For a plate girder web, yielding governs the web failure if the ratio of clear web depth to web thickness (d_c / t_w) is less than which approximate limiting value?

Introduction / Context:
Webs of plate girders resist shear and contribute to bending. Their limit state can be governed by yielding (stocky webs) or by buckling (slender webs). The slenderness indicator is the ratio of clear web depth to web thickness. Recognizing the threshold helps select whether stiffeners or thicker webs are required.

Given Data / Assumptions:

• d_c = clear depth of the web plate between flanges.
• t_w = thickness of the web plate.
• We seek the approximate ratio below which yielding (not buckling) is the controlling mode.

Concept / Approach:
A lower d_c / t_w implies a comparatively thick (stocky) web, which has sufficient stiffness to avoid elastic buckling under shear; the web then reaches yield before buckling. Classical plate-girder design adopts a practical limit around 60 for this transition, beyond which intermediate or end stiffeners and shear buckling checks are necessary.

Step-by-Step Solution:
Evaluate the web slenderness using d_c / t_w. Compare with the empirical threshold ≈ 60. If less than 60, design for web shear yielding; if greater, check for shear buckling and provide stiffeners as needed.

Verification / Alternative check:
Modern limit-state codes use more refined buckling curves and tension-field action, yet the traditional teaching threshold near 60 aligns with many exam problems and legacy working-stress provisions.

Why Other Options Are Wrong:

• 45 or 55: More conservative than the commonly taught threshold.
• 75 or 82: Too high; such webs are typically slender enough to require buckling checks.

Common Pitfalls:

• Confusing overall beam slenderness with web slenderness.
• Ignoring bearing/buckling near concentrated loads where special checks are still required.

Final Answer:
60.