A cord supported at A and B carries a load of 10 kN at D and a load of W at C as shown in
figure. Find the value of W so that CD remains horizontal.

To solve the problem of finding the value of the load W that keeps the segment CD horizontal, we need to analyze the forces acting on the cord and apply some principles of static equilibrium. Let's break this down step by step.

Understanding the Setup

We have a cord supported at points A and B, with a load of 10 kN acting downward at point D and an unknown load W acting downward at point C. The goal is to determine the value of W such that the segment CD remains horizontal.

Static Equilibrium Principles

For the cord to remain in static equilibrium, the sum of the vertical forces must equal zero, and the moments about any point must also sum to zero. This means that the upward forces must balance the downward forces.

Analyzing Forces

Let’s denote the vertical reactions at supports A and B as \( R_A \) and \( R_B \) respectively. The vertical forces acting on the system are:

• Downward force at D: 10 kN
• Downward force at C: W
• Upward reactions at A and B: \( R_A \) and \( R_B \)

Setting Up the Equations

From the equilibrium of vertical forces, we can write the equation:

R_A + R_B = 10 kN + W

Moments for Horizontal Condition

Next, we need to ensure that the segment CD remains horizontal. This condition can be satisfied by ensuring that the moments about point A (or any point) are balanced. Assuming the distances from A to C and A to D are known (let's denote them as \( L_{AC} \) and \( L_{AD} \)), we can write the moment equation about point A:

W \cdot L_{AC} = 10 kN \cdot L_{AD}

Solving for W

From the moment equation, we can isolate W:

W = \frac{10 kN \cdot L_{AD}}{L_{AC}}

Example Calculation

Let’s say, for example, that the distance from A to C (L_{AC}) is 4 meters and the distance from A to D (L_{AD}) is 2 meters. Plugging these values into our equation gives:

W = \frac{10 kN \cdot 2 m}{4 m} = 5 kN

This means that for the segment CD to remain horizontal, the load W must be 5 kN.

Final Thoughts

In summary, by applying the principles of static equilibrium and analyzing the moments about a point, we can determine the necessary load W to keep the cord in a horizontal position. Always remember to check the distances and ensure that your units are consistent when performing these calculations.