Shear design in reinforced concrete beams: Based on working-stress era thumb rules, how should shear reinforcement and section sizing be decided from the computed nominal shear stress (kg/cm²)?

Introduction / Context:
Shear design in reinforced concrete beams ensures that inclined cracking and brittle web failures are prevented. Older working-stress practice (expressed here in kg/cm²) uses simple decision thresholds for the nominal shear stress to decide whether stirrups are needed and whether the section must be resized. This question checks recognition of those classical ranges and the intent behind them.

Given Data / Assumptions:

• Nominal shear stress τv has been computed from V / (b * d) in kg/cm².
• The values 5, 20 kg/cm² represent traditional guideposts from elementary design texts.
• Behavioral intent: very low shear → concrete alone adequate; moderate shear → provide stirrups; very high shear → resize the section (or redesign).

Concept / Approach:

Concrete has limited diagonal tension resistance. Below a small bound, web cracking is unlikely, so stirrups may be waived. In an intermediate band, standard stirrups (or bent-up bars) are provided to carry diagonal tension. If shear is excessive, simply adding stirrups can become uneconomical or ineffective; increasing b and/or d reduces τv and improves shear and flexural capacity simultaneously.

Step-by-Step Solution:

Verification / Alternative check:

Increasing effective depth d directly reduces τv = V / (b * d). Basic checks for bearing, anchorage, and serviceability accompany any redesign. Modern limit-state codes use different symbols and limits but the qualitative decisions remain similar.

Why Other Options Are Wrong:

Options (a), (b), and (c) are partial truths applicable only in their ranges. Option (d) correctly assembles the full decision tree. Option (e) contradicts standard practice.

Common Pitfalls:

Ignoring minimum stirrups even when τv is very low; relying on stirrups alone for extremely high shear; mixing units (N/mm² vs kg/cm²) without conversion; forgetting to check shear near supports where V is highest.

Final Answer:

All of the above (applied in their respective ranges)