Fixed End Moment Calculation for a Fixed Beam with UDL

The question asks for the value of the fixed end moment on the right support of a fixed beam. A fixed beam is supported in such a way that rotation is prevented at the supports. When a fixed beam is subjected to a uniformly distributed load (UDL) over its entire span, moments are developed at both fixed supports, known as fixed end moments.

For a fixed beam of span length \(L\) subjected to a uniformly distributed load of intensity \(w\) over the entire span, the magnitude of the fixed end moment at each support (left and right) is given by the formula:

\(M = \frac{wL^2}{12}\)

Where:

• \(M\) is the fixed end moment
• \(w\) is the intensity of the uniformly distributed load
• \(L\) is the span length of the beam

Applying the Given Values

From the question, we are given:

• Uniformly distributed load, \(w = 3 \text{ kN/m}\)
• Span length of the beam, \(L = 4 \text{ m}\)

Now, we can substitute these values into the formula for the fixed end moment:

\(M = \frac{(3 \text{ kN/m}) \times (4 \text{ m})^2}{12}\)

\(M = \frac{3 \text{ kN/m} \times 16 \text{ m}^2}{12}\)

\(M = \frac{48 \text{ kN-m}}{12}\)

\(M = 4 \text{ kN-m}\)

The magnitude of the fixed end moment is the same at both the left and right supports for a fixed beam subjected to a UDL over the full span. Therefore, the value of the fixed end moment on the right support is \(4 \text{ kN-m}\).

The unit of the moment is kN-m, which is the unit of force multiplied by distance.

Comparing this result with the given options, we find that Option 2 matches our calculated value.

The final value of the fixed end moment on the right support is 4 kN-m.