Structural Engineering

RCC — Limit State Design

IS 456 limit-state design of singly-reinforced sections: stress block, neutral axis and moment capacity.

PART 1

Topic Breakdown & Traps

In limit state of collapse (flexure), concrete carries compression through a rectangular stress block of intensity

0.36 f_{c k}

over depth

x_{u}

, and steel yields in tension at

0.87 f_{y}

. Force equilibrium fixes

x_{u}

; the lever arm gives the moment of resistance. A balanced section reaches both limits together at

x_{u, ma x}

Tensile force:

T = 0.87 f_{y} A_{s t}

Compressive force:

C = 0.36 f_{c k} b x_{u}

Depth of NA:

x_{u} = \frac{0.87 f _{y} A _{s t}}{0.36 f _{c k} b}

**Limiting

x_{u} / d

**: Fe250 →

0.53

, Fe415 →

0.48

, Fe500 →

0.46

.

Moment of resistance:

M_{u} = 0.87 f_{y} A_{s t} (d - 0.42 x_{u})

⚠
Stress-block factors. $0.36 f_{c k}$ for the force and $0.42 x_{u}$ for the centroid depth — memorise both.
⚠
Over- vs under-reinforced. If $x_{u} > x_{u, ma x}$ the section is over-reinforced (brittle); IS 456 disallows it for design.
⚠
**Use $0.87 f_{y}$ , not $f_{y}$ ** for the design strength of steel.

Reinforced Concrete Design (RCC Designs) — B.C. Punmia, A.K. Jain & A.K. Jain
IS 456:2000 — Plain & Reinforced Concrete Code of Practice — Bureau of Indian Standards

PART 2

Q1BASIC1 Mark · MCQ

As per IS 456, the limiting neutral-axis depth ratio

x_{u, ma x} / d

for Fe415 steel is:

Q2MEDIUM2 Marks · NAT

A singly-reinforced beam has

b = 300 mm

A_{s t} = 1000 mm^{2}

, Fe415, M20. The depth of the stress block

x_{u}

is _____ mm.

Q3HARD2 Marks · NAT

For

A_{s t} = 1200 mm^{2}

of Fe500 steel, the design tensile force

0.87 f_{y} A_{s t}

is _____ kN.