For continuous reinforced concrete beams under typical loading, the distance between adjacent points of contraflexure (zero bending moment) within a span is approximately what fraction of the effective span l?

Introduction / Context:
Continuous beams develop negative moments over supports and positive moments near mid-spans. The locations where the bending moment changes sign are called points of contraflexure (zero moment). Estimating the spacing between these points helps with detailing of tension steel (top vs bottom) and quick checks of bending diagrams in preliminary design.

Given Data / Assumptions:

• Member: continuous beam.
• Loading: typical uniform loading patterns producing standard moment shapes.
• l is the effective span.

Concept / Approach:

For prismatic continuous members under uniform load, classical analysis shows zero-moment points occurring roughly at about 0.21 l from each support (as in the fixed-end or well-restrained case). Hence, the distance between the two zero-moment points is approximately l − 2 * 0.21 l = 0.58 l, often rounded off to 0.6 l for design thumb rules.

Step-by-Step Solution:

Verification / Alternative check:

Other load cases produce similar magnitudes; detailing guides commonly use ≈0.6 l to position cut-offs and distribution steel in spans of continuous beams.

Why Other Options Are Wrong:

• 0.5 l or 0.4 l: Underestimate the spacing for standard patterns.
• 0.7 l or 0.8 l: Overestimate; would move zero-moment points unrealistically close to supports.

Common Pitfalls:

• Treating all spans as simply supported; continuous action shifts moment distribution.
• Ignoring load type; concentrated loads alter exact positions but not the useful 0.6 l heuristic.

Final Answer:

0.6 l