Continuous steel beams with cover plates – “modified” moment of inertia: For sections with a single web, the modified moment of inertia at a support (maximum bending moment region) is taken as the section's I about the Y–Y axis at that location multiplied by which area ratio related to the compression flange?

Introduction / Context:
In continuous steel beams where flange areas vary (e.g., due to cover plates curtailed between spans), an adjusted or “modified” moment of inertia is sometimes used for distribution calculations. The aim is to reflect how changes in the compression flange area influence stiffness in regions of different bending moment signs and magnitudes.

Given Data / Assumptions:

• Single-web I-sections (rolled or built-up) with variable flange area along the beam.
• Compression flange governs flexural stiffness; tension flange may differ between spans.
• We focus on the region of maximum bending moment (support for negative moment or midspan for positive moment).

Concept / Approach:

The compression flange is the primary contributor to flexural stiffness because instability and yielding limit its effectiveness first. A common adjustment multiplies the geometric moment of inertia I (about the Y–Y axis at the point of maximum moment) by a ratio of compression flange areas between a less severe region (often the minimum bending moment region) and the severe region (maximum bending moment). This reduces the stiffness used in analysis to reflect the flange curtailment effects.

Step-by-Step Solution:

Verification / Alternative check:

Where cover plates are curtailed, the compression flange width/thickness varies. Using this ratio provides a pragmatic stiffness modification that mirrors the actual flange participation.

Why Other Options Are Wrong:

• Ratio using tension flange (option b) does not represent compression-side stiffness control.
• Option c simplifies to 1 and ignores the variation; not meaningful.
• “None of these” is incorrect because the compression-flange ratio is used.

Common Pitfalls:

• Confusing which flange is in compression at different spans (negative vs positive bending).
• Using gross I without accounting for flange curtailment, leading to overly stiff models.

Final Answer:

Area of compression flange at the minimum bending moment / area of compression flange at the maximum bending moment.