Limit state strain profile — compression steel strain in a rectangular RC section (Given effective cover to compression steel = d' and neutral axis depth from compression face = x_u.)

Introduction / Context:
In limit state design of reinforced concrete, plane sections remain plane and the extreme compression-fiber strain is taken as 0.0035 at the ultimate limit state. Knowing the neutral axis depth allows computing strains at any fiber, including the compression steel at an effective cover d' from the compression face.

Given Data / Assumptions:

• Rectangular RC section in flexure at ULS.
• Extreme compression-fiber strain = 0.0035.
• Neutral axis depth from compression face = x_u.
• Compression steel centerline located at distance d' from compression face.

Concept / Approach:
With the plane-sections assumption, the strain distribution is linear from 0.0035 at the compression face to 0 at the neutral axis. Therefore, the strain at any fiber a distance y from the compression face is epsilon(y) = 0.0035 * (1 - y/x_u). Substituting y = d' yields the strain at the compression steel level.

Step-by-Step Solution:
1) Adopt linear strain: epsilon(y) = 0.0035 * (1 - y/x_u).2) Set y = d' for the compression steel layer.3) Compute epsilon_s' = 0.0035 * (1 - d'/x_u).4) Choose the matching option.

Verification / Alternative check:
At y = 0 (compression face), epsilon = 0.0035; at y = x_u, epsilon = 0, confirming linearity and the adopted formula.

Why Other Options Are Wrong:
Options with 0.002 apply to serviceability strains, not ULS; options using x_u/d' invert the ratio, giving nonphysical results (negative or excessive strains).

Common Pitfalls:
Confusing effective cover d' with overall cover; mixing service and ultimate strain limits; assuming nonlinear strain without justification.

Final Answer:
0.0035 (1 - d'/x_u)