Design assumptions for prestressed concrete members: which set of statements appropriately reflects the standard working assumptions used in analysis and service-level design?

Introduction / Context:
Prestressed concrete (PSC) analysis commonly uses a set of simplifying assumptions at the serviceability stage. These assumptions allow the designer to apply linear elastic methods, distribute stresses, and estimate losses with reasonable accuracy for everyday bridge and building members.

Given Data / Assumptions:

• Service-level behavior is considered (pre-cracking or limited cracking conditions).
• Members may be pretensioned or post-tensioned; bonded systems are typical in building/bridge practice.
• Small strain, linear elasticity is assumed at service to enable transformed-section analysis.

Concept / Approach:
The core assumptions are: (1) plane sections remain plane, so strain varies linearly over depth; (2) within working ranges, concrete and steel are treated as linearly elastic (Hook’s law); (3) in fully prestressed, bonded members, changes in tendon stress under modest service load variations are limited, enabling simplified checks that emphasize concrete service stresses and crack control rather than precise tendon stress increments.

Step-by-Step Solution:
Adopt the plane-sections assumption to relate curvature to strain distribution.Use elastic moduli to transform steel to an equivalent concrete area (modular ratio) for service stress calculations.For bonded systems, treat tendon stress changes at service as modest; focus on concrete fiber stresses and allowable limits in compression/tension.

Verification / Alternative check:
Where higher accuracy is required (e.g., ultimate strength or unbonded tendons), employ non-linear or refined methods that capture tendon stress increments and cracked-section behavior; this confirms the service assumptions are a reasonable simplification, not a universal rule.

Why Other Options Are Wrong:

• Each of options a–c is valid in the stated service context; hence “All the above” is correct.
• “None of these” contradicts standard service design assumptions in PSC.

Common Pitfalls:
Applying these assumptions at ultimate limit states without appropriate modifications, ignoring time-dependent effects, or forgetting that unbonded tendons can experience larger stress variations under load changes.

Final Answer:
All the above.