The problem shown involves a beam subjected to a distributed load. The goal is to determine the resultant force of the load and specify where it acts on the beam measured from point A.

Problem Breakdown:

1. Type of Load: The beam has a uniformly distributed load (UDL) of 6 kN/m acting along a 6-meter section from point A to point B.
2. Span: The total span of the beam is 9 meters, with point A being 3 meters from the start of the UDL and point B 6 meters from point A.

Solution Outline:

Step 1: Determine the Total Load (Resultant Force)

The total load $W$ due to a uniformly distributed load (UDL) is calculated as: $W = w \cdot L$ Where:

• $w$ is the intensity of the load (6 kN/m),
• $L$ is the length over which the load is applied (6 m).

$W = 6 \, \text{kN/m} \times 6 \, \text{m} = 36 \, \text{kN}$

Step 2: Location of the Resultant Force

For a uniformly distributed load, the resultant force acts at the centroid of the load distribution. For a UDL, this centroid is located at the midpoint of the load.

Thus, the distance of the resultant force from point A is half of the length of the loaded span: $x_{\text{R}} = \frac{6 \, \text{m}}{2} = 3 \, \text{m}$ Since the load starts at point A, the resultant force will be $3 \, \text{m} + 3 \, \text{m} = 6 \, \text{m}$ from point A.

Final Result:

• Resultant Force: 36 kN
• Location of the Resultant Force from A: 6 meters

Would you like more details on any step or further clarifications?

Related Questions:

1. What is the method to calculate the resultant of a non-uniformly distributed load?
2. How would the result change if the load intensity varied linearly along the beam?
3. How can you determine reactions at supports A and B based on the resultant force?
4. What would be the effect on the location of the resultant if the load only spanned 4 meters?
5. How is the shear force diagram constructed for this type of loading?

Tip:

When dealing with uniformly distributed loads, remember that the resultant force acts at the centroid, which simplifies the calculation of moments and reactions.