RC Column Analysis & Design

P-M Interaction Diagram

0. Design Standard
ACI 318 (USA/Intl) Eurocode 2 SS EN 1992 (SG) IS 456 (India) BS 8110 (UK) GB 50010 (China) JSCE (Japan)

1. Column Geometry
Section Shape	Rectangular (Tied) Circular (Spiral)
Width (b)		mm
Depth/Dia (h)		mm
Clear Height (Lu)		m
Clear Cover (cc)		mm

2. Material Properties
Concrete (f'c)		MPa
Main Steel (fy)		MPa
Tie/Spiral (fyt)		MPa

3. Applied Factored Loads (ULS)
Axial Load (Pu)		kN
Major Axis Moment (Mux)		kN·m
Concurrent Shear (Vu)		kN

4. Rebar Selection
Rebar Qty Mode	Auto-Optimize Manual Override
Total Bars ($N_{bars}$)
Main Bar Dia. ($d_b$)
Tie/Spiral Dia. ($d_v$)
Tie Spacing ($s$)	mm
Rebar Arrangement	Equal All Faces 2 Faces (Bending Axis)

Capacity Check

Demand/Capacity 0.00

Design Axial $\phi P_n$ 0.0 kN

Design Moment $\phi M_n$ 0.0 kN·m

Failure Mode

Governing State Compression
Controlled

Structural Detailing

SECTION 1

ELEVATION A

P-M Diagram

Key Control Points on Interaction Diagram

Condition / State	Neutral Axis $c$ (mm)	Steel Strain $\epsilon_t$	Strength Red. $\phi$	Nominal $P_n$ (kN)	Nominal $M_n$ (kN·m)	Design $\phi P_n$ (kN)	Design $\phi M_n$ (kN·m)

Longitudinal Detailing (Main)

Required Steel Area ($A_{s,req}$) 0 mm²

Provided Steel Area ($A_{s,prov}$) 0 mm²

Gross Steel Ratio ($\rho_g$) 0.00%

Provided Arrangement -

* Minimum required area is bounded by 1% of gross section ($A_g$) or structural demand. Max code limit is 8%.

Transverse Detailing (Ties)

Calculated Max Tie Spacing 0 mm

Provided Tie Detailing -

Shear Capacity ($\phi V_n$) 0 kN

* Tie spacing $s \le \min(16 d_{main}, 48 d_{tie}, \text{least dimension})$.

Bill of Quantities (Material Takeoff)

Material	Qty	Unit

Detailed Calculation Report

Interaction Diagram Theory (ACI 318)

A column's capacity is defined by the interaction between axial load ($P_n$) and bending moment ($M_n$). The P-M curve is generated by establishing strain compatibility and internal force equilibrium across the cross-section for various neutral axis depths ($c$).

1. Strain Compatibility

Assuming plane sections remain plane, the strain in any steel layer $\epsilon_{si}$ at depth $d_i$ is linearly proportional to the distance from the neutral axis $c$:

$$\epsilon_{si} = 0.003 \left( \frac{c - d_i}{c} \right)$$

Stress is then $f_{si} = E_s \epsilon_{si}$, limited by yield $\pm f_y$.

2. Internal Forces

Concrete compression block depth $a = \beta_1 c$.

$$C_c = 0.85 f'_c a b$$

$$F_{si} = A_{si} (f_{si} - 0.85 f'_c)$$

* Concrete stress is subtracted from steel in the compression zone to avoid double counting area.

3. Equilibrium & Capacity

Summing forces and moments about the plastic centroid:

$$P_n = C_c + \sum F_{si}$$

$$M_n = C_c (y_c - a/2) + \sum F_{si} (y_c - d_i)$$

Strength reduction factor $\phi$ varies from 0.65 (comp) to 0.90 (tension) based on extreme tension steel strain $\epsilon_t$.

Design Methodology Workflow

References

• ACI 318: Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute.
• EN 1992-1-1 (Eurocode 2): Design of concrete structures - Part 1-1: General rules and rules for buildings. European Committee for Standardization.
• SS EN 1992-1-1: Singapore National Annex to Eurocode 2. Enterprise Singapore.
• IS 456: Plain and Reinforced Concrete - Code of Practice. Bureau of Indian Standards.
• BS 8110-1: Structural use of concrete. Code of practice for design and construction. British Standards Institution.
• GB 50010: Code for design of concrete structures. Ministry of Housing and Urban-Rural Development of the PRC.
• JSCE: Standard Specifications for Concrete Structures - Design. Japan Society of Civil Engineers.

Version 1.0 CivilSheets by Sothearith Seak