Flexural Design – Beam end partially restrained in a built-up wall: Design the beam for negative (hogging) moment at the face of support under a design load W and clear span L.

Introduction:
When a beam end is built into or partially restrained by a wall, some fixity develops. This produces a negative (hogging) moment at the face of the support that must be resisted in design to avoid cracking and rotation at the bearing.

Given Data / Assumptions:

• Uniformly distributed design load W on span L.
• End provides partial restraint due to embedment in a built-up wall.
• Design convention uses a codal negative moment coefficient at the face.

Concept / Approach:

End restraints reduce mid-span sagging moment and introduce end hogging. Classical coefficients for a partially fixed end commonly adopt an equivalent negative moment of W L / 12 at the face. This is a conservative and widely used detailing/design value.

Step-by-Step Solution:

Verification / Alternative check:

In the limiting cases, simply supported gives zero end moment; fully fixed would give a larger negative moment. The value W L / 12 sits between these, aligning with partial fixity practice.

Why Other Options Are Wrong:

W L / 8 and W L / 10 overestimate typical partial fixity; W L / 16 and W L / 24 underestimate the required end capacity, risking cracks.

Common Pitfalls:

Ignoring end fixity in detailing, placing insufficient top bars at supports, or checking only mid-span sagging moment.

Final Answer:

W L / 12