35 \, \text{kN}
\]

Thus, the force in rod A is \( 0 \, \text{kN} \), and the force in rod B is \( 35 \, \text{kN} \).

### Conclusion

The correct answer appears not to be listed among the options provided. Please confirm if the problem has any additional constraints or different interpretations.

Determine the load/force in rod A when a load of P = 35 kN is applied.

Solve the statics problem to find the load/force in rod A when a 35 kN load is applied to a pinned beam supported by two rods. Learn the step-by-step solution involving equilibrium conditions and moment calculations, suitable for undergraduate engineering students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation